Accardi, L. and Fedullo, A. (1982). ‘On the statistical meaning of complex numbers in quantum mechanics.’ Lettere al nuovo cimento 34(7): 161–172. Gives a technical acount of the necessity for using complex rather than real Hilbert spaces in quantum mechanics. There is no equivalent argument for IR (yet)
Aerts, D. (1999). ‘Foundations of quantum physics: a general realistic and operational approach.’ International Journal of Theoretical Physics 38(1): 289–358. This is a careful statement of the basic concepts of quantum mechanics. Most of it is done from first principles and the paper is almost self-contained. The foundations are presented from an operational point of view
Aerts, D., A. A. Grib, B. van Bogaert and R. R. Zupatrin (1993). ‘Quantum structures in macroscopic reality.’ International Journal of Theoretical Physics 32(3): 489–498. They construct an artificial, macroscopic device that has quantum properties. The corresponding lattic is non-Boolean. This example may help in grasping non-Boolean lattices in the abstract
Albert, D. Z. (1994). Quantum Mechanics and Experience, Harvard University Press. This is one of the best elementary introductions to quantum mechanics, written with precision and very clear. The examples are very good and presented with considerable flair. It uses the Dirac notation and thus provides a good entry point for that too, although the mathematical basis for it is never explained
Albert, D. and Loewer, B. (1988). ‘Interpreting the many worlds interpretation.’ Synthese 77: 195–213. The many worlds interpretation is worth considering as a possible model for interpreting the geometry of information retrieval. Albert and Loewer give a clear and concise introduction to the many world approach as pioneered by Everett (DeWitt and Graham, 1973)
Amari, S.-i. and H. Nagaoka (2000). Methods of Information Geometry, Oxford University Press. This one is not for the faint hearted. It covers the connection between geometric structures and probability distribution, but in a very abstract way. Chapter 7 gives an account of ‘information geometry’ for quantum systems. It defines a divergence measure for quantum systems equivalent to the Kullback divergence. For those interested in quantum information this may prove of interest
Amati, G. and C. J. van Rijsbergen (1998). ‘Semantic information retrieval.’ In Information Retrieval: Uncertainty and Logics, F. Crestani, M. Lalmas and C. J. van Rijsbergen (eds.). Kluwer, pp. 189–219. Contains a useful discussion on various formal notions of information content
Arveson, W. (2000). A short course on spectral theory. Springer Verlag. Alternative to Halmos (1951). A fairly dense treatment
Auletta, G. (2000). Foundations and Interpretation of Quantum Mechanics; in the Light of a Critical-Historical Analysis of the Problem and of a Synthesis of the Results. World Scientific. This book is encyclopedic in scope. It is huge – 981 pages long and contains a large bibliography with a rough guide as to where each entry is relevant, and the book is well indexed. One can find a discussion of almost any aspect of the interpretation of QM. The mathematics is generally given in its full glory. An excellent source reference. The classics are well cited
Auyang, S. Y. (1995). How is Quantum Field Theory Possible? Oxford University Press. Here one will find a simple and clear introduction to the basics of quantum mechanics. The mathematics is kept to a minimum
Bacciagaluppi, G. (1993). ‘Critique of Putnam's quantum logic.’ International Journal of Theoretical Physics 32(10): 1835–1846. Relevant to Putnam (1975)
Baeza-Yates, R. and B. Ribeiro-Neto (1999). Modern Information Retrieval, Addison Wesley. A solid introduction to information retrieval emphasising the computational aspects. Contains an interesting and substantial chapter on modelling. Contains a bibliography of 852 references, also has a useful glossary
Baggott, J. (1997). The Meaning of Quantum Theory, Oxford University Press. Fairly leisurely introduction to quantum mechanics. Uses physical intuition to motivate the Hilbert space mathematics. Nice examples from physics, and a good section on the Bohr–Einstein debate in terms of their thought experiment ‘the photon box experiment’. It nicely avoids mathematical complications
Barrett, J. A. (1999). The Quantum Mechanics of Minds and Worlds, Oxford University Press. This book is for the philosophically minded. It concentrates on an elaboration of the many-worlds interpretation invented by Everett, and first presented in his doctoral dissertation in 1957
Barwise, J. and J. Seligman (1997). Information Flow: The Logic of Distributed Systems, Cambridge University Press. Barwise has been responsible for a number of interesting developments in logic. In particular, starting with the early work of Dretske, he developed together with Perry an approach to situation theory based on notions of information, channels and information flow. What is interesting about this book is that in the last chapter of the book, it relates their work to quantum logic. For this it used the theory of manuals developed for quantum logic, which is itself explained in detail in Cohen (1989)
Belew, R. (2000). Finding Out About: a Cognitive Perspective on Search Engine Technology and the WWW. Cambridge University Press. Currently one of the best textbooks on IR in print. It does not shy away from using mathematics. It contains a good section introducing the vector space model pioneered by Salton (1968) which is useful material as background to the Hilbert space approach adopted in GIR. The chapter on mathematical foundations will also come in handy and is a useful reference for many of the mathematical techniques used in IR. There is a CD insert on which one will find, among other useful things, a complete electronic version of Van Rijsbergen (1979a)
Bell, J. S. (1993). Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press. A collection of previously published papers by the famous Bell, responsible for the Bell inequalities. Several papers deal with hidden variable theories. Of course it was Bell who spotted a mistake in Von Neumann's original proof that there was no hidden-variable theory for quantum mechanics. It contains a critique of Everett's many-worlds interpretation of quantum mechanics. It also contains ‘Beables for quantum field theory’
Beltrametti, E. G. and Cassinelli, G. (1977). ‘On state transformation induced by yes–no experiments, in the context of quantum logic.’ Journal of Philosophical Logic 6: 369–379. The nature of the conditional in logic as presented by Stalnaker and Hardegree can be shown to play a special role in quantum logic. Here we have a discussion of how YES–NO experiments can be useful in giving meaning to such a conditional
Beltrametti, E. G. and G. Cassinelli (1981). The Logic of Quantum Mechanics. Addison-Wesley Publishing Company. This is a seminal book, a source book for many authors writing on logic and probability theory in quantum mechanics. Most of the mathematical results are derived from first principles. Chapter 9 is a good summary of the Hilbert space formulation which serves as an introduction to Part II: one of the best introductions to the mathematical structures for quantum logics. It is well written. Chapter 20 is a very good brief introduction to quantum logic
Beltrametti, E. G. and B. C. van Fraassen, eds. (1981). Current Issues in Quantum Logic. Plenum Press. This volume collects together a number of papers by influential thinkers on quantum logic. Many of the papers are written as if from first principles. It constitutes an excellent companion volume to Beltrametti and Cassinelli (1981) and Van Fraassen (1991). Many of the authors cited in this bibliography have a paper in this volume, for example, Aerts, Bub, Hardegree, Hughes and Mittelstaedt. A good place to start one's reading on quantum logic
Bigelow, J. C. (1976). ‘Possible worlds foundations for probability.’ Journal of Philosophical Logic 5: 299–320. Based on the notion of similarity heavily used by David Lewis to define a semantics for counterfactuals; Bigelow uses it to define probability. This is good background reading for Van Rijsbergen (1986)
Bigelow, J. C. (1977). ‘Semantics of probability.’ Synthese 36: 459–472. A useful follow-on paper to Bigelow (1976)
Birkhoff, G. and S. MacLane (1957). A Survey of Modern Algebra. The Macmillan Company. One of the classic textbooks on algebra by two famous and first rate mathematicians. This is the Birkhoff that collaborated with John von Neumann on the logic of quantum mechanics and in 1936 published one of the first papers ever on the subject. Most elementary results in linear algebra can be found in the text. There is a nice chapter on the algebra of classes which also introduces partial orderings and lattices
Birkhoff, G. and , J. von Neumann (1936). ‘The logic of quantum mechanics.’ Annals of Mathematics 37: 823–843. Reprinted in Hooker (1975), this is where it all started! ‘The object of the present paper is to discover what logical structure one may hope to find in physical theories which, like quantum mechanics, do not conform to classical logic. Our main conclusion, based on admittedly heuristic arguments, is that one can reasonable expect to find a calculus of propositions which is formally indistinguishable from the calculus of linear subspaces with respect to set products, linear sums, and orthogonal complements – and resembles the usual calculus of propositions with respect to and, or, and not.’ Ever since this seminal work there has been a steady output of papers and ideas on how to make sense of it
Blair, D. C. (1990). Language and Representation in Information Retrieval. Elsevier. A thoughtful book on the philosophical foundations of IR, it contains elegant descriptions of some of the early formal models for IR. Enjoyable to read
Blum, K. (1981). ‘Density matrix theory and applications.’ In Physics of Atoms and Molecules, P. G. Burke (ed.) Plenum Press, pp. 1–62. It is difficult to find an elementary introduction to density matrices. This is one, although it is mixed up with applications to atomic physics. Nevertheless Chapter 2, which is on general density matrix theory, is a good self-contained introduction which uses the Dirac notation throughout
Borland, P. (2000). Evaluation of Interactive Information Retrieval Systems. Abo Akademi University. Here one will find a methodology for the evaluation of IR systems that goes beyond the now standard ‘Cranfield paradigm’. There is a good discussion of the concept of relevance and the book concentrates on retrieval as an interactive process. The framework presented in GIR should be able to present and formalise such a process
Bouwmeester, D., A. Ekert and A. Zeiliager, eds. (2001). The Physics of Quantum Information, Springer-Verlag. Although not about quantum computation per se, there are some interesting connections to be made. This collection of papers covers quantum cryptography, teleportation and computation. The editors are experts in their field and have gone to some trouble to make the material accessible to the non-expert
Bruza, P. D. (1993). Stratified Information Disclosure: a Synthesis between Hypermedia and Information Retrieval. Katholieke University Nijmegen. A good example of the use of non-standard logic in information retrieval
Bub, J. (1977). ‘Von Neumann's projection postulate as a probability conditionalization rule in quantum mechanics.’ Journal of Philosophical Logic 6: 381–390. The title says it all. The Von Neumann projection postulate has been a matter of debate ever since he formulated it; it was generalised by Lüders in 1951. Bub gives a nice introduction to it in this paper. The interpretation as a conditionalisation rule is important since it may be a useful way of interpreting the postulate in IR. Van Fraassen (1991, p. 175) relates it to Jeffrey conditionalisation (Jeffrey,1983)
Bub, J. (1982). ‘Quantum logic, conditional probability, and interference.’ Philosophy of Science 49: 402–421. Good commentary on Friedman and Putnam (1978)
Bub, J. (1997). Interpreting the Quantum World, Cambridge University Press. Bub has been publishing on the interpretation of quantum mechanics for many years. One of his major interests has been the projection postulates, and their interpretation as a collapse of the wave function. The first two chapters of the book are well worth reading, introducing many of the main concepts in QM. The mathematical appendix is an excellent introduction to Hilbert space machinery
Busch, P., M. Grabowski and P. J. Lanti (1997). Operational Quantum Physics, Springer-Verlag. There is a way of presenting quantum theory from the point of view of positive operator valued measures, which is precisely what this book does in great detail
Butterfield, J. and Melia, J. (1993). ‘A Galois connection approach to superposition and inaccessibility.’ International Journal of Theoretical Physics 32(12): 2305–2321. In Chapter 2 on inverted files and natural kinds, we make use of a Galois connection. In this paper quantum logic is discussed in terms of a Galois connection. A fairly technical paper, most proofs are omitted
Campbell, I. and C. J. van Rijsbergen (1996). The Ostensive Model of Developing Information Needs. CoLIS 2, Second International Conference on Conceptions of Library and Information Science: Integration in Perspective, Copenhagen, The Royal School of Librarianship. A description of an IR model to which the theory presented in GIR will be applied. It is the companion paper to Van Rijsbergen (1996)
Carnap, R. (1977). Two Essays on Entropy, University of California Press. For many years these essays remained unpublished. An introduction by Abner Shimony explains why. Carnap's view on the nature of information diverged significantly from that of Von Neumann's. John Von Neumann maintained that there was one single physical concept of information, whereas Carnap, in line with his view of probability, thought this was not adequate. Perhaps these essays should be read in conjunction with Cox (1961) and Jaynes (2003)
Cartwright, N. (1999). How the Laws of Physics Lie, Clarendon Press. Essay 9 of this book contains a good introduction to what has become known in QM as ‘The Measurement Problem’: the paradox of the time evolution of the wave function versus the collapse of the wave function. A clear and elementary account
Casti, J. L. (2000). Five More Golden Rules: Knots, Codes, Chaos, and Other Great Theories of Twentieth Century Mathematics. Wiley. Contains a semi-popular introduction to functional analysis. The section on quantum mechanics is especially worth reading
Cohen, D. W. (1989). An Introduction to Hilbert Space and Quantum Logic, Springer-Verlag. Good introduction to quantum logics, explaining the necessary Hilbert space as needed. It gives a useful proof of Gleason's Theorem, well actually almost, as it leaves it to be proved as a number of guided projects. Here the reader will also find a good introduction to ‘manuals’ with nice illustrative examples. Note in particular the ‘firefly in a box’ example
Cohen-Tannoudji, B. Diu and F. Laloë (1977). Quantum Mechanics. Wiley. A standard and popular textbook on QM. It is one of the few that has a comprehensive section on density operators
Collatz, L. (1966). Functional Analysis and Numerical Mathematics, Academic Press. Contrary to what the title may lead one to believe, almost half of this book is devoted to a very clear, self-contained, introduction to functional analysis. For example, it is has a thorough introduction to operators in Hilbert space
Colodny, R. G., ed. (1972). Paradigms and Paradoxes. The Philosophical Challenge of the Quantum Domain, University of Pittsburgh Press. The lion's share of this book is devoted to a lengthy paper by C. A. Hooker on quantum reality. However, the papers by Arthur Fine and David Finkelstein on conceptual issues to do with probability and logic in QM are well worth reading
Cooke, R., Keane, M. and , W. Moran (1985). ‘An Elementary Proof of Gleason's Theorem.’ Mathematical Proceedings of the Cambridge Philosophical Society 98: 117–128. Gleason's Theorem is central to the mathematical approach in GIR. Gleason published his important result in 1957. The proof was quite difficult and eventually an elementary proof was given by Cooke et al. in 1985. Hughes (1989) has annotated the proof in an Appendix to his book. Richman and Bridges (1999) give a constructive prooof. The theorem is of great importance in QM and hence is derived in a number of standard texts on quantum theory, for example Varadarajan (1985), Parthasarathy (1992) and Jordan (1969)
Cox, R. T. (1961). The Algebra of Probable Inference. The Johns Hopkins Press. This is a much cited and quoted book on the foundations of probability. For example, in his recent book on Probability Theory, Jaynes (2003) quotes results from Cox. The book has sections on probability, entropy and expectation. It was much influenced by Keynes' A Treatise on Probability (1929), another good read
Crestani, F., M. Lalmas and C. J. van Rijsbergen, eds. (1998). Information Retrieval: Uncertainty and Logics: Advanced Models for the Representation and Retrieval of Information. Kluwer. After the publication of Van Rijsbergen (1986), which is reprinted here, a number of researchers took up the challenge to define and develop appropriate logics for information retrieval. Here we have a number of research papers showing the progress that was made in this field, that is now often called the ‘Logical model for IR’. The papers trace developments from around 1986 to roughly 1998. The use of the Stalnaker conditional (Stalnaker, 1970) for IR was first proposed in the 1986 paper discussed in some detail in Chapter 5 in GIR
Crestani, F. and Rijsbergen, C. J. (1995). ‘Information retrieval by logical imaging.’ Journal of Documentation 51: 1–15. A detailed account of how to use imaging (Lewis, 1976) in IR
Croft, W. B. (1978). Organizing and Searching Large Files of Document Descriptions. Cambridge, Computer Laboratory, Cambridge University. A detailed evaluation of document clustering based on the single link hierarchical classification method
Croft, W. B. and J. Lafferty, eds. (2003). Language Modeling for Information Retrieval. Kluwer. The first book on language modelling. It contains excellent introductory papers by Lafferty and Xhia, as well as by Lavrenk and Croft
Dalla Chiara, M. L. (1986). ‘Quantum logic.’ In Handbook of Philosophical Logic, D. Gabbay and F. Guenthner (eds.). Reidel Publishing Company III, pp. 427–469. A useful summary of quantum logic given by a logician
Dalla Chiara, M. L. (1993). ‘Empirical Logics.’ International Journal of Theoretical Physics 32(10): 1735–1746. A logician looks at quantum logics. The result is a fairly sceptical view not too dissimilar from Gibbins (1987)
Davey, B. A. and H. A. Priestley (1990). Introduction to Lattices and Order, Cambridge University Press. Here you will find all you will ever need to know about lattices. The final chapter on formal concept analysis introduces the Galois Connection
De Broglie, L. (1960). Non-Linear Wave Mechanics. A Causal Interpretation, Elsevier Publishing Company. A classic book. Mainly of historical interest now. De Broglie is credited with being the first to work out the implications of l = h/mv (page 6), the now famous connection between wavelength and momentum, h is Planck's constant
De Finetti, B. (1974). Theory of Probability. Wiley. A masterpiece by the master of the subjectivist school of probability. Even though it has been written from the point of view of a subjectivist, it is a rigorous complete account of the basics of probability theory. He discusses fundamental notions like independence in great depth. The book has considerable philosophical depth; De Finetti does not shy away from defending his point of view at length, but since it is done from a deep knowledge of the subject, following the argument is always rewarding
Debnath, L. and P. Mikusinski (1999). Introduction to Hilbert spaces with Applications, Academic Press. A standard textbook on Hilbert spaces. Many of the important results are presented and proved here. It treats QM as one of a number of applications
Deerwester, S., Dumais, S. T., Furnas, G. F. W., , T. K. Landauer and , R. Harsman (1990). ‘Indexing by Latent Semantic Analysis.’ Journal of the American Society for Information Science 4: 391–407. This is one of the earliest papers on latent semantic indexing. Despite many papers on the subject since the publication of this one, it is still worth reading. It presents the basics ideas in a simple and clear way. It is still frequently cited
D'Espagnat, B. (1976). Conceptual Foundations of Quantum Mechanics, W. A. Benjamin, Inc. Advanced Book Program. This must be one of the very first books on the conceptual foundations of QM. It takes the approach that a state vector represents an ensemble of identically prepared quantum systems. It gives a very complete account of the density matrix formalism in Chapter 6, but beware of some trivial typos. It is outstanding for its ability to express and explain in words all the important fundamental concepts in QM. It also gives accurate mathematical explanations. This book is worth studying in detail
D'Espagnat, B. (1990). Reality and the Physicist. Knowledge, Duration and the Quantum World, Cambridge University Press. This is a more philosophical and leisurely treatment of some of the material covered in d'Estaganat (1976)
Deutsch, D. (1997). The Fabric of Reality, Allen Lane. The Penguin Press. This is a very personal account of the importance of quantum theory for philosophy and computation. David Deutsch was one of the early scientists to lay the foundations for quantum computation. His early papers sparked much research and debate about the nature of computation. This book is written entirely without recourse to rigorous mathematical argument. It contains copious references to Turing's ideas on computability
Deutsch, F. (2001). Best Approximation in Inner Product Spaces, Springer. Inner products play an important role in the development of quantum theory. Here one will find inner products discussed in all their generality. Many other algebraic results with a geometric flavour are presented here
DeWitt, B. S. and N. Graham, eds. (1973). The Many-Worlds Interpretation of Quantum Mechanics. Princeton Series in Physics, Princeton University Press. Here are collected together a number of papers about the many-worlds interpretation, including a copy of Everett's original dissertation on the subject, entitled, ‘The Theory of the Universal Wave Function’. This latter paper is relatively easy to read. It makes frequent use of statistical information theory in a way not unknown to information retrievalists
Dirac, P. A. M. (1958). The Principles of Quantum Mechanics, Oxford University Press. One of the great books of quantum mechanics. The first one hundred pages are still worth reading as an introduction to QM. Dirac motivates the introduction of the mathematics. In particular he defends the use of the Dirac notation. He takes as one of his guiding principles the superposition of states, and takes some time to defend his reason. This book is still full of insights, well worth spending time on
Dirac, P. A. M. (1978). ‘The mathematical foundations of quantum theory.’ In The Mathematical Foundations of Quantum Theory. A. R. Marlow (ed.). Academic Press: 1–8. This paper is by way of a preface to the edited volume by Marlow. It contains a late statement of the master's personal philosophy concerning foundational research. The quote: ‘Any physical or philosophical ideas that one has must be adjusted to fit the mathematics.’ is taken from this paper
Dominich, S. (2001). Mathematical Foundations of Information Retrieval, Kluwer Academic Publishers. A very mathematical approach to information retrieval
Dowty, D., R. Wall and S. Peters (1981). Introduction to Montague Semantics. Reidel. Still one of the best introductions to Montague Semantics. Is is extremely well written. If one wishes to read Montague's original writings this is a good place to start
Einstein, A., , B. Podolsky and , N. Rosen (1935). Can quantum mechanical descriptions of physical reality be considered complete?Physical Review 47: 777–780
Engesser, K. and Gabbay, D. M. (2002). ‘Quantum Logic, Hilbert Space, Revision Theory.’ Artificial Intelligence 136: 61–100. This is a look at quantum logic by logicians with a background in computer science. It has a little to say about probability measures on the subspaces of a Hilbert space
Fairthorne, R. A. (1958). ‘Automatic Retrieval of Recorded Information.’ The Computer Journal 1: 36–41. Fairthorne's paper, reprinted in Fairthorne (1961), is now mainly of historical interest. The opening section of the paper throws some light on the history of IR; Vannevar Bush is usually cited as the source of many of the early ideas in IR, but Fairthorne gives details about much earlier original work
Fairthorne, R. A. (1961). Towards Information Retrieval, Butterworths. One of the very first books on information retrieval, it is of particular interest because Fairthorne was an early proponent of the use of Brouwerian logics in IR. A useful summary of this approach is given in Salton (1968)
Fano, G. (1971). Mathematical Methods of Quantum Mechanics, McGraw-Hill Book Company. A fine introduction to the requisite mathematics for QM. It is clearly geared to QM although the illustrations are mostly independent of QM. It contains a useful explanation of the Dirac notation (section 2.5). Its section (5.8) on the spectral decomposition of a self-adjoint operator is important and worth reading in detail
Feller, W. (1957). An Introduction to Probability Theory and Its Applications. One of the classic mathematical introductions to probability theory
Feynman, R. P. (1987). ‘Negative probability.’ In Quantum Implications, B. J. Hiley and F. D. Peat (eds.) Routledge & Kegan Paul, pp. 235–248. This paper is of interest because it represents an example of using a ‘non-standard’ model for probability theory, to be compared with using complex numbers instead of real numbers. It illustrates how intermediate steps in analysis may fail to have simple naïve interpretations
Feynman, R. P., R. B. Leiguton and M. Sands (1965). The Feynman Lectures on physics, vol. III, Addison-Wesley
Finch, P. D. (1975). ‘On the structure of quantum logic.’ In The Logico-Algebraic Approach to Quantum Mechanics, Vol I., C. A. Hooker (ed.) pp. 415–425. An account of quantum logic without using the usual physical motivation
Fine, A. (1996). The Shaky Game. Einstein Realism and the Quantum Theory, The University of Chicago Press. Einstein never believed in the completeness of quantum mechanics. He did not accept that probability had an irreducible role in fundamental physics. He famously coined the sentence ‘God does not play dice’. Here we have an elaboration of Einstein's position. This book should be seen as a contribution to the philosophy and history of QM
Finkbeiner, D. T. (1960). Matrices and Linear Transformations, W. H. Freeman and Company. A standard textbook on linear algebra. It is comparable to Halmos (1958), and it covers similar material. It uses a postfix notation for operator application which can be awkward. Nevertheless it is clearly written, even though with less flair than Halmos. It contains numerous good examples and exercises
Fisher, R. A. (1922). On the Dominance Ratio. Royal Society of Edinburgh. This paper is referred to by Wootters (1980a). The claim is that it is one of the first papers to describe a link between probability and geometry for vector spaces. It is not easy to establish that. The reference is included for the sake of completeness
Frakes, W. B. and R. Baeza-Yates, eds. (1992). Information Retrieval – Data Structures & Algorithms, Prentice Hall. A good collection of IR papers covering topics such as file structures, NLP algorithms, ranking and clustering algorithms. Good source for technical details of well-known algorithms
Friedman, A. (1982). Foundations of Modern Analysis, Dover Publications, Inc. The first chapter contains a good introduction to measure theory
Friedman, M. and Putnam, H. (1978). ‘Quantum logic, conditional probability, and interference.’ Dialectica 32(3–4): 305–315. The authors wrote this now influential paper, claiming ‘The quantum logical interpretation of quantum mechanics gives an explanation of interference that the Copenhagen interpretation cannot supply.’ It all began with Putnam's original 1968 ‘Is logic empirical?’, subsequently updated and published as Putnam (1975). It has been a good source for debate ever since, for example, Gibbins (1981) Putnam (1981) and Bacciagaluppi (1993), to name but a few papers
Ganter, B. and R. Wille (1999). Formal Concept Analysis – Mathematical Foundations, Springer-Verlag. This is a useful reference for the material in Chapter 2 of this book
Garden, R. W. (1984). Modern Logic and Quantum Mechanics, Adam Hilger Ltd., Bristol. One could do a lot worse than start with this as a first attempt at understanding the role of logic in classical and quantum mechanics. Logic is first used in classical mechanics, which motivates its use in quantum mechanics. The pace is very gentle. The book finishes with Von Neumann's quantum logic as first outlined in the paper by Birkhoff and Von Neumann (1936)
Gibbins, P. (1981). ‘Putnam on the Two-Slit Experiment.’ Erkenntnis 16: 235–241. A critique of Putnam's 1969 paper (Putnam, 1975)
Gibbins, P. (1987). Particles and Paradoxes: the Limits of Quantum Logic, Cambridge University Press. An outstanding informal introduction to the philosophy and interpretations of QM. It has a unusual Chapter 9, which gives a natural deduction formulation of quantum logic. Gibbins is quite critical of the work on quantum logic and in the final chapter he summarises some of his criticisms
Gillespie, D. T. (1976). A Quantum Mechanics Primer. An Elementary Introduction to the Formal Theory of Non-relativistic Quantum Mechanics, International Textbook Co. Ltd. A modest introduction to QM. Avoids the use of Dirac notation. It was an Open University Set Book and is clearly written
Gleason, A. M. (1957). ‘Measures on the closed subspaces of a Hilbert space.’ Journal of Mathematics and Mechanics 6: 885–893. This is the original Gleason paper containing the theorem frequently referred to in GIR. Simpler versions are to found in Cooke et al. (1985), and Hughes (1989)
Gleason, A. M. (1975). ‘Measures of the closed subspaces of a Hilbert space.’ In The Logico-Algebraic Approach to Quantum Mechanics, C. A. Hooker (ed.) pp. 123–133. This is a reprint of Gleason's original paper published in 1957
Goffman, W. (1964). ‘On relevance as a measure.’ Infomation Storage and Retrieval 2: 201–203. Goffman was one of the early dissenters from the standard view of the concept of relevance
Goldblatt, R. (1993). Mathematics of Modality, CSLI Publications. The material on orthologic and orthomodular structures is relevant. The treatment is dense and really aimed at logicians
Golub, G. H. and C. F. van Loan (1996). Matrix Computations, The Johns Hopkins University Press. A standard textbook on matrix computation
Good, I. J. (1950). Probability and the weighing of evidence. Charles Griffin & Company Limited. Mainly of historical interest now, but contains a short classification of theories of probability
Greechie, R. J. and S. P. Gudder (1973). ‘Quantum logics.’ In Contemporary Research in the Foundations and Philosophy of Quantum Theory, C. A. Hooker (ed.), D. Reidel Publishing Company, pp. 143–173. A wonderfully clear account of the mathematical tools neeeded for the study of axiomatic quantum mechanics
Greenstein, G. and A. G. Zajonc (1997). The Quantum Challenge. Modern Research on the Foundations of Quantum Mechanics, Jones and Bartlett. A relatively short and thorough introduction to QM. The emphasis is on conceptual issues, mathematics is kept to a minimum. Examples are taken from physics
Gribbin, J. (2002). Q is for Quantum: Particle Physics from A to Z. Phoenix Press. A popular glossary for particle physics, but contains a large number of entries for QM
Griffiths, R. B. (2002). Consistent Quantum Theory, Cambridge University Press. A superb modern introduction to quantum theory. The important mathematics is introduced very clearly. Toy examples are used to avoid complexities. It contains a thorough treatment of histories in QM, which although not used in this book, could easily be adapted for IR purposes. Tensor products are explained. Some the paradoxical issues in logic for QM are addressed. This is possibly one of the best modern introductions to QM for those interested in applying it outside physics
Grover, L. K. (1997). ‘Quantum mechanics helps in searching for a needle in a haystack.’ Physical Review Letters 79(2): 325–328. The famous paper on ‘finding a needle in a haystack’ by using quantum computation and thereby speeding up the search compared with what is achievable on a computer with a Von Neumann architecture
Gruska, J. (1999). Quantum Computing, McGraw Hill. For the sake of completeness a number of books on quantum computation are included. This is one of them. It contains a brief introduction to the fundamentals of Hilbert space; useful for someone in a hurry to grasp the gist of it
Halmos, P. R. (1950). Measure Theory. Van Nostrand Reinhold Company. A classic introduction to the subject. It is written with the usual Halmos upbeat style. It has an excellent chapter on probability from the point of view of measure theory
Halmos, P. R. (1951). Introduction to Hilbert Space and the Theory of Spectral Multiplicity, Chelsea Publishing Company. This is a very lively introduction to Hilbert space and explains the details behind spectral measures. This book should be read and consulted in conjunction with Halmos (1958). Even though it is very high powered it is written in an easy style, and it should be compared with Arveson (2002) and Retherford (1993); both these are more recent introductions to spectral theory
Halmos, P. R. (1958). Finite-Dimensional Vector Spaces, D. van Nostrand Company, Inc. This is one of the best books on finite-dimensional vector spaces, even though it was published so many years ago. It is written in a deceptively simple and colloquial style. It is nicely divided into ‘bite size’ chunks and probably you will learn more than you ever would want to know about vector spaces. It is also a good introduction to Halmos's much more sophisticated and harder book on Hilbert spaces
Halmos, P. R. (1963). Lectures on Boolean Algebra. D. Van Nostrand Company. All you might ever want to know about Boolean Algebra can be found here. Contains a proof of the Stone Representation Theorem
Halpin, J. F. (1991). ‘What is the logical form of probability assignment in quantum mechanics?’ Philosophy of Science 58: 36–60. Looks at a number of proposals taking into account the work of Stalnaker and Lewis on counterfactuals
Hardegree, G. M. (1975). ‘Stalnaker conditionals and quantum logic.’ Journal of Philosophical Logic 4: 399–421. The papers by Hardegree are useful reading as background to Chapter 5
Hardegree, G. M. (1976). ‘The conditional in quantum logic.’ In Logic and Probability in Quantum Mechanics, P. Suppes (ed.), D. Reidel Publishing Company, pp. 55–72. The material in this paper is drawn on significantly for Chapter 5 on conditonal logic for IR
Hardegree, G. M. (1979). ‘The conditional in abstract and concrete quantum logic.’ In Logico-Algebraic Approach to Quantum Mechanics. II. C. A. Hooker (ed.), D. Reidel Publishing Company, pp. 49–108. This is a much more extensive paper than Hardegree (1976). It deals with a taxonomy of quantum logics. The emphasis is still on the conditional
Hardegree, G. M. (1982). ‘An approach to the logic of natural kinds.’ Pacific Philosophical Quarterly 63: 122–132. This paper is relevant to Chapter 2, and would make good background reading
Harman, D. (1992). Ranking algorithms. In Information Retrieval – Data Structures, and Algorithms, Frakes, W. B. and R. Baeza-Yates (eds.), Prentice Hall, pp. 363–392
Harper, W. L., R. Stalnaker and G. Peare eds. (1981). Ifs. Reidel. This contains reprints of a number of influential papers on counterfactual reasoning and conditionals. In particular it contains important classic papers by Stalnaker and Lewis
Hartle, J. B. (1968). ‘Quantum mechanics of individual systems.’ American Journal of Physics 36(8): 704–712. A paper on an old debate: does it make sense to make probabilistic assertions about individual systems, or should we stick to only making assertions about ensembles?
Healey, R. (1990). The Philosophy of Quantum Mechanics. An Interactive Interpretation, Cambridge University Press. Despite its title this is quite a technical book. The idea of interaction is put centre stage and is to be compared with the approach by Kochen and Specker (1965a)
Hearst, M. A. and J. O. Pedersen (1996). ‘Re-examining the cluster hypothesis: scatter/gather on retrieval results.’ Proceedings of the 19th Annual ACM SIGIR Conference. pp. 76–84. Another test of the cluster hypothesis
Heelan, P. (1970a). ‘Quantum and classical logic: their respective roles.’ Synthese 21: 2–23. An attempt to clear up some of the confused thinking about quantum logics
Heelan, P. (1970b). ‘Complementarity, context dependence, and quantum logic.’ Foundations of Physics 1(2): 95–110. Mainly interesting because of the role that context plays in descriptions of quantum-mechanical events
Heisenberg, W. (1949). The Physical Principles of the Quantum Theory, Dover Publications, Inc. By one of the pioneers of QM. It is mainly of historical interest now
Hellman, G. (1981). ‘Quantum logic and the projection postulate.’ Philosophy of Science 48: 469–486. Another forensic examination of the ‘Projection Postulate’
Herbut, F. (1969). ‘Derivation of the change of state in measurement from the concept of minimal measurement.’ Annals of Physics 55: 271–300. A detailed account of how to define a simple and basic concept of physical measurement for an arbitrary observable. Draws on the research surrounding the Lüders–Von Neumann debate on the projection postulate. The paper is well written and uses sensible notation
Herbut, F. (1994). ‘On state-dependent implication in quantum mechanics.’ J. Phys. A: Math. Gen. 27: 7503–7518. This paper should be read after Chapter 5 in GIR
Hiley, B. J. and F. D. Peat (1987). Quantum Implications. Essays in honour of David Bohm. Routlege & Kegan Paul. The work of David Bohm, although much respected, was controversial. He continued to work on hidden variable theories despite the so-called impossibility proofs. The contributors to this volume include famous quantum physicists, such as Bell and Feynman, and well known popularisers, such as Kilmister and Penrose. A book worth dipping into. It contains the article by Feynman on negative probability
Hirvensalo, M. (2001). Quantum Computing, Springer-Verlag. A clearly written book with good appendices to quantum physics and its mathematical background
Holland, S. P. (1970). ‘The current interest in orthomodular lattices.’ Trends in Lattice Theory, J. C. Abbott (ed.). Van Nostrand Reinhold. There are many introductions to lattice theory. What distinguishes this one is that it relates the material to subspace structures of Hilbert space and to quantum logic. The explanations are relatively complete and easy to follow
Hooker, C. A., ed. (1975). The Logico-Algebraic Approach to Quantum Mechanics. Vol. 1: Historical Evolution. The University of Western Ontario Series in Philosophy of Science. D. Reidel Publishing Company. This is Volume 1 of a two-volume set containing a number of classic papers, for example, reprints of Birkhoff and Von Neumann (1936), Gleason (1957), Kochen and Specker (1965b) and Holland (1970)
Hooker, C. A., ed. (1979). The Logico-Algebraic Approach to Quantum Mechanics. Vol. 2: Contemporary Consolidation. The University of Western Ontario Series in Philosophy of Science. D. Reidel Publishing Company. Following the historical papers in Volume 1, this second volume contains more recent material. A useful paper is Hardegree (1979) as a companion to Hardegree (1976)
Horn, R. A. and C. R. Johnson (1999). Matrix Analysis, Cambridge University Press. One of several well-known, standard references on matrix theory, excellent companion for Golub and Van Loan (1996)
Hughes, R. I. G. (1982). ‘The logic of experimental questions.’ Philosophy of Science 1: 243–256. A simple introduction to how a quantum logic arises out of giving a mathematical structure to the process of asking experimental questions of a quantum system. Chapter 5 of Jauch (1968) gives a more detailed account of this mode of description, and presents the necessary preliminary mathematics in the earlier chapters. This particular way of viewing the logic of quantum mechanics was also explained synoptically by Mackey (1963)
Hughes, R. I. G. (1989). The Structure and Interpretation of Quantum Mechanics. Harvard University Press. A lucid and well-written book. It introduces the relevant mathematics at the point where it is needed. It contains an excellent discussion of Gleason's Theorem. It has a good chapter on quantum logic. It also introduces density operators in a simple manner. Much attention is paid to the philosophical problem of ‘properties’. An appendix contains an annotated version of the proof of Gleason's Theorem by Cooke et al. (1985)
Huibers, T. (1996). An Axiomatic Theory for Information Retrieval. Katholieke University Nijmegen. Presents a formal set of inference rules that are intended to capture retrieval. A proof system is specified for the rules, and used to prove theorems about ‘aboutness’
Ingwersen, P. (1992). Information Retrieval Interaction. Taylor Graham. This is a formulation of IR from a cognitive standpoint. In many ways it is in sympathy with the approach taken in GIR, especially in that it puts interaction with the user at the centre of the discipline. Its approach is non-mathematical
Isham, C. J. (1989). Lectures on Groups and Vector Spaces for Physicists. World Scientific. A well-paced introduction to vector spaces amongst other things. It starts from first principles and introduces groups before it discusses vector spaces. Gives examples from physics and quantum mechanics. It is a good companion volume to Isham (1995)
Isham, C. J. (1995). Lectures on Quantum Theory: Mathematical and Structural Foundations. Imperial College Press. The two books by Isham (1989,1995) go together. This book is a fairly complete lecture course on QM. The 1989 book contains a thorough introduction to vector spaces which is needed for the book on QM. Although a technical introduction, it also contains considerable philosophical comment and is very readable. In introducing quantum theory it begins with a statement of four simple rules that define a general mathematical framework within which all quantum-mechanical systems can be described. Technical developments come after a discussion of the rules
Jauch, J. M. (1968). Foundations of Quantum Mechanics, Addison-Wesley Publishing Company. Another classic monograph on QM. Jauch is a proponent of the mode of description of physical systems in terms of so-called ‘yes-no experiments’. Section 3–4 on projections is extremely interesting, it shows how the operation of union and intersection of subspaces are expressed algebraically in terms of the corresponding projections. An excellent introduction, one of the best, to foundations of QM
Jauch, J. M. (1972). ‘On bras and kets.’ In Aspects of Quantum Theory, A. Salam and E. P. Wigner (eds.). Cambridge University Press, pp. 137–167. Exactly that!
Jauch, J. M. (1973). Are Quanta Real? A Galilean Dialogue. Indiana University Press. A three-way discussion written by a fine quantum physicist. Perhaps this could be read after the prologue in GIR which has been done in the same spirit. It contains a physical illustration, in terms of polarising filters, of the intrinsic probability associated with measuring a property of a single photon
Jauch, J. M. (1976). ‘The quantum probability calculus.’ In Logic and Probability in Quantum Mechanics, Suppes, P. (ed.). D. Reidel Publishing Company, pp. 123–146. Starting with the classical probability calculus, it gives an account, from first principles, of the probability calculus in quantum mechanics
Jaynes, E. T. (2003). Probability Theory: The Logic of Science. Cambridge University Press. Jaynes' magnum opus. He is has worked for many years on probability theory and maximum entropy. This book is the result of over sixty years of thinking about the nature of probability, it is tour de force. It is one of the best modern reference works on probability. It contains a good annotated bibliography
Jeffrey, R. C. (1983). The Logic of Decision. University of Chicago Press. This is the best source for a discussion of Jeffrey Conditionalisation and the role that the ‘passage of experience’ plays in that. The Von Neumann projection postulate can be related to this form of conditonalisation (see Van Fraassen, 1991, p. 175)
Jeffreys, H. (1961). Theory of Probability. Oxford University Press. One of the classic introductions to probability theory. Jeffreys is sometimes associated with the subjectivist school of probability – which is somewhat surprising since he was he was a distinguished mathematical physicist. He was an early proponent of Bayesian inference and the use of priors. The first chapter on fundamental notions is still one of the best elementary introductions to probable inference ever written
Jordan, T. F. (1969). Linear Operators for Quantum Mechanics, John Wiley & Sons, Inc. There are a number of books frequently referred to in the quantum mechanics literature for the relevant background mathematics. Here we have identified three: Jordan (1969), Fano (1971) and Reed and Simon (1980). All three cover similar material, perhaps Reed and Simon is the most pure-mathematical in approach, whereas Jordan makes explicit connections with quantum mechanics
Kägi-Romano, U. (1977). ‘Quantum logic and generalized probability theory.’ Journal of Philosophical Logic 6: 455–462. A brief attempt to modify the classical Kolmogorov (1933) theory so that it becomes applicable to quantum mechanics
Keynes, M. (1929). A Treatise on Probability. Macmillan. Keynes' approach to probability theory represents a logical approach; probability is seen as a logical relation between propositions. After Frank Ramsey's devastating critique of it, it lost favour. However, it may be that there is more to be said about Keynes' theory, especially in the light of the way quantum probability is defined. The first one hundred pages of Keynes' treatise is still a wonderful historical account of the evolution of the theory of probability – full of insights that challenge the foundations of the subject
Kochen, S. and E. P. Specker (1965a). ‘Logical structures arising in quantum theory.’ In Symposium on the Theory of Models, eds. J. Addison, J. L. Henkin and A. Tarski. North Holland, pp. 177–189. An early account of how logical structures arise in quantum theory by two eminent theoreticians
Kochen, S. and E. P. Specker (1965b). ‘The calculus of partial propositional functions.’ In Logic, Methodology, and Philosophy of Science. Y. Bar-Hillel (ed.). North-Holland, pp. 45–57. A follow-on paper to their earlier 1965 paper; in fact here they deny a conjecture made in the first paper
Kolmogorov, A. N. (1950). Foundations of the theory of probability. Chelsea Publishing Co. Translation of Kolmogorov's original 1933 monograph. An approach to probability theory phrased in the language of set theory and measure theory. Kolmogorov's axiomatisation is now the basis of most current work on probability theory. For important dissenters consult Jaynes (2003)
Korfhage, R. R. (1997). Information Storage and Retrieval. Wiley Computer Publishing. A simple and elementary introduction to information retrieval, presented in a traditional way
Kowalski, G. J. and M. T. Maybury (2000). Information Retrieval Systems: Theory and Implementation. Kluwer. ‘This work provides a theoretical and practical explanation of the advancements in information retrieval and their application to existing systems. It takes a system approach, discussing all aspects of an Information Retrieval System. The major difference between this book and the first edition is the addition to this text of descriptions of the automated indexing of multimedia documents, as items in information retrieval are now considered to be a combination of text along with graphics, audio, image and video data types.’ – publisher's note
Kyburg, H. E., Jr. and C. M. Teng (2001). Uncertain Inference. Cambridge University Press. A comprehensive, up-to-date survey and explanation of various theories of uncertainty. Has a good discussion on the range of interpretations of probability. Also, does justice to Dempster–Shafer belief revision. Covers the work of Carnap and Popper in some detail
Lafferty, J. and C. X. Zhia (2003). ‘Probabilistic relevance models based on document and query generation.’ In Language Modeling for Information Retrieval. W. B. Croft and J. Lafferty (eds.). Kluwer, pp. 1–10. A very clear introduction to language modeling in IR
Lakoff, G. (1987). Women, Fire, and Dangerous Things. What Categories Reveal about the Mind. The University of Chicago Press. A wonderfully provocative book about the nature of classification. It also discusses the concept of natural kinds in a number of places. A real page turner
Lavrenko, V. and W. B. Croft (2003). ‘Relevance models in information retrieval.’ In Language Modeling for Information Retrieval. W. B. Croft and J. Lafferty (eds.). Kluwer. Describes how relevance can be brought into language models. Also, draws parallels between language models and other forms of plausible inference in IR
Lewis, D. (1973). Counterfactuals. Basil Blackwell. Classic reference on the possible world semantics for counterfactuals
Lewis, D. (1976). ‘Probabilities of conditionals and conditional probabilities.’ Philosophy of Science 85: 297–315. Lewis shows here how the Stalnaker Hypothesis is subject to a number of triviality results. He also defines a process known as imaging that was used in Crestani and Van Rijsbergen (1995a) to evaluate the probability of conditonals in IR
Lo, H.-K., S. Popescu and T. Spiller, eds. (1998). Introduction to Quantum Computation and Information. World Scientific Publishing. A collection of semi-popular papers on quantum computation. Mathematics is kept to a minimum
Lock, P. F. and , G. M. Hardegree (1984). ‘Connections among quantum logics. Part 1. Quantum propositional logics.’ International Journal of Theoretical Physics 24(1): 43–61. The work of Hardegree is extensively used in Chapter 5 of GIR
Lockwood, M. (1991). Mind, Brain and the Quantum. The Compound ‘I’. Blackwell Publishers. This book is concerned with QM and consciousness. It is almost entirely philosophical and uses almost no mathematics. It should probably be read at the same time as Penrose (1989, 1994)
Lomonaco, S. J., Jr., ed. (2002). Quantum Computation: A Grand Mathematical Challenge for the Twenty-First Century and the Millennium. Proceedings of Symposia in Applied Mathematics. Providence, Rhode Island, American Mathematical Society. The first lecture by Lomonaco, ‘A Rosetta stone for quantum mechanics with an introduction to quantum computation’, is one of the best introductions this author has seen. It accomplishes in a mere 65 pages what most authors would need an entire book for. The material is presented with tremendous authority. A good collection of references
London, F. and E. Bauer (1982). ‘The theory of observation in quantum mechanics.’ In Quantum Theory and Measurement. J. A. Wheeler and W. H. Zurek (eds.) Princeton University Press, pp. 217–259. The authors claim this to be a ‘treatment both concise and simple’ as an introduction to the problem of measurement in quantum mechanics. They have taken their cue from Von Neumann's original 1932 foundations and tried to make his deep discussions more accessible. They have succeeded. The original version was first published in 1939 in French
Lüders, G. (1951). ‘Über die Zustandsänderung durch den Messprozess.’ Annalen der Physik 8: 323–328. The original paper by Lüders that sparked the debate about the Projection Postulate
Mackay, D. (1950). ‘Quantal aspects of scientific information’, Philosophical Magazine, 41, 289–311
Mackay, D. (1969). Information, Mechanism and Meaning, MIT Press
Mackey, G. W. (1963). Mathematical Foundations of Quantum Mechanics. Benjamin. One of the early well known mathematical introductions, it is much cited. He introduced the suggestive terminology ‘question-valued measure’
Marciszewski, W., ed. (1981). Dictionary of Logic – as Applied in the Study of Language. Nijhoff International Philosophy Series, Martinus Nijhoff Publishers. This dictionary contains everything that you have always wanted to know about logic (but were ashamed to ask). It contains entries for the most trivial up to the most sophisticated. Everything is well explained and references are given for further reading
Maron, M. E. (1965). ‘Mechanized documentation: The logic behind a probabilistic interpretation.’ In Statistical Association Methods for Mechanized Documentation. M. E. Stevens et al., (eds.) National Bureau of Standards Report 269: 9–13. ‘The purpose of this paper is to look at the problem of document identification and retrieval from a logical point of view and to show why the problem must be interpreted by means of probability concepts.’ This quote from Maron could easily be taken as a part summary of the approach adopted in GIR. Maron was one of the very first to start thinking along these lines, less surprising if one considers that Maron's Ph.D. dissertation, ‘The meaning of the probability concept’, was supervised by Hans Reichenbach, one of early contributors to the foundations of QM
Martinez, S. (1991). ‘Lüders's rule as a description of individual state transformations.’ Philosophy of Science 58: 359–376. Lüders paper on the projection postulate generalising Von Neumann's rule has played a critical role in quantum theory. A number of papers have examined it in detail. Here is one such paper
Mirsky, L. (1990). An Introduction to Linear Algebra. Dover Publications, Inc. A traditional introduction emphasising matrix representation for linear operators. It contains a nice chapter on orthogonal and unitary matrices, an important class of matrices in QM. This material is used in Chapter 6 to explain relevance feedback
Mittelstaedt, P. (1972). ‘On the interpretation of the lattice of subspaces of the Hilbert space as a propositional calculus.’ Zeitschrift für Naturforschung 1358–1362. Here is a very nice and concise set of lattice-theoretic results derived from the original paper by Birkhoff and Von Neumann (1936). In particular it shows how a quasi-implication, defined in the paper, is a generalisation of classical implication
Mittelstaedt, P. (1998). The Interpretation of Quantum Mechanics and the Measurement Process. Cambridge University Press. A recent examination of the measurement problem in QM
Mizzaro, S. (1997). ‘Relevance: the whole history.’ Journal of the American Society for Information Science 48: 810–832. Mizzaro brings the debate on ‘relevance’ up to date. It is worth reading Saracevic (1975) first
Murdoch, D. (1987). Niels Bohr's Philosophy of Physics Cambridge University Press. This is of historical interest. Amongst other things it traces the development of Bohr's ideas on complementarity. Worth reading at the same time as Pais' (1991) biography of Bohr
Nie, J.-Y., , M. Brisebois and , F. Lepage (1995). ‘Information retrieval as counterfactual.’ The Computer Journal 38(8): 643–657. Looks at IR as counterfactual reasoning, drawing heavily on Lewis (1973)
Nie, J.-Y. and F. Lepage (1998). ‘Toward a broader logical model for information retrieval.’ In Information Retrieval: Uncertainty and Logics: Advanced Models for the Representation and Retrieval of Information. F. Crestani, M. Lalmas and C. J. van Rijsbergen (eds.). Kluwer: 17–38. In this paper the logical approach to IR is revisited and the authors propose that situational factors be included to enlarge the scope of logical modelling
Nielsen, M. A. and I. L. Chuang (2000). Quantum Computation and Quantum Information Cambridge University Press. Without doubt this is currently one of the best of its kind. The first one hundred pages serves extremely well as an introduction to quantum mechanics and its relevant mathematics. It has a good bibliography with references to www.arXiv.org whenever a paper is available for downloading. It is also well indexed
Ochs, W. (1981). ‘Some comments on the concept of state in quantum mechanics.’ Erkenntnis 16: 339–356. The notion of state is fundamental both in classical and quantum mechanics. The difference between a pure and mixed state in QM is of some importance, and the mathematics is designed to reflect this difference. There is an interpretation of mixed states as the ‘ignorance interpretation of states’. Here is a discussion of that interpretation
Omnès, R. (1992). ‘Consistent interpretations of quantum mechanics.’ Reviews of Modern Physics 64(2): 339–382. Excellent supplementary reading to Griffiths (2002)
Omnès, R. R. (1994). The Interpretation of Quantum Mechanics Princeton University Press. A complete treatment of the interpretation of QM. It is hard going but all the necessary machinery is introduced. There is a good chapter on a logical framework for QM. Gleason's Theorem is presented. His other book, Omnès (1999), is a much more leisurely treatment of some of the same material
Omnès, R. (1999). Understanding Quantum Mechanics Princeton University Press. See Omnes (1994)
Packel, E. W. (1974). ‘Hilbert space operators and quantum mechanics.’ American Mathematical Monthly 81: 863–873. Convenient self-contained discussion of Hilbert space operators and QM. Written with mathematical rigour
Pais, A. (1991). Niels Bohr's Times, in Physics, Philosophy, and Polity, Oxford University Press. A wonderful book on the life and times of Niels Bohr. Requisite reading before seeing the play Copenhagen by Michael Frayn
Park, J. L. (1967). ‘Nature of quantum states.’ American Journal of Physics 36: 211–226. Yet another paper on states in QM. This one explains in detail the difference between pure and mixed states
Parthasarathy, K. R. (1970). ‘Probability theory on the closed subspaces of a Hilbert space.’ Les Probabilites sur Structures Algebriques, CNRS. 186: 265–292. An early version of a proof of Gleason's Theorem, it is relatively self-contained. The version in the author's 1992 book may be easier to follow since the advanced mathematics is first introduced
Parthasarathy, K. R. (1992). An Introduction to Quantum Stochastic Calculus, Birkhäuser Verlag. The first chapter on events, observable and states is an extraordinarily clear and condensed exposition of the underlying mathematics for handling probability in Hilbert space. Central to the chapter is yet another proof of Gleason's Theorem. The mathematical concepts outer product and trace are very clearly defined
Pavicic, M. (1992). ‘Bibliography on quantum logics and related structures.’ International Journal of Theoretical Physics 31(3): 373–461. A useful bibliography emphasising papers on quantum logic
Penrose, R. (1989). The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics, Oxford University Press. A popular book containing a section on quantum magic and mystery, writtten with considerable zest
Penrose, R. (1994). Shadows of the Mind. A Search for the Missing Science of Consciousness, Oxford University Press. A popular book containing a substantial section on the quantum world
Peres, A. (1998). Quantum Theory: Concepts and Methods, Kluwer Academic Publishers. This book is much liked by researchers in quantum computation for providing the necessary background in quantum mechanics. Contains good discussion of Bell's inequalities, Gleason's Theorem and the Kochen–Specker Theorem
Petz, D. and Zemánek, J. (1988). Characterizations of the Trace. Linear Algebra and Its Applications, Elsevier Science Publishing. 111: 43–52. Useful if you want to know more about the properties of the trace function
Pippard, A. B., N. Kemmer, M. B. Hesse, M. Pryce, D. Bohn and N. R. Hanson (1962). Quanta and Reality, The Anchor Press Ltd. Popular book
Piron, C. (1977). ‘On the logic of quantum logic.’ Journal of Philosophical Logic 6: 481–484. A clarification of the connection between classical logic and quantum logic. Very short and simply written
Pitowsky, I. (1989). Quantum Probability – Quantum Logic Springer-Verlag. A thorough and detailed analysis of the two ideas. Many of the arguments are illustrated with simple concrete examples. Recommended reading after first consulting Appendix III in GIR
Pittenger, A. O. (2000). An Introduction to Quantum Computing Algorithms, Birkhäuser. A slim volume giving a coherent account of quantum computation
Plotnitsky, A. (1994). Complementarity. Anti-Epistemology after Bohr and Derrida, Duke University Press. Incomprehensible but fun
Polkinghorne, J. C. (1986). The Quantum World. Pelican. Elementary, short and simple. It also contains a nice glossary; for example, non-locality – the property of permitting a cause at one place to produce immediate effects at a distant place
Polkinghorne, J. C. (2002). Quantum Theory: a Very Short Introduction. Oxford University Press. The title says it all. Nice mathematical appendix
Popper, K. R. (1982). Quantum Theory and the Schism in Physics Routledge. An exhilarating read. Popper is never uncontroversial! Contains a thought-provoking analysis of the Heisenberg Uncertainty Principle
Priest, G. (2001). An Introduction to Non-classical Logic. Cambridge University Press. An easy-going introduction to non-classical logics. It begins with classical logic, emphasising the material conditional, and then moves on to to the less standard logics. The chapter devoted to conditional logics is excellent and worth reading as background to the logical discussion in Chapter 5 in GIR
Putnam, H. (1975). ‘The logic of quantum mechanics.’ In Mathematics, Matter and Method: Philosophical Papers, vol. I (ed.). H. Putnam. Cambridge University Press. pp. 174–197. The revised version of the 1968 paper that sparked a continuing debate about the nature of logic, arguing that ‘logic is, in a certain sense, a natural science’
Putnam, H. (1981). ‘Quantum mechanics and the observer.’ Erkenntnis 16: 193–219. A revision of some of Putnam's views as expressed in Putnam (1975)
Quine, W. v. O. (1969). Ontological Relativity and Other Essays. Columbia University Press. Contains a Chapter on natural kinds that is relevant to Chapter 2 of GIR
Rae, A. (1986). Quantum Physics: Illusion or Reality? Cambridge University Press. A fine short popular introduction to quantum mechanics
Rédei, M. (1998). Quantum Logic in Algebraic Approach Kluwer Academic Publishers. A very elaborate book on quantum logic and probability. It builds on the early work of Von Neumann. It mainly contains pure mathematical results and as such is a useful reference work. To be avoided unless one is interested in pursuing quantum logic (and probability) on various kinds of lattices in great depth
Rédei, M. and M. Stöltzner, eds. (2001). John von Neumann and the Foundations of Quantum Physics. Vienna Circle Institute Yearbook, Kluwer Academic Publishers. A collection of papers dealing with the contributions that John von Neumann made to QM. It also contains some previously unpublished material by John von Neumann. One of the unpublished lectures, ‘Unsolved Problems in Mathematics’, is extensively quoted from in Chapter 1
Redhead, M. (1999). Incompleteness Non-locality and Realism. A Prolegomenon to the Philosophy of Quantum Mechanics, Clarendon Press. Although philosophical in thrust and intent, it is quite mathematical. It gives a competent introduction to QM. The Einstein–Podolsky–Rosen incompleteness argument is discussed, followed by non-locality and the Bell inequality as well the Kochen–Specker Paradox. It has a good mathematical appendix
Reed, M. and B. Simon (1980). Methods of Modern Mathematical Physics, Vol. I Functional Analysis Academic Press. Compare this book with Fano (1971) and Jordan (1969)
Reichenbach, H. (1944). Philosophic Foundations of Quantum Mechanics, University of California Press. Still a valuable and well-written account. His views on multi-valued and three-valued logic for QM are now discounted
Retherford, J. R. (1993). Hilbert Space: Compact Operators and the Trace Theorem, Cambridge University Press. Slim volume, worth consulting on elementary spectral theory
Richman, F. and , D. Bridges (1999). ‘A constructive proof of Gleason's Theorem.’ Journal of Functional Analysis 162: 287–312. Another version of the proof of Gleason's Theorem
Riesz, F. and B. Sz.-Nagy (1990). Functional Analysis, Dover Publications, Inc. A classic reference on functional analysis. It contains a good section on self-adjoint transformations
Robertson, S. E. (1977). ‘The probability ranking principle in IR.’ Journal of Documentation 33: 294–304. A seminal paper. It is the first detailed formulation of why ranking documents by the probability of relevance can be optimal. Contains an interesting discussion of the principle in relation to the Cluster Hypothesis, and makes reference to Goffman's early work. It is reprinted in Sparck Jones and Willett (1997)
Román, L. (1994). ‘Quantum logic and linear logic.’ International Journal of Theoretical Physics 33(6): 1163–1172. Linear logic is an important development in computer science; here is a paper that clarifies its relation to quantum logic
Roman, S. (1992). Advanced Linear Algebra, Springer-Verlag. A fairly recent textbook on linear algebra. Excellent chapter on eigenvectors and eigenvalues
Sadun, L. (2001). Applied Linear Algebra. The Decoupling Principle Prentice Hall. It is hard to find any textbooks on linear algebra that deal with bras, kets and duality. This is such a rare find. It also discusses the Heisenberg Uncertainty Principle for bandwidth and Fourier transforms, that is, independent of QM. Apart from that, it is a clear and well presented introduction to linear algebra
Salton, G. (1968). Automatic Information Organization and Retrieval McGraw-Hill Book Company. A classic IR reference. This is a compendium of early results in IR based on the Smart system that was originally designed at Harvard between 1962 and 1965. It continues to operate at Cornell to this day. Even though this book is dated it still contains important ideas that are not readily accessible elsewhere
Salton, G. and M. J. McGill (1983). Introduction to Modern Information Retrieval, McGraw-Hill Book Company. An early textbook on IR, still much used and cited
Saracevic, T. (1975). ‘Relevance: A review of and a framework for the thinking on the notion in information science.’ Journal of the American Society for Information Science 26: 321–343. Although somewhat dated, this is still one of the best surveys of the concept of relevance. It takes the reader through the different ways of conceptualising relevance. One gets a more up-to-date view of this topic by reading Mizzaro (1997), and the appropriate sections in Belew (2000)
Schmeidler, W. (1965). Linear Operators in Hilbert Space Academic Press. A gentle introduction to linear operators in Hilbert space, it begins with a simple introduction to Hilbert spaces
Schrödinger, E. (1935). ‘Die gegenwartige Situation in der Quantenmechanik.’ Naturwissenschaften 22: 807–812, 823–828, 844–849. The original of the translated version in Wheeler and Zurek (1983, pp. 152–167). In our Prologue there is a quote from the translation. Schrödinger was at odds with the quantum mechanics orthodoxy for most of his life. He invented the Schrödinger's Cat Paradox to illustrate the absurdity of some of its tenets
Schwarz, H. R., H. Rutishauser and E. Stiefel (1973). Numerical Analysis of Symmetric Matrices. Prentice-Hall, Inc. Despite its title this is an excellent introduction to vector spaces and linear algebra. The numerical examples are quite effective in aiding the understanding of the basic theory. It uses a very clear notation
Schwinger, J. (1959). ‘The algebra of microscopic measurement.’ Proceedings of the National Academy of Science 45: 1542–1553. Full version of the paper reprinted in Schwinger (1991)
Schwinger, J. (1960). ‘Unitary operator bases.’ Proceedings of the National Academy of Science 46: 570–579. Reprinted in Schwinger (1991)
Schwinger, J. (1960). ‘The geometry of quantum states.’ Proceedings of the National Academy of Science 46: 257–265. Reprinted in Schwinger (1991)
Schwinger, J. (1991). Quantum Kinematics and Dynamics, Perseus Publishing. A preliminary and less formal version of material in Schwinger (2001). This is a good book to start with if one wishes to read Schwinger in detail
Schwinger, J. (2001). Quantum Mechanics: Symbolism of Atomic Measurements, Springer-Verlag. Schwinger received the Nobel prize for physics at the same time as Feynman in 1965. His approach to QM was very intuitive, motivated by the process of measurement. The first chapter introduces QM through the notion of measurement algebra. It is an idiosyncratic approach but some may find it a more accessible way than through Hilbert space theory
Sibson, R. (1972). ‘Order invariant methods for data analysis.’ The Journal of the Royal Statistical Society, Series B(Methodology) 34(3): 311–349. A lucid discussion on classification methods without recourse to details of specifc algorithms
Simmons, G. F. (1963). Introduction to Topology and Modern Analysis, McGraw-Hill. Contains an excellent introduction to Hilbert spaces
Sneath, P. H. A. and R. R. Sokal (1973). Numerical Taxonomy, W. H. Freeman and Company. An excellent compendium on classification methods. Although now over thirty years old, it is still one of the best books on automatic classification. It contains an very thorough and extensive bibliography
Sneed, J. D. (1970). ‘Quantum mechanics and classical probability theory.’ Synthese 21: 34–64. The author argues that ‘there is an interpretation of the quantum mechanical formalism which is both physically acceptable and consistent with classical probability theory (Kolmogorov's)’
Sober, E. (1985). ‘Constructive empiricism and the problem of aboutness.’ British Journal of the Philosophy of Science 1985: 11–18. The concept of ‘aboutness’ is a source of potential difficulty in IR. Here is a philosophical discussion of the notion
Sparck Jones, K. and P. Willett, eds. (1997). Readings in Information Retrieval. The Morgan Kaufmann Series in Multimedia Information and Systems, Morgan Kaufmann Publishers, Inc. A major source book for important IR papers published in the last fifty years. It contains, for example, the famous paper by Maron and Kuhns. It also has a chapter on models describing the most important ones. Not covered are latent semantic indexing and language models in IR
Stairs, A. (1982). ‘Discussion: quantum logic and the Lüders rule.’ Philosophy of Science 49: 422–436. Contribution to the debate sparked by Putnam (1975). A response to the Friedman and Putnam (1978) paper
Stalnaker, R. (1970). ‘Probability and conditionals.’ Philosophy of Science 37: 64–80. It is here that Stalnaker stated the Stalnaker Hypothesis that the probability of a conditional goes as the conditional probability. David Lewis subsequently produce a set of triviality results. All this is well documented in Harper et al. (1981)
Suppes, P., ed. (1976). Logic and Probability in Quantum Mechanics. Synthese Library. D. Reidel Publishing Company. This still remains one of the best collections of papers on logic and probability in quantum mechanics despite its age. It contains an excellent classified bibliography of almost one thousand references. The headings of the classification are very helpful, for example, ‘quantum logic’ is a heading under which one will find numerous references to items published before 1976. It is well indexed: the author index gives separate access to the bibliography
Sutherland, R. I. (2000). ‘A suggestive way of deriving the quantum probability rule.’ Foundations of Physics Letters 13(4): 379–386. An elementary and simple derivation of the rule that probability in QM goes as the ‘modulus squared’
Teller, P. (1983). ‘The projection postulate as a fortuitous approximation.’ Philosophy of Science 50: 413–431. Another contribution to the debate sparked by Friedman and Putnam (1978). It also contains an excellent section on the Projection Postulate
Thomason, R. H., ed. (1974). Formal Philosophy: Selected papers of Richard Montague. Yale University Press. Once one has read the introduction by Dowty et al. (1981) on Montague Semantics one may wish to consult the master. Thomason has collected together probably the most important papers published by Montague. Montague's papers are never easy going but always rewarding
Tombros, A. (2002). The Effectiveness of Query-based Hierarchic Clustering of Documents for Information Retrieval. Computing Science Department, Glasgow University. A thorough examination of document clustering. Contains a very good up-to-date literature survey. There is an excellent discussion on how to measure the effectiveness of document clustering
Van der Waerden, B. L., ed. (1968). Sources of Quantum Mechanics, Dover Publications, Inc. Contains original papers by Bohr, Born, Dirac, Einstein, Ehrenfest, Jordan, Heisenberg and Pauli, but sadly omits any by Schrödinger
Van Fraassen, B. C. (1976). ‘Probabilities of conditionals.’ In Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science. W. L. Harper and C. A. Hooker (eds.). Reidel, pp. 261–300. This is a beautifully written paper, it examines the Stalnaker Thesis afresh and examines under what conditions it can be sustained
Fraassen, B. C. (1991). Quantum Mechanics. An Empiricist View Clarendon Press. This is a superb introduction to modern quantum mechanics. Its notation is slightly awkward, and it avoids the use of Dirac notation. It aims to present and discuss a number of interpretations of quantum mechanics. For example, there is an extensive consideration of modal interpretations. Hilbert space theory is kept to a minimum. The mathematics is intended to be understood by philosophers with little or no background
Rijsbergen, C. J. (1970). ‘Algorithm 47. A clustering algorithm.’ The Computer Journal 13: 113–115. Contains a programme for the L∗ algorithm mentioned in Chapter 2
Van Rijsbergen, C. J. (1979a). Information Retrieval. Butterworths. A popular textbook on IR, still much used. It has been made available on number of web sites, for example, a search with Google on the author's name will list www.dcs.gla.ac.uk/Keith/Preface.html. An electronic version on CD is also contained in Belew (2000)
Van Rijsbergen, C. J. (1979b). ‘Retrieval effectiveness.’ In Progress in Communication Sciences. M. J. Voigt and G. J. Hanneman, (eds.). ABLEX Publishing Corporation. Vol. I, pp. 91–118. A foundational paper on the measurement of retrieval effectiveness, paying particular attention to averaging techniques. Expresses some of the standard parameters of effectiveness, such as precision and recall, in terms of general measures
Rijsbergen, C. J. (1979c). ‘Foundation of evaluation.’ Journal of Documentation 30: 365–373. Contains a complete derivation of the E and F measure for measuring retrieval effectiveness based on the theory of measurement
Rijsbergen, C. J. (1986). ‘A non-classical logic for information retrieval.’ The Computer Journal 29: 481–485. The paper that launched a number of papers dealing with the logical model for information retrieval. Reprinted in Sparck Jones and Willett (1997)
Van Rijsbergen, C. J. (1992) ‘Probabilistic retrieval revisited.’ The Computer Journal35: 291–298
Van Rijsbergen, C. J. (1996). Information, Logic, and Uncertainty in Information Science. CoLIS 2, Second International Conference on Conceptions of Library and Information Science: Integration in Perspective, Copenhagen, The Royal School of Librarianship. Here is the first detailed published account of the conceptualisation underlying the approach in GIR. An argument is made for an interaction logic taking its inspiration from quantum logic
Rijsbergen, C. J. (2000). ‘Another look at the logical uncertainty principle.’ Information Retrieval 2: 15–24. Useful background reading for Chapter 2
Varadarajan, V. S. (1985). Geometry of Quantum Theory Springer-Verlag. A one volume edition of an earlier, 1968, two-volume set. It contains a very detailed and thorough treatment of logics for quantum mechanics followed by logics associated with Hilbert spaces. The material is beautifully presented, a real labour of love
Varadarajan, V. S. (1993). ‘Quantum theory and geometry: sixty years after Von Neumann.’ International Journal of Theoretical Physics 32(10): 1815–1834. Mainly of historical interest, but written by one of the foremost scholars of quantum theory. It reviews some of the developments in mathematical foundations of QM since the publication of Von Neumann (1932). Written with considerable informality
Von Neumann, J. (1932). Mathematische Grundlagen der Quantenmechanik. Springer. The original edition of his now famous book on QM
Neumann, J. (1961). Collected Works. Vol. I: Logic, Theory of Sets and Quantum Mechanics, Pergamon Press. This volume contains most of John von Neumann's published papers on quantum mechanics (in German)
Neumann, J. (1983). Mathematical Foundations of Quantum Mechanics, Princeton University Press. This is the 1955 translation by Robert T. Beyer of John von Neumann (1932), originally published by Princeton University Press. It is the starting point for most work in the last 70 years on the philosophy and interpretation of quantum mechanics. It contains a so-called proof of the ‘no hidden variables’ result, a result that was famously challenged in detail by Bell (1993), and much earlier by Reichenbach (1944, p. 14). Nevertheless, this book was and remains one of the great contributions to the foundations of QM. Its explanations, once the notation has been mastered, are outstanding for their clarity and insight
Weizsäcker, C. F. (1973). ‘Probability and quantum mechanics.’ British Journal of Philosophical Science 24: 321–337. An extremely informal but perceptive account of probability in QM
Voorhees, E. M. (1985). The Effectiveness and Efficiency of Agglomerative Hierarchic Clustering in Document Retrieval. Computing Science Department, Cornell University. One of the first thorough evaluations of the Cluster Hypothesis
Wheeler, J. A. (1980). ‘Pregeometry: motivation and prospects.’ In Quantum Theory and Gravitation. A. R. Marlow (ed.). Academic Press, pp. 1–11. Provocative article about the importance and role of geometry in quantum mechanics. The quote: ‘No elementary phenomenon is a phenomenon until it is an observed (registered) phenomenon’ is taken from this essay
Wheeler, J. A. and W. H. Zurek, eds. (1983). Quantum Theory and Measurement. Princeton University Press. Here is a collection of papers that represents a good snapshot of the state of debate about the ‘measurement problem’. Many of the classic papers on the problem are reprinted here, for example, Schrödinger (1935), London and Bauer (1982) and Einstein, Podolsky and Rosen (1935)
Whitaker, A. (1996). Einstein, Bohr and the Quantum Dilemma, Cambridge University Press. Should the reader get interested in the debate between Bohr and Einstein that took place between 1920 and 1930, this is a good place to start
Wick, D. (1995). The Infamous Boundary: Seven Decades of Heresy in Quantum Physics. Copernicus. This is a wonderfully lucid book about the well-known paradoxes in quantum mechanics. It is written in an informal style and pays particular attention to the history of the subject. It contains a substantial appendix on probability in quantum mechanics prepared by William G. Farris
Wilkinson, J. H. (1965). The Algebraic Eigenvalue Problem. Clarendon Press. This is perhaps the ‘Bible’ of mathematics for dealing with the numerical solutions of the eigenvalue problem. It is written with great care
Williams, D. (2001). Weighing of Odds: a Course in Probability and Statistics. Cambridge University Press. A modern introduction. It would make a good companion to Jaynes (2003) simply because it presents the subject in a neutral and mathematical way, without the philosophical bias of Jaynes. It contains a useful chapter on quantum probability and quantum computation: a rare thing for books on probability theory
Witten, I. H., A. Moffat and T. C. Bell (1994). Managing Gigabytes – Compressing and Indexing Documents and Images Van Nostrand Reinhold. A useful book about the nuts and bolts of IR. There is now a second edition published in 1999
Wootters, W. K. (1980a). The Acquisition of Information from Quantum Measurements. Center for Theoretical Physics, Austin, The University of Texas at Austin. Wootters summarises his results in this thesis by ‘… the observer's ability to distinguish one state from another seems to be reflected in the structure of quantum mechanics itself’. He gives an information-theoretic argument for a particular form of a probabilistic law which is used in the Prologue of this book
Wootters, W. K. (1980b). ‘Information is maximised in photon polarization measurements.’ In Quantum Theory and Gravitation. A. R. Marlow (ed.). Academic Press, pp. 13–26. A self-contained account of a central idea described in the thesis by Wootters (1980a). His idea is used in the Prologue of GIR
Zeller, Eduard (1888). Plato and the Older Academy, translated by Sarah Alleyne and Alfred Goodwin, Longmens, Green and Co., pp. 21–22, note 41
Zhang, F. (1999). Matrix Theory: Basic Results and Techniques Springer. A standard modern reference on matrices; contains a good chapter on Hermitian matrices
