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Mathematical Reasoning Vs. Abductive Reasoning: A Structural Approach

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REFERENCES

  • Aliseda, A.: 1997, Seeking Explanations: Abduction in Logic, Philosophy of Science and Artificial Intelligence, Ph.D. dissertation, Philosophy Department, Stanford University. Published by the Institute for Logic, Language and Computation, University of Amsterdam. (ILLC Dissertation Series 1997-4).

  • van Benthem, J.: 1984, Lessons from Bolzano, Center for the Study of Language and Information, Technical Report CSLI-84-6, Stanford University. Later published as ‘The Variety of Consequence, According to Bolzano’, Studia Logica 44, 389–403.

  • van Benthem, J.: 1990, General Dynamics, ILLC Prepublication Series LP-90-11, Institute for Logic, Language, and Information. University of Amsterdam.

  • van Benthem, J.: 1991, Language in Action. Categories, Lambdas and Dynamic Logic, North Holland, Amsterdam.

    Google Scholar 

  • van Benthem, J.: 1996, Exploring Logical Dynamics, CSLI Publications, Stanford University.

  • van Benthem, J. and G. Cepparello: 1994, Tarskian Variations: Dynamic Parameters in Classical Semantics, Technical Report CS-R9419, Centre for Mathematics and Computer Science (CWI), Amsterdam.

    Google Scholar 

  • Carnap, T.: 1955, Statistical and Inductive Probability, Galois Institute of Mathematics and Art, Brooklyn, NY.

    Google Scholar 

  • Chaitin, G. J.: 198, The Limits of Mathematics: A Course on Information Theory and the Limits of Formal Reasoning, Springer Series in Discrete Mathematics and Theoretical Computer Science.

  • Dosen, K. and P. Schroeder-Heister (eds.): 1993, Substructural Logics, Oxford Science Publications, Clarendon Press, Oxford.

    Google Scholar 

  • Flach, P. A.: 1995, Conjectures: An Inquiry Concerning the Logic of Induction, Ph.D. Thesis, Tilburg University.

  • Gabbay, D. M.: 1985, ‘Theoretical Foundations for Non-Monotonic Reasoning in Expert Systems’, in K. Apt (ed.), Logics and Models of Concurrent Systems, Springer-Verlag, Berlin, pp. 439–457.

    Google Scholar 

  • Gabbay, D. M.: 1994a, Labelled Deductive Systems. Part I, Oxford University Press.

  • Gabbay, D. M.: 1994b, ‘Classical vs Non-Classical Logics (The Universality of Classical Logic)’, in D. M. Gabbay, C. J. Hogger and J. A. Robinson (eds.), Handbook of Logic in Artificial Intelligence and Logic Programming. Volume 2, Deduction Methodologies, Clarendon Press, Oxford Science Publications, pp. 359–500.

  • Gillies, S.: 1996, Artificial Intelligence and Scientific Method, Oxford University Press.

  • Groeneveld, W.: 1995, Logical Investigations into Dynamic Semantics. PhD Dissertation, Institute for Logic, Language and Information, University of Amsterdam. (ILLC Dissertation Series 1995-18).

  • Hanson, N. R.: 1961, Patterns of Scientific Discovery, The University Press, Cambridge.

    Google Scholar 

  • Hempel, C.: 1965, ‘Aspects of Scientific Explanation’, in C. Hempel (ed.), Aspects of Scientific Explanation and Other Essays in the Philosophy of Science, The Free Press, New York.

    Google Scholar 

  • Kraus, S., D. Lehmann, and M. Magidor: 1990, ‘Nonmonotonic Reasoning, Preferential Models and Cumulative Logics’, Artificial Intelligence 44, 167–207.

    Google Scholar 

  • Lakatos, I.: 1976, Proofs and Refutations. The Logic of Mathematical Discovery, Cambridge Universiity Press.

  • Makinson, D.: 1994, ‘General Patterns in Nonmonotonic Reasoning’, in D. M. Gabbay, C. J. Hogger and J. A. Robinson (eds), Handbook of Logic in Artificial Intelligence and Logic Programming. Volume 3, Nonmonoptonic Reasoning and Uncertain Reasoning, Chapter 2.2, Clarendon Press, Oxford Science Publications.

  • McCarthy, J.: 1980, ‘Circumscription: A Form of Non-Monotonic Reasoning’, Artificial Intelligence 13, 27–39.

    Google Scholar 

  • Mendelson, E.: 1964, Introduction to Mathematical Logic, Van Nostrand, New York.

    Google Scholar 

  • Peirce, C. S.: 1958, in C. Hartshorne and P. Weiss (eds.), Collected Papers of Charles Sanders Peirce, Volumes 1-6, Harvard University Press, Cambridge; and Volumes 7-8 edited by A. W. Burks, Harvard University Press, Cambridge (1958).

    Google Scholar 

  • Popper, K.: 1958, The Logic of Scientific Discovery, Hutchinson, London.

    Google Scholar 

  • Quine, W. V.: 1961, ‘On What There Is’, in From a Logical Point of View, 2nd edn, Cambridge and Harvard University Press.

  • Scott, D.: 1971, 'On Engendering an Illusion of Understanding, Journal of Philosophy 68, 787–808.

    Google Scholar 

  • Shoham, Y.: 1988, Reasoning about Change. Time and Causation from the standpoint of Artificial Intelligence, The MIT Press, Cambridge, MA.

    Google Scholar 

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  1. Instituto de Investigaciones Filosóficas, Universidad Nacional Autónoma de México Ciudad Universitaria, Coyoacán, 04510, México E-mail

    Atocha Aliseda

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  1. Atocha Aliseda
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Aliseda, A. Mathematical Reasoning Vs. Abductive Reasoning: A Structural Approach. Synthese 134, 25–44 (2003). https://doi.org/10.1023/A:1022127429205

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