Abstract
This paper deals with various substructural propositional logics, in particular with substructural subsystems of Nelson's constructive propositional logics N− and N. DoŽen's groupoid semantics is extended to these constructive systems and is provided with an informational interpretation in terms of information pieces and operations on information pieces.
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References
Almukdad, A. and Nelson, D.: 1984, ‘Constructible falsity and inexact predicates’,Journal of Symbolic Logic 49, pp. 231–233.
Avron, A.: 1988, ‘The semantics and proof theory of linear logic’,Theoretical Computer Science 57, pp. 161–184.
van Benthem, J.F.A.K.: 1986,Essays in Logical Semantics, Dordrecht: Reidel.
van Benthem, J.F.A.K.: 1988, ‘The Lambek Calculus’, pp. 35–68 inCategorial Grammars and Natural Language Structures, R. Oehrleet al., eds., Dordrecht: Reidel.
Blamey, S.: 1986, ‘Partial Logic’, pp. 1–70 inHandbook of Philosophical Logic, Vol. III: Alternatives to Classical Logic, D.M. Gabbay and F. Guenthner, eds., Dordrecht: Reidel.
Church, A.: 1950, ‘The weak theory of implication’, pp. 22–37 inKontrolliertes Denken, Untersuchungen zum Logikkalkül und der Logik der Einzelwissenschaften, A. Menneet al., eds., Munich: Kommissions-Verlag Karl Alber.
Došen, K.: 1988, ‘Sequent systems and groupoid models, I’,Studia Logica 47, pp. 353–389.
Došen, K.: 1989, ‘Sequent systems and groupoid models, II’,Studia Logica 48, pp. 41–65.
Dunn, J.M.: 1986, ‘Relevance Logic and Entailment’, pp. 177–224 inHandbook of Philosophical Logic, Vol. III: Alternatives to Classical Logic, D.M. Gabbay and F. Guenthner, eds., Dordrecht:Reidel.
Fenstad, J-E., Halvorsen, P-K., Langholm, T. and & van Benthem, J.F.A.K.: 1987,Situations, Language and Logic, Dordrecht: Reidel.
Gabbay, D.M.: 1991, ‘A general theory of structured consequence relations’, Technical Report, Imperial College of Science, Technology and Medicine, London, to appear.
Girard, J-Y.: 1987, ‘Linear Logic’,Theoretical Computer Science 50, pp. 1–102.
Girard, J-Y., Lafont, Y. and Taylor, P.: 1989,Proofs and Types, Cambridge University Press.
Grzegorczyk, A.: 1964, ‘A philosophically plausible formal interpretation of intuitionistic logic’,Indagationes Mathematicae 26, pp. 596–601.
Gurevich, Y: 1977, ‘Intuitionistic logic with strong negation’,Studia Logica 36, pp. 49–59.
Kripke, S.A.: 1965, ‘Semantical analysis of intuitionistic logic I’, pp. 92–129 inFormal Systems and Recursive Functions, J. Crossley and M. Dummett, eds., Amsterdam: North-Holland.
von Kutschera, F.: 1969, ‘Ein verallgemeinerter Widerlegungsbegriff für Gentzenkalküle’,Archiv für Mathematische Logik und Grundlagenforschung 12, pp. 104–118.
Lambek, J.: 1958, ‘The mathematics of sentence structure’,American Mathematical Monthly 65, pp. 154–170.
López-Escobar, E.G.K.: 1972, ‘Refutability and elementary number theory’,Indagationes Mathematicae 34, pp. 362–374.
Markov, A.A.: 1950, ‘Konstruktivnaja logika’,Usp. Mat. Nauk. 5, pp. 187–188.
Moh, S-K.: 1950, The deduction theorems and two new logical systems’,Methodos 2, pp. 56–75.
Nelson, D.: 1949, ‘Constructible falsity’,Journal of Symbolic Logic 14, pp. 16–26.
Pearce, D.: 1991, ‘n reasons for choosingN’, Technical Report, Gruppe für Logik, Wissenstheorie und Information 14/91, Freie Universität Berlin, to appear.
Pearce, D. and Rautenberg, W: 1991, ‘Propositional logic based on the dynamics of disbelief’, pp. 311–326 inThe Logic of Theory Change — Lecture Notes in Artificial Intelligence 465, A. Fuhrmann and M. Morreau, eds., Berlin: Springer Verlag.
Pearce, D. and Wagner, G.: 1990, ‘Reasoning with negative information I: strong negation in logic programs’, pp. 430–453 inLanguage, Knowledge, and Intentionality, L. Haaparantaet al., eds., (=Acta Philosophica Fennica 49), Helsinki.
Popper, K.R.: 1963,Conjectures and Refutations: the Growth of Scientific Knowledge, London: Routledge.
Rasiowa, H.: 1974,An Algebraic Approach to Non-classical Logics, Amsterdam: North-Holland.
Routley, R.: 1974, ‘Semantical analyses of propositional systems of Fitch and Nelson’,Studia Logica 33, pp. 283–298.
Thijsse, E.G.C.: 1990, ‘Partial logic and modal logic: a systematic survey’, Technical Report, Institute for Language Technology and Artificial Intelligence, Tilburg University.
Thomason, R.H.: 1969, ‘A semantical study of constructive falsity’,Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 15, pp. 247–257.
Troelstra, A.S.: 1992,Lectures on Linear Logic, CSLI Lecture Notes 29, Stanford.
Urquhart, A.: 1972, ‘Semantics for relevant logics’,Journal of Symbolic Logic 37, pp. 159–169.
Wagner, G.: 1991, ‘Logic programming with strong negation and inexact predicates’,Journal of Logic and Computation 1, 835–859.
Wansing, H.: 1993,The Logic of Information Structures, Lecture Notes in AI 681, Berlin: Springer Verlag.
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Wansing, H. Informational interpretation of substructural propositional logics. J Logic Lang Inf 2, 285–308 (1993). https://doi.org/10.1007/BF01181683
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DOI: https://doi.org/10.1007/BF01181683