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Abstrakty
We provide some illustrations of consequence relations extending that associated with intuitionistic propositional logic but lacking the Deduction Theorem, together with a discussion of issues of some interest in their own right raised by these examples. There are two main examples, with some minor variations: one in which the language of intuitionistic logic is retained, and one in which this language is expanded.
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Tom
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45-82
Opis fizyczny
Bibliogr. 57 poz.
Twórcy
autor
- Department of Philosophy School of Philosophy & Bioethics Monash University Clayton, Vic Australia 3800, LLoyd.Humberstone@arts.monash.edu.au
Bibliografia
- [1] N. D. Belnap, Tonk, Plonk, and Plink, Analysis 22 (1962), pp. 130-134.
- [2] C. Bergman, Structural Completeness in Algebra and Logic, pp.59-73 in H, Andréka,J. D. Monk and I. Németi (eds.), Algebraic Logic, North-Holland, Amsterdam 1991.
- [3] C. Bergman and R. McKenzie, Minimal Varieties and Quasivarieties, Journal of the Australian Mathemantical Society (Series A) 48 (1990), pp. 133-147.
- [4] A. Biela, On the So-Called Tarski's Property in the Theory of Lindenbaum's Over-systems, I. Nonnitely axiomatizable systems, Reports on Mathematical Logic 7(1978), pp. 3-20.
- [5] S. Blamey, Partial Logic, pp.261-353 in D. Gabbay and F. Guenthner (eds.), Handbookof Philosophical Logic, Second Edition, Vol. 5, Kluwer, Dordrecht 2002.
- [6] W. J. Blok and D. L. Pigozzi, Algebraizable Logics, Memoirs of the American Math.Soc. 77 (1989), #396.
- [7] W. J. Blok and D. L. Pigozzi, Local Deduction Theorems in Algebraic Logic, pp.75-109 in H. Andréka, J. D. Monk and I. Németi (eds.), Algebraic Logic, North-Holland,Amsterdam 1991.
- [8] P. Bystrov, Non-Standard Sequent Calculi for Modal and Relevant Logics, pp.235-255 in P. I. Bystrov and V. N. Sadovsky (eds.), Philosophical Logic and Logical Philosophy, Kluwer, Dordrecht 1996.
- [9] H. B. Curry and R. Feys, Combinatory Logic, Vol. 1, North-Holland, Amsterdam 1958.
- [10] J. Czelakowski, Protoalgebraic Logics, Kluwer, Dordrecht 2001.
- [11] W. Darsow and P. M. Kittel, On Intermediate Consequence Relations, Zeitschrift für math. Logik und Grundlagen der Math. 26 (1980), pp. 33-34.
- [12] K. Došen, A Historical Introduction to Substructural Logics, pp.1-30 in P. Schroeder-Heister and K. Došen (eds.), Substructural Logics, Clarendon Press, Oxford 1993.
- [13] M. Dummett, Frege: Philosophy of Language, First Edition, Duckworth, London 1973.
- [14] W. Dzik and M. Tokarz, Invariant Matrix Consequences, Reports on Mathematical Logic 18 (1984), pp. 37-43.
- [15] B. van Fraassen, Formal Semantics and Logic, Macmillan, New York 1971.
- [16] D. M. Gabbay, Semantical Investigations in Heyting's Intuitionistic Logic, Reidel, Dordrecht 1981.
- [17] K. Gödel, On Intuitionistic Arithmetic and Number Theory, orig. publ. 1933, appearing in translation in pp.287-295 of S. Feferman, J. W. Dawson, S. C. Kleene, G. H. Moore, R. M. Solovay and J. van Heijenoort (eds.), Kurt Gödel: Collected Works, Vol.I, Publications 1929-1936, Oxford University Press, New York 1986.
- [18] R. Goré, Dual Intuitionistic Logic Revisited, pp.252-267 in R. Dyckhoff (ed.), Automated Reasoning with Analytic Tableaux and Related Methods, Springer-Verlag, Berlin 2000.
- [19] L. Humberstone, Interval Semantics for Tense Logic: Some Remarks, Journal of Philosophical Logic 8 (1979), pp. 171-196.
- [20] L. Humberstone, The Pleasures of Anticipation: Enriching Intuitionistic Logic, Journal of Philosophical Logic 30 (2001), pp. 395-438.
- [21] L. Humberstone, Two-Dimensional Adventures, Philosophical Studies 118 (2004), pp. 17-65.
- [22] L. Humberstone, Identical Twins, Deduction Theorems, and Pattern Functions: Exploring the Implicative BCSK Fragment of S5, to appear in Journal of Philosophical Logic.
- [23] R. Iemhoff, On The Admissible Rules of Intuitionistic Propositional Logic, Journal of Symbolic Logic 66 (2001), pp. 281-294.
- [24] H. Kamp, Formal Properties of „Now", Theoria 37 (1971), pp. 227-273.
- [25] S. A. Kripke, Semantical Analysis of Intuitionistic Logic. I, pp.92{129 in J. N. Crossley and M. A. E. Dummett (eds.), Formal Systems and Recursive Functions, North-Holland, Amsterdam 1965.
- [26] G. Lakoff Global Rules, Language 46 (1970), pp. 627-639.
- [27] P. Latocha, The Problem of Structural Completeness of the Intuitionsitic Propositional Logic and its Fragments, Reports on Mathematical Logic 16 (1983), pp.17-22.
- [28] J. Łoś, and R. Suszko, Remarks on Sentential Logics, Indagationes Math. 20 (1958), pp. 177-183.
- [29] D. Makinson, A characterization of structural completeness of a structural consequence operation, Reports on Mathematical Logic 6 (1976), pp. 99-102.
- [30] C. A. Meredith and A. N. Prior, Investigations into Implicational S5, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 10 (1964), pp. 203-220.
- [31] C. A. Meredith and A. N. Prior, Modal Logic with Functorial Variables and a Contingent Constant, Notre Dame Journal of Formal Logic 6 (1965), pp. 99-109.
- [32] W. P. M. Meyer Viol, Instantial Logic, University of Utrecht Proefschrift, CIPGegevens Koninklijke Bibliotheek, The Hague 1996.
- [33] G. E. Mints, Derivability of Admissible Rules, Journal of Soviet Mathematics 6 (No. 4) 1976, 417-421. (Russian original publ. 1972)
- [34] J. Perzanowski, A Linguistic Criterion of Structural Incompleteness, Reports on Mathematical Logic 1 (1973), pp. 13-14.
- [35] W. A. Pogorzelski, Structural Completeness of the Propositional Calculus, Bull. de l'Académie Polonaise des Sciences, ser. des sciences math., astr., et phys. 19 (1971), pp. 349-351.
- [36] J. Porte, Antitheses in Systems of Relevant Implication, Journal of Symbolic Logic 48 (1983), pp. 97-99.
- [37] T. Prucnal, On the Structural Completeness of Some Pure Implicational Propositional Calculi, Studia Logica 30 (1972), pp. 45-50.
- [38] C. Rauszer, Applications of Kripke Models to Heyting-Brouwer Logic, Studia Logica 36 (1977), pp. 61-71.
- [39] W. Rautenberg, A Note on Implicational Intermediate Consequences, Bulletin of the Section of Logic 14 (1985), pp. 103-108.
- [40] W. Rautenberg, Applications of Weak Kripke Semantics to Intermediate Consequences, Studia Logica 45 (1986), pp. 119-134.
- [41] V. Rybakov, Admissibility of Logical Inference Rules, Elsevier, Amsterdam 1997.
- [42] D. S. Scott, Rules and Derived Rules, pp.147-161 in Logical Theory and Semantic Analysis, ed. S. Stenlund, Reidel, Dordrecht 1974.
- [43] S. J. Scroggs, Extensions of the Lewis System S5, Journal of Symbolic Logic 16 (1951), pp. 112-120.
- [44] K. Segerberg, Propositional Logics Related to Heyting's and Johansson's, Theoria 34 (1968), pp. 26-61.
- [45] K. Segerberg, An Essay in Classical Modal Logic, Filosofiska Studier, Uppsala 1971.
- [46] K. Segerberg, Classical Propositional Operators, Clarendon Press, Oxford 1982.
- [47] J. K. Slaney and R. K. Meyer, A Structurally Complete Fragment of Relevant Logic, Notre Dame Journal of Formal Logic 33 (1992), pp. 561-566.
- [48] T. Smiley, The Independence of Connectives, Journal of Symbolic Logic 27 (1962), pp. 426-436.
- [49] T. Smiley, Relative Necessity, Journal of Symbolic Logic 28 (1963), pp. 113-134.
- [50] R. H. Thomason, Indeterminist Time and Truth-Value Gaps, Theoria 36 (1970), pp. 264-281.
- [51] M. Tokarz, Connections Between Some Notions of Completeness of Structural Propositional Calculi, Studia Logica 32 (1973), pp. 77-89.
- [52] A. I. Tsitkin (Citkin), On Admissible Rules of Intuitionistic Propositional Logic, Math. USSR (Sbornik) 31 (1977), pp. 279-288.
- [53] Hao Wang, Note on Rules of Inference, Zeitschr. für math. Logik und Grundlagen der Math. 11 (1965), pp. 193-196.
- [54] R. Wójcicki, Theory of Logical Calculi, Kluwer, Dordrecht 1988.
- [55] P. Wojtylak, On Structural Completeness of Implicational Logics, Studia Logica 50 (1991), pp. 275-297.
- [56] A. Wroński, On Cardinalitities of Matrices Strongly Adequate for Intuitionistic Propositional Logic, Reports on Mathematical Logic 3 (1974), pp. 67-72.
- [57] A. Wroński, On Factoring by Compact Congruences in Algebras of Certain Varieties Related to Intuitionistic Logic, Bulletin of the Section of Logic 15 (1986), pp. 48-51.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-BUJ3-0005-0008