Skip to main content
Log in

Logical Connectives for Constructive Modal Logic

Synthese Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

Model-theoretic proofs of functional completenes along the lines of [McCullough 1971, Journal of Symbolic Logic 36, 15–20] are given for various constructive modal propositional logics with strong negation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • A. Almukdad D. Nelson (1984) ArticleTitle‘Constructible Falsity and Inexact Predicates’ Journal of Symbolic Logic 49 231–233 Occurrence Handle10.2307/2274105

    Article  Google Scholar 

  • van Benthem, J. (1988), ‘Games in Logic: A Survey’, in J. Hoepelman (ed.), Representation and Reasoning, Max Niemeyer Verlag, Tübingen, pp. 3–15.

  • van Benthem, J. (1996), Exploring Logical Dynamics, CSLI Publications, Stanford.

  • T. Braüner (2003) ‘Functional Completeness for a Natural Deduction Formulation of Hybridized S5’ P. Balbiani N.-Y. Suzuki F. Wolter M. Zakharyaschev (Eds) Advances in Modal Logic Vol 4 King’s College Press London 31–49

    Google Scholar 

  • Felscher, W. (1986), ‘Dialogues as a Foundation for Intuitionistic Logic’, in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, Vol. 3, Reidel, Dordrecht, pp. 341–372

  • Gentzen, G. (1969), ‘Investigations into Logical Deduction’, in M.E. Szabo (ed.), The Collected Papers of Gerhard Gentzen, North Holland, Amsterdam, pp. 68–131. English translation of: Untersuchungen über das logische Schließen, Mathematische Zeitschrift 39, (1934), I 176–210, II 405–431.

    Google Scholar 

  • S. Gottwald (1989) Mehrwertige Logik Eine Einführung in Theorie und Anwendungen. Akademie-Verlag Berlin

    Google Scholar 

  • Hacking, I. (1994), ‘What is Logic?’, The Journal of Philosophy 76, 285–319. Reprinted in D. Gabbay (ed.), What is a Logical System?, Oxford University Press, Oxford, pp. 1–33. (Cited after the reprint.)

  • J. Hintikka (1973) Logic, Language Games and Information Clarendon Press Oxford

    Google Scholar 

  • J. Hintikka J. Kulas (1983) The Game of Language Reidel Dordrecht

    Google Scholar 

  • Hintikka, J. and G. Sandu (1997), ‘Game-theoretical Semantics’, in J. van Benthem and A. ter Meulen (eds.), Handbook of Logic and Language, Elsevier, Amsterdam and MIT Press, Cambridge (Mass.), pp. 361–410.

  • von Kutschera, F. (1968), ‘Die Vollständigkeit des Operatorensystems {\(\neg, \wedge, \vee, \supset\)} für die intuitionistische Aussagenlogik im Rahmen der Gentzensemantik’, Archiv für Mathematische Logik und Grundlagenforschung 11:3–16.

  • F. Kutschera Particlevon (1969) ArticleTitle‘Ein verallgemeinerter Widerlegungsbegriff für Gentzenkalküle’ Archiv für Mathematische Logik und Grundlagenforschung 12 104–118 Occurrence Handle10.1007/BF01969697

    Article  Google Scholar 

  • Lorenz, K. (1978), ‘Dialogspiele als semantische Grundlage von Logikkalkülen’, Archiv für mathematische Logik und Grundlagenforschung 11, 32–55, 73–100. Reprinted in P. Lorenzen and K. Lorenz, Dialogische Logik, Wissenschaftliche Buchgesellschaft, Darmstadt, pp. 96–162.

  • D. McCullough (1971) ArticleTitle‘Logical Connectives for Intuitionistic Propositional Logic’ Journal of Symbolic Logic 36 15–20 Occurrence Handle10.2307/2271511

    Article  Google Scholar 

  • Odintsov, S. and H. Wansing (2004), ‘Constructive Predicate Logic and Constructive Modal Logic. Formal Duality versus Semantical Duality’, in V. Hendricks et al. (eds.), First-Order Logic Revisited, Berlin, Logos Verlag, pp. 269–286.

  • E. Post (1920) ArticleTitle‘Determination of All Closed Systems of Truth Tables’ Bulletin of the American Mathematical Society 26 437

    Google Scholar 

  • Prawitz, D. (1979), ‘Proofs and the Meaning and Completenes of the Logical Constants’, in J. Hintikka et al. (eds.), Essays on Mathematical and Philosophical Logic, Reidel, Dordrecht, pp. 25–40.

  • Rosenberg, I. (1979), ‘Über die funktionale Vollständigkeit in den mehrwertigen ’, Rozpravy Československé Akademie Věd, Řada Matematických a Přirodnich Věd 80, 3–93.

  • P. Schroeder-Heister (1984) ArticleTitle‘A Natural Extension of Natural Deduction’ Journal of Symbolic Logic 49 1284–1300 Occurrence Handle10.2307/2274279

    Article  Google Scholar 

  • P. Schroeder-Heister (1991) ArticleTitle‘Uniform Proof-theoretic Semantics for Logical Constants (Abstract)’ Journal of Symbolic Logic 56 1142

    Google Scholar 

  • G. Sundholm (1994) ArticleTitle‘Proof-theoretical Semantics and Fregean Identity-Criteria for Propositions’ The Monist 77 294–314

    Google Scholar 

  • N. Tennant (1978) Natural Logic Edinburgh University Press Edinburgh

    Google Scholar 

  • H. Wansing (1993a) ArticleTitle‘Functional Completeness for Subsystems of Intuitionistic Propositional Logic’ Journal of Philosophical Logic 22 303–321 Occurrence Handle10.1007/BF01049305

    Article  Google Scholar 

  • H. Wansing (1993) ‘The Logic of Information Structures’, Lecture Notes in AI 681 Springer-Verlag Berlin

    Google Scholar 

  • H. Wansing (1995) ArticleTitle‘Tarskian Structured Consequence Relations and Functional Completeness’ Mathematical Logic Quarterly 41 73–92

    Google Scholar 

  • H. Wansing (1996) ‘A Proof-theoretic Proof of Functional Completeness for Many Modal and Tense Logics’ H. Wansing (Eds) Proof Theory of Modal Logic Kluwer Academic Publishers Dordrecht 123–136

    Google Scholar 

  • H. Wansing (1998) Displaying Modal Logic Kluwer Academic Publishers Dordrecht

    Google Scholar 

  • H. Wansing (2000) ArticleTitle‘The Idea of a Proof-Theoretic Semantics and the Meaning of the Logical Operations’ Studia Logica 64 3–20 Occurrence Handle10.1023/A:1005217827758

    Article  Google Scholar 

  • Wansing, H. (2002), ‘Sequent Systems for Modal Logics’, in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, Vol. 8, Kluwer Academic Publishers, pp. 61–145.

  • L. Wittgenstein (1953) Philosophical Investigations Blackwell Oxford

    Google Scholar 

  • J. Zucker R. Tragesser (1978) ArticleTitle‘The Adequacy Problem for Inferential Logic’ Journal of Philosophical Logic 7 501–516

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Heinrich Wansing.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wansing, H. Logical Connectives for Constructive Modal Logic. Synthese 150, 459–482 (2006). https://doi.org/10.1007/s11229-005-5518-5

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11229-005-5518-5

Keywords

Navigation