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Refutations, Proofs, and Models in the Modal Logic K4

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Abstract

In this paper we study the method of refutation rules in the modal logic K4. We introduce refutation rules with certain normal forms that provide a new syntactic decision procedure for this logic. As corollaries we obtain such results for the following important extensions: S4, the provability logic G, and Grzegorczyk's logic. We also show that tree-type models can be constructed from syntactic refutations of this kind.

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References

  1. Goranko, V., 'Refutation systems in modal logic', Studia Logica 53, 299-324, 1994.

    Google Scholar 

  2. Lemmon, E. J., An Introduction to Modal Logic, in collaboration with D. Scott, Blackwell, Oxford, 1977.

    Google Scholar 

  3. Łukasiewicz, J., 'O sylogistyce Arystotelesa', Sprawozdania PAU 44, 220-227, 1939.

    Google Scholar 

  4. Łukasiewicz, J., Aristotle's Syllogistic from the Standpoint of Modern Formal Logic, Clarendon, Oxford, 1951.

    Google Scholar 

  5. Mints, G., 'Gentzen-type systems and resolution rules', Lecture Notes in Computer Science 417, Springer-Verlag, pp. 198-231, 1990.

  6. Scott, D., 'Completeness proofs for the intuitionistic sentential calculus', Summaries of talks presented at the Summer Institute of Symbolic Logic, Cornell University, pp. 231-241, 1957, second edition Princeton, 1960.

  7. Segerberg, K., An Essay in Classical Modal Logic, Uppsala, 1971.

  8. Skura, T., 'On decision procedures for sentential logics', Studia Logica 50, 173-179, 1991.

    Google Scholar 

  9. Skura, T., 'Syntactic refutations against finite models in modal logic', Notre Dame Journal of Formal Logic 35, 595-605, 1994.

    Google Scholar 

  10. Skura, T., 'Refutations and proofs in S4', pp. 45-51, in Proof Theory of Modal Logic, edited by H. Wansing, Kluwer Academic Publishers, Dordrecht, 1996.

    Google Scholar 

  11. Skura, T., Aspects of Refutation Procedures in the Intuitionistic Logic and Related Modal Systems, Wrocław, 1999.

  12. Wajsberg, M., 'Untersuchungen über den Aussagenkalkül von A. Heyting', Wiadomości Matematyczne 46, 45-101, 1938.

    Google Scholar 

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  1. Department of Logic, University of Wrocław, Koszarowa 3, 51-149, Wrocław, Poland

    Tomasz Skura

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  1. Tomasz Skura
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Skura, T. Refutations, Proofs, and Models in the Modal Logic K4. Studia Logica 70, 193–204 (2002). https://doi.org/10.1023/A:1015174332202

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