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A Sequent Calculus for Bilattice-Based Logic and Its Many-Sorted Representation

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Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4548))

Abstract

We introduce a sequent calculus for bilattice-based annotated logic (BAL). We show that this logic can be syntactically and semantically translated into a fragment MSL* of conventional many-sorted logic MSL. We show deductive equivalence of sequent calculus for BAL and sequent calculus for MSL*.

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References

  1. Baaz, M., Fremuller, C.G., Sazler, G.: Automated deduction for many-valued logics. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. 2, pp. 1355–1402. Elsevier, Amsterdam (2001)

    Chapter  Google Scholar 

  2. Baldoni, M.: Normal Multimodal Logics: Automatic Deduction and Logic Programming extension. PhD thesis, Torino, Italy (2003)

    Google Scholar 

  3. Church, A.: Introduction to Mathematical Logic. Princeton (1944)

    Google Scholar 

  4. Ebbinghaus, H.D., Flum, J., Thomas, W.: Mathematical Logic. Springer, Berlin (1984)

    MATH  Google Scholar 

  5. Fitting, M.: Bilattices in logic programming. In: Epstein, G. (ed.) The twentieth International Symposium on Multiple-Valued Logic, pp. 238–246. IEEE, Washington (1990)

    Chapter  Google Scholar 

  6. Fitting, M.: Bilattices and the semantics of logic programming. Journal of logic programming 11, 91–116 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  7. Fitting, M.: Many-valued modal logics. Fundamenta informaticae 15, 234–235 (1992)

    Google Scholar 

  8. Fitting, M.: Kleene’s three-valued logics and their children. Fundamenta informaticae 20, 113–131 (1994)

    MATH  MathSciNet  Google Scholar 

  9. Fitting, M.: Tableaus for many-valued modal logic. Studia Logica 55, 63–87 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  10. Fitting, M.: Bilattices are nice things. Self-Reference, pp. 53–77 (2006)

    Google Scholar 

  11. Ginsberg, M.L.: Multivalued logics: a uniform approach to reasoning in artificial intelligence. Computational Intelligence 4, 265–316 (1988)

    Article  Google Scholar 

  12. Grätzer, G.: General Lattice Theory. Birkauser Verlag, Basel, Switzerland (1978)

    Google Scholar 

  13. Hähnle, R.: Commodious axiomatizations of quantifiers in multiple-valued logic. Studia Logica 61(1), 101–121 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  14. Hähnle, R., Escalado-Imaz, G.: Deduction in many-valued logics: a survey. Mathware and soft computing IV(2), 69–97 (1997)

    Google Scholar 

  15. Kifer, M., Lozinskii, E.L.: RI: A logic for reasoning with inconsistency. In: LICS. Proceedings of the 4th IEEE Symposium on Logic in Computer Science, pp. 253–262. IEEE Computer Press, Asilomar (1989)

    Google Scholar 

  16. Kifer, M., Subrahmanian, V.S.: Theory of generalized annotated logic programming and its applications. Journal of logic programming 12, 335–367 (1991)

    Article  MathSciNet  Google Scholar 

  17. Komendantskaya, E.: A many-sorted semantics for many-valued annotated logic programs. In: Proceedings of the Fourth Irish Conference on the Mathematical Foundations of Computer Science and Information Technology (MFCSIT), pp. 225–229, Cork, Ireland (August 1–5, 2006)

    Google Scholar 

  18. Komendantskaya, E., Power, J.: Fibrational semantics for many-valued logic programs (submitted, 2007)

    Google Scholar 

  19. Komendantskaya, E., Seda, A.K., Komendantsky, V.: On approximation of the semantic operators determined by bilattice-based logic programs. In: Proceedings of the Seventh International Workshop on First-Order Theorem Proving (FTP 2005), pp. 112–130, Koblenz, Germany, (September 15–17, 2005)

    Google Scholar 

  20. Lu, J.J.: Logic programming with signs and annotations. Journal of Logic and Computation 6(6), 755–778 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  21. Lu, J.J., Murray, N.V., Rosenthal, E.: A framework for automated reasoning in multiple-valued logics. Journal of Automated Reasoning 21(1), 39–67 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  22. Lu, J.J., Murray, N.V., Rosenthal, E.: Deduction and search strategies for regular multiple-valued logics. Journal of Multiple-valued logic and soft computing 11, 375–406 (2005)

    MATH  MathSciNet  Google Scholar 

  23. Manzano, M.: Introduction to many-sorted logic. In: Meinke, K., Tucker, J.V. (eds.) Many-Sorted logic and its Applications, pp. 3–88. John Wiley and Sons, UK (1993)

    Google Scholar 

  24. Salzer, G.: MUltlog 1.0: Towards an expert system for many-valued logics. In: McRobbie, M.A., Slaney, J.K. (eds.) Automated Deduction - Cade-13. LNCS, vol. 1104, pp. 226–230. Springer, Heidelberg (1996)

    Google Scholar 

  25. Sazler, G.: Optimal axiomatizations of finitely-valued logics. Information and Computation 162(1–2), 185–205 (2000)

    MathSciNet  Google Scholar 

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Nicola Olivetti

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Komendantskaya, E. (2007). A Sequent Calculus for Bilattice-Based Logic and Its Many-Sorted Representation. In: Olivetti, N. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2007. Lecture Notes in Computer Science(), vol 4548. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73099-6_14

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  • DOI: https://doi.org/10.1007/978-3-540-73099-6_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73098-9

  • Online ISBN: 978-3-540-73099-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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