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*.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
Baldoni, M.: Normal Multimodal Logics: Automatic Deduction and Logic Programming extension. PhD thesis, Torino, Italy (2003)
Church, A.: Introduction to Mathematical Logic. Princeton (1944)
Ebbinghaus, H.D., Flum, J., Thomas, W.: Mathematical Logic. Springer, Berlin (1984)
Fitting, M.: Bilattices in logic programming. In: Epstein, G. (ed.) The twentieth International Symposium on Multiple-Valued Logic, pp. 238–246. IEEE, Washington (1990)
Fitting, M.: Bilattices and the semantics of logic programming. Journal of logic programming 11, 91–116 (1991)
Fitting, M.: Many-valued modal logics. Fundamenta informaticae 15, 234–235 (1992)
Fitting, M.: Kleene’s three-valued logics and their children. Fundamenta informaticae 20, 113–131 (1994)
Fitting, M.: Tableaus for many-valued modal logic. Studia Logica 55, 63–87 (1995)
Fitting, M.: Bilattices are nice things. Self-Reference, pp. 53–77 (2006)
Ginsberg, M.L.: Multivalued logics: a uniform approach to reasoning in artificial intelligence. Computational Intelligence 4, 265–316 (1988)
Grätzer, G.: General Lattice Theory. Birkauser Verlag, Basel, Switzerland (1978)
Hähnle, R.: Commodious axiomatizations of quantifiers in multiple-valued logic. Studia Logica 61(1), 101–121 (1998)
Hähnle, R., Escalado-Imaz, G.: Deduction in many-valued logics: a survey. Mathware and soft computing IV(2), 69–97 (1997)
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)
Kifer, M., Subrahmanian, V.S.: Theory of generalized annotated logic programming and its applications. Journal of logic programming 12, 335–367 (1991)
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)
Komendantskaya, E., Power, J.: Fibrational semantics for many-valued logic programs (submitted, 2007)
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)
Lu, J.J.: Logic programming with signs and annotations. Journal of Logic and Computation 6(6), 755–778 (1996)
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)
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)
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)
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)
Sazler, G.: Optimal axiomatizations of finitely-valued logics. Information and Computation 162(1–2), 185–205 (2000)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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)