Abstract
The problem of computing a uniform interpolant of a given formula on a sublanguage is known in Artificial Intelligence as variable forgetting. In propositional logic, there are well known methods for performing variable forgetting. Variable forgetting is more involved in modal logics, because one must forget a variable not in one world, but in several worlds. It has been shown that modal logic K has the uniform interpolation property, and a method has recently been proposed for forgetting variables in a modal formula (of mu-calculus) given in disjunctive normal form. However, there are cases where information comes naturally in a more conjunctive form. In this paper, we propose a method, based on an extension of resolution to modal logics, to perform variable forgetting for formulae in conjunctive normal form, in the modal logic K .
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References
D’Agostino, G., Lenzi, G.: On modal mu-calculus with explicit interpolants. Journal of Applied Logic 4(3), 256–278 (2006)
Kohlas, J., Moral, S., Haenni, R.: Propositional Information Systems. Journal of Logic and Computation 9(5), 651–681 (1999)
Lang, J., Marquis, P.: Resolving inconsistencies by variable forgetting. In: Fensel, D., Giunchiglia, F., McGuinness, D.L., Williams, M.A. (eds.) Proceedings of the Eights International Conference on Principles of Knowledge Representation and Reasoning (KR 2002), pp. 239–250. Morgan Kaufmann, San Francisco (2002)
Visser, A.: Bisimulations, model descriptions and propositional quantifiers. In: Hájek, P. (ed.) Gödel 1996: Logical foundations of mathematics, computer science and physics – Kurt Gödel’s legacy. A K Peters Ltd (2001)
Ghilardi, S., Zawadowski, M.W.: Undefinability of propositional quantifiers in the modal system s4. Studia Logica 55(2), 259–271 (1995)
Ghilardi, S., Zawadowski, M.W.: Sheaves, Games, and Model Completions. Trends in Logic, vol. 14. Kluwer, Dordrecht (2002)
Bílková, M.: Uniform interpolation and propositional quantifiers in modal logics. Studia Logica 85, 1–31 (2007)
Kracht, M.: Modal consequence relations. In: Blackburn, P., van Benthem, J., Wolter, F. (eds.) Handbook of Modal Logic. Elsevier, Amsterdam (2006)
Bienvenu, M.: Prime Implicates and Prime Implicants in Modal Logic. In: Holte, R.C., Howe, A. (eds.) Proceedings of the 22nd National Conference on Artifcial Intelligence (AAAI 2007), pp. 379–384. AAAI Press, Menlo Park (2007)
Enjalbert, P., del Cerro, L.F.: Modal resolution in clausal form. Theoretical Computer Science 65(1), 1–33 (1989)
ten Cate, B., Conradie, W., Marx, M., Venema, Y.: Definitorially complete description logics. In: Doherty, P., Mylopoulos, J., Welty, C.A. (eds.) Proceedings of the Tenth International Conference on Principles of Knowledge Representation and Reasoning (KR 2006), pp. 79–89. AAAI Press, Menlo Park (2006)
Besnard, P., Quiniou, R., Quinton, P.: A theorem prover for a decidable subset of default logic. In: Proceedings of the Third National Conference on Artificial Intelligence, pp. 27–30. Morgan Kaufmann, San Francisco (1983)
Areces, C., de Rijke, M., de Nivelle, H.: Resolution in modal, description and hybrid logic. Journal of Logic and Computation 11(5), 717–736 (2001)
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Herzig, A., Mengin, J. (2008). Uniform Interpolation by Resolution in Modal Logic. In: Hölldobler, S., Lutz, C., Wansing, H. (eds) Logics in Artificial Intelligence. JELIA 2008. Lecture Notes in Computer Science(), vol 5293. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87803-2_19
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DOI: https://doi.org/10.1007/978-3-540-87803-2_19
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