Abstract
The algorithm to compute prime implicates and prime implicants in modal logic \({\mathcal{K}}\) has been suggested in [1]. In this paper we suggest an incremental algorithm to compute the prime implicates of a knowledge base KB and a new knowledge base F from Π(KB) ∧ F in modal logic \({\mathcal{K}}\), where Π(KB) is the set of prime implicates of KB and we also prove the correctness of the algorithm.
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References
Bienvenu, M.: Prime implicates and prime implicants: From propositional to modal logic. J. Artif. Intell. Res. (JAIR) 36, 71–128 (2009)
Bienvenu, M.: Consequence Finding in Modal Logic. PhD Thesis, Universit Paul Sabatier (May 7, 2009)
Cook, S.A.: The complexity of theorem-proving procedures. In: Proc. 3rd ACM Symp. on the Theory of Computing, pp. 151–158. ACM Press (1971)
Cadoli, M., Donini, F.M.: A survey on knowledge compilation. AI Communications-The European Journal for Articial Intelligence 10, 137–150 (1998)
Coudert, O., Madre, J.: Implicit and incremental computation of primes and essential primes of boolean functions. In: Proceedings of the 29th ACM/IEEE Design Automation Conference, pp. 36–39. IEEE Computer Society Press (1991)
Darwiche, A., Marquis, P.: A knowledge compilation map. Journal of Artificial Intelligence Research 17, 229–264 (2002)
Jackson, P., Pais, J.: Computing prime implicants. In: Stickel, M.E. (ed.) CADE 1990. LNCS, vol. 449, pp. 543–557. Springer, Heidelberg (1990)
Kean, A., Tsiknis, G.: An incremental method for generating prime implicants/implicates. J. Symb. Comput. 9(2), 185–206 (1990)
de Kleer, J.: An assumption-based tms. In: Ginsberg, M.L. (ed.) Readings in Nonmonotonic Reasoning, pp. 280–297. Kaufmann, Los Altos (1987)
de Kleer, J.: An improved incremental algorithm for generating prime implicates. In: Proceedings of the Tenth National Conference on Artificial Intelligence, AAAI 1992, pp. 780–785. AAAI Press (1992)
Ngair, T.H.: A new algorithm for incremental prime implicate generation. In: Proc. of the 13th IJCAI, Chambery, France, pp. 46–51 (1993)
Raut, M.K., Singh, A.: Prime implicates of first order formulas. IJCSA 1(1), 1–11 (2004)
Reiter, R., de Kleer, J.: Foundations of assumption-based truth maintenance systems. In: Proceedings of the Sixth National Conference on Artificial Intelligence (AAAI 1987), pp. 183–188 (1987)
Shiny, A.K., Pujari, A.K.: Computation of prime implicants using matrix and paths. J. Log. Comput. 8(2), 135–145 (1998)
Slagle, J.R., Chang, C.L., Lee, R.C.T.: A new algorithm for generating prime implicants. IEEE Trans. on Comp. C-19(4), 304–310 (1970)
Strzemecki, T.: Polynomial-time algorithm for generation of prime implicants. Journal of Complexity 8, 37–63 (1992)
Tison, P.: Generalized consensus theory and application to the minimisation of boolean functions. IEEE Trans. on Elec. Comp. EC-16(4), 446–456 (1967)
Pagnucco, M.: Knowledge compilation for belief change. In: Sattar, A., Kang, B.-H. (eds.) AI 2006. LNCS (LNAI), vol. 4304, pp. 90–99. Springer, Heidelberg (2006)
Przymusinski, T.C.: An algorithm to compute circumscription. Artif. Intell. 38(1), 49–73 (1989)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2002)
Blackburn, P., van Benthem, J., Wolter, F.: Handbook of modal logic. Elsevier, Amsterdam (2007)
Jackson, P.: Computing prime implicants incrementally. In: Proceedings of the 11th International Conference on Automated Deduction, vol. 607, pp. 253–267 (1992)
Raut, M.K.: An incremental knowledge compilation in first order logic. CoRR, abs/1110.6738 (2011)
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Raut, M.K. (2014). An Incremental Algorithm for Computing Prime Implicates in Modal Logic. In: Gopal, T.V., Agrawal, M., Li, A., Cooper, S.B. (eds) Theory and Applications of Models of Computation. TAMC 2014. Lecture Notes in Computer Science, vol 8402. Springer, Cham. https://doi.org/10.1007/978-3-319-06089-7_13
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DOI: https://doi.org/10.1007/978-3-319-06089-7_13
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