Abstract
Autoepistemic logic is one of the principal formalisms for nonmonotonic reasoning. It extends propositional logic by offering the ability to reason about an agent’s (lack of) knowledge or beliefs. Moreover, it is well known to generalize the stable model semantics of answer set programming. Fuzzy logics on the other hand are multi-valued logics, which allow to model the intensity with which a property is satisfied. We combine these ideas to a fuzzy autoepistemic logic which can be used to reason about one’s knowledge about the degrees to which proporties are satisfied. In this paper we show that many properties from classical autoepistemic logic remain valid under this generalization and that the important relation between autoepistemic logic and answer set programming is preserved in the sense that fuzzy autoepistemic logic generalizes fuzzy answer set programming.
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References
Banerjee, M., Dubois, D.: A simple modal logic for reasoning about revealed beliefs. In: Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, pp. 805–816 (2009)
Bauters, K., Schockaert, S., De Cock, M., Vermeir, D.: Possibilistic answer set programming revisited. In: Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence (2010)
Damásio, C.V., Medina, J., Ojeda-Aciego, M.: Sorted multi-adjoint logic programs: termination results and applications. In: Proceedings of the 9th European Conference on Logics in Artificial Intelligence, pp. 260–273 (2004)
Dubois, D., Prade, H., Schockaert, S.: Règles et méta-règles dans le cadre de la théorie des possibilités et de la logique possibiliste. In: Rencontres Francophones sur la Logique Floue et ses Applications, pp. 115–122 (2010)
Egly, U., Eiter, T., Tompits, H., Woltran, S.: Solving advanced reasoning tasks using quantified boolean formulas. In: Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence, pp. 417–422 (2000)
Gelfond, M.: On stratified autoepistemic theories. In: Proceedings of the Sixth National Conference on Artificial Intelligence, pp. 207–211 (1987)
Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Proceedings of the Fifth International Conference and Symposiom on Logic Programming, pp. 1070–1080 (1988)
Hajek, P.: Metamathematics of Fuzzy Logic. Springer, Heidelberg (2001)
Hajek, P.: On fuzzy modal logics. Fuzzy Sets and Systems 161, 18 (2010)
Janssen, J., Schockaert, S., Vermeir, D., De Cock, M.: General fuzzy answer set programs. In: Proceedings of the International Workshop on Fuzzy Logic and Applications, pp. 353–359 (2009)
Koutras, C.D., Koletsos, G., Zachos, S.: Many-valued modal non-monotonic reasoning: Sequential stable sets and logics with linear truth spaces. Fundamenta Informaticae 38(3), 281–324 (1999)
Koutras, C.D., Zachos, S.: Many-valued reflexive autoepistemic logic. Logic Journal of the IGPL 8(1), 403–418 (2000)
Lifschitz, V., Schwarz, G.: Extended logic programs as autoepistemic theories. In: Proceedings of the Second International Workshop on Logic Programming and Nonmonotonic Reasoning, pp. 101–114 (1993)
Marek, W.: Stable theories in autoepistemic logic. Unpublished note, Department of Computer Science, University of Kentucky (1986)
Marek, W., Truszczynski, M.: Autoepistemic logic. Journal of the Association for Computing Machinery 38(3), 587–618 (1991)
Moore, R.C.: Semantical considerations on nonmonotonic logic. In: Proceedings of the Eighth International Joint Conference on Artificial Intelligence, pp. 272–279 (1983)
Moore, R.C.: Possible-world semantics in autoepistemic logic. In: Proceedings of the Non-Monotonic Reasoning Workshop, pp. 344–354 (1984)
Schockaert, S., Janssen, J., Vermeir, D., De Cock, M.: Answer sets in a fuzzy equilibrium logic. In: Proceedings of the 3rd International Conference on Web Reasoning and Rule Systems, pp. 135–149 (2009)
Sim, K.M.: Epistemic logic and logical omniscience: A survey. International Journal of Intelligent Systems 12, 57–81 (1997)
Stalnaker, R.: A note on non-monotonic modal logic. Artificial Intelligence 64(2), 183–196 (1993)
Straccia, U.: Annotated answer set programming. In: Proceedings of the 11th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (2006)
von Wright, G.: An Essay in Modal Logic. In: Studies in Logic and the Foundations of Mathematics. North-Holland Pub. Co., Amsterdam (1951)
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Blondeel, M., Schockaert, S., De Cock, M., Vermeir, D. (2011). Fuzzy Autoepistemic Logic: Reflecting about Knowledge of Truth Degrees. In: Liu, W. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2011. Lecture Notes in Computer Science(), vol 6717. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22152-1_52
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DOI: https://doi.org/10.1007/978-3-642-22152-1_52
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