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Towards Rational Closure for Fuzzy Logic: The Case of Propositional Gödel Logic

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8312))

Abstract

In the field of non-monotonic logics, the notion of rational closure is acknowledged as a landmark and we are going to see whether such a construction can be adopted in the context of mathematical fuzzy logic, a so far (apparently) unexplored journey. As a first step, we will characterise rational closure in the context of Propositional Gödel Logic.

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References

  1. Ansotegui, C., Bofill, M., Manyà, F., Villaret, M.: Building automated theorem provers for infinitely-valued logics with satisfiability modulo theory solvers. In: Proceedings of ISMVL 2012, pp. 25–30. IEEE Computer Society (2012)

    Google Scholar 

  2. Benferhat, S., Dubois, D., Prade, H.: Representing default rules in possibilistic logic. In: Proceedings of KR 1992, pp. 673–684. Morgan Kaufman (1992)

    Google Scholar 

  3. Benferhat, S., Dubois, D., Prade, H.: Nonmonotonic reasoning, conditional objects and possibility theory. Artificial Intelligence 92(1-2), 259–276 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  4. Benferhat, S., Dubois, D., Prade, H.: Towards fuzzy default reasoning. In: Proceedings of NAFIPS 1999, pp. 23–27. IEEE Computer Society (1999)

    Google Scholar 

  5. Casini, G., Straccia, U.: Rational closure for defeasible description logics. In: Janhunen, T., Niemelä, I. (eds.) JELIA 2010. LNCS (LNAI), vol. 6341, pp. 77–90. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  6. de Dupin Saint-Cyr, F., Prade, H.: Possibilistic handling of uncertain default rules with applications to persistence modeling and fuzzy default reasoning. In: Proceedings of KR 2006, pp. 440–451. AAAI Press (2006)

    Google Scholar 

  7. Dubois, D., Prade, H.: Default reasoning and possibility theory. Artificial Intelligence Journal 35(2), 243–257 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dubois, D., Mengin, J., Prade, H.: Possibilistic uncertainty and fuzzy features in description logic. A preliminary discussion. In: Capturing Intelligence: Fuzzy Logic and the Semantic Web. Elsevier (2006)

    Google Scholar 

  9. Dubois, D., Prade, H.: What are fuzzy rules and how to use them. Fuzzy Sets and Systems 84(2), 169–185 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  10. de Dupin Saint-Cyr, F., Prade, H.: Handling uncertainty and defeasibility in a possibilistic logic setting. International Journal of Approximate Reasoning 49(1), 67–82 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gabbay, D.M., Hogger, C.J., Robinson, J.A. (eds.): Handbook of logic in artificial intelligence and logic programming: nonmonotonic reasoning and uncertain reasoning, vol. 3. Oxford University Press, Inc., New York (1994)

    MATH  Google Scholar 

  12. Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L.: A minimal model semantics for nonmonotonic reasoning. In: del Cerro, L.F., Herzig, A., Mengin, J. (eds.) JELIA 2012. LNCS, vol. 7519, pp. 228–241. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  13. Giordano, L., Olivetti, N., Gliozzi, V., Pozzato, G.L.: A minimal model semantics for rational closure. In: Proceedings of NMR 2012 (2012), http://www.dbai.tuwien.ac.at/NMR12/proceedings.html

  14. Guller, D.: On the satisfiability and validity problems in the propositional Gödel logic. In: Madani, K., Dourado Correia, A., Rosa, A., Filipe, J. (eds.) Computational Intelligence. SCI, vol. 399, pp. 211–227. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  15. Hähnle, R.: Advanced many-valued logics. In: Gabbay, D.M., Guenthner, F. (eds.) Handbook of Philosophical Logic, 2nd edn., vol. 2. Kluwer (2001)

    Google Scholar 

  16. Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer (1998)

    Google Scholar 

  17. Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44(1-2), 167–207 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  18. Lehmann, D., Magidor, M.: What does a conditional knowledge base entail? Artificial Intelligence 55(1), 1–60 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  19. Lukasiewicz, T., Straccia, U.: Managing uncertainty and vagueness in description logics for the semantic web. Journal of Web Semantics 6, 291–308 (2008)

    Article  Google Scholar 

  20. Raha, S., Hossain, S.: Fuzzy set in default reasoning. In: Pal, N.R., Sugeno, M. (eds.) AFSS 2002. LNCS (LNAI), vol. 2275, pp. 27–33. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  21. Raha, S., Ray, K.S.: Reasoning with vague default. Fuzzy Sets and Systems 91(3), 327–338 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  22. Straccia, U.: A fuzzy description logic for the semantic web. In: Fuzzy Logic and the Semantic Web, Capturing Intelligence, ch. 4, pp. 73–90. Elsevier (2006)

    Google Scholar 

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Casini, G., Straccia, U. (2013). Towards Rational Closure for Fuzzy Logic: The Case of Propositional Gödel Logic. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2013. Lecture Notes in Computer Science, vol 8312. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45221-5_16

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  • DOI: https://doi.org/10.1007/978-3-642-45221-5_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45220-8

  • Online ISBN: 978-3-642-45221-5

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