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A substructural connective for possibilistic logic

  • Luca Boldrin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 946)

Abstract

We investigate the use of substructural logics for dealing with uncertainty. In this paper possibilistic logic is enriched with a new connective for combining information; the language allows then for two combinators: the usual ”and” for performing expansion and the new ”and” for combining information from distinct independent sources, as argued in [Dubois and Prade 85]. A negation is introduced which corresponds to fuzzy set complementation. The resulting logic is given the expected semantics and a proof system in sequent calculus, which is proved sound and complete.

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References

  1. [Alechina and Smets 94]
    N. Alechina and P. Smets. A note on modal logics for partial beliefe (manuscript), 1994.Google Scholar
  2. [Boldrin 94]
    Substructural connectives for merging information in possibilistic logic. LADSEB-CNR Int. Rep. 09, 1994.Google Scholar
  3. [Dubois and Prade 85]
    D. Dubois and H. Prade. A review of fuzzy set aggregation connectives. Information Sciences 36, 1985, pp. 85–121.Google Scholar
  4. [Dubois and Prade 94]
    D. Dubois and H. Prade. A survey of belief revision and updating rules in various uncertainty models. Int. J. of Intelligent Systems 9, 1994, pp. 61–100.Google Scholar
  5. [Dubois, Lang and Prade 94]
    D. Dubois, J. Lang and H. Prade. Possibilistic logic In: D. Gabbay, C. Hogger and J. Robinson (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3. Clarendon Press 1994.Google Scholar
  6. [Fagin and Halpern 94]
    R. Fagin and J. Y. Halpern. Reasoning about knowledge and probability. J. of the ACM, 41, 1994, pp. 340–367.Google Scholar
  7. [Gabbay 92]
    D. Gabbay. Fibred semantics and the weaving of logics. Draft, Imperial College, 1992.Google Scholar
  8. [Girard 87]
    J. Y. Girard. Linear logic. Theoretical computer science, 50, 1987, pp. 1–101.CrossRefGoogle Scholar
  9. [Hajek et. al 94]
    P. Hajek, D. Harmancova and R. Verbrugge. A qualitative fuzzy possibilistic logic. Int. J. of Approximate Reasoning 7, 1994.Google Scholar
  10. [Ketonen and Weyhrauch 84]
    J. Ketonen and R. Weyhrauch. A decidable fragment of predicate calculus. Theoretical computer science 32, 1984, pp. 297–307.Google Scholar
  11. [Murai et al. 93]
    T. Murai, M. Miyakoshi and M. Shimbo. Measure-based semantics for modal logic. In: R. Lowen and M. Roubens (eds.). Fuzzy logic. Kluwer Academic Publishers, 1993, pp. 395–405.Google Scholar
  12. [Pavelka 79]
    J. Pavelka. On fuzzy logic II. Zeitschr. f. math. Logik und Grundlagen d. Math 25, 1979, pp. 119–131.Google Scholar
  13. [de Rijke 94]
    Meeting some neighbours. A dynamic logic meets theories of change and knowledge representation. In J. van Eijck and A. Visser: Logic and information flow. The MIT Press, 1994.Google Scholar
  14. [Rosenthal 90]
    K. I. Rosenthal. Quantales and their applications. Longman 1990.Google Scholar
  15. [Saffiotti 92]
    A. Saffiotti. A belief function logic. Proceedings of AAAI 1992, pp. 642–647.Google Scholar
  16. [Sambin 95]
    G. Sambin. Pretopologies and the completeness proof. To appear in The J. of Symbolic Logic.Google Scholar
  17. [Voorbraak 93]
    F. Voorbraak. As far as I know. Epistemic logic and uncertainty. Phd dissertation, Dept. of Philosophy — Utrecht University, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Luca Boldrin
    • 1
  1. 1.Dept. of Pure and Applied MathematicsUniversity of PadovaPadovaItaly

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