Many-Valued First-Order Logics with Probabilistic Semantics

  • Thomas Lukasiewicz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1584)


We present n-valued first-order logics with a purely probabilistic semantics. We then introduce a new probabilistic semantics of n-valued first-order logics that lies between the purely probabilistic semantics and the truth-functional semantics of the n-valued Łukasiewicz logics Ł n . Within this semantics, closed formulas of classical first-order logics that are logically equivalent in the classical sense also have the same truth value under all n-valued interpretations. Moreover, this semantics is shown to have interesting computational properties. More precisely, n-valued logical consequence in disjunctive logic programs with n-valued disjunctive facts can be reduced to classical logical consequence in n-1 layers of classical disjunctive logic programs. Moreover, we show that n-valued logic programs have a model and a fixpoint semantics that are very similar to those of classical logic programs. Finally, we show that some important deduction problems in n-valued logic programs have the same computational complexity like their classical counterparts.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Thomas Lukasiewicz
    • 1
  1. 1.Institut für InformatikUniversität GießenGießenGermany

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