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Many-Valued First-Order Logics with Probabilistic Semantics

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Computer Science Logic (CSL 1998)

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

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Abstract

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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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Gießen, Arndtstraße 2, D-35392, Gießen, Germany

    Thomas Lukasiewicz

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  1. Thomas Lukasiewicz
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Editor information

Editors and Affiliations

  1. Computing Laboratory, Oxford University, Wolfson Building Parks Road Oxford,, OX1 3QD, United Kingdom

    Georg Gottlob

  2. GREYC, Université de Caen, CNRS, Campus 2, F-14032, Caen cedex, France

    Etienne Grandjean

  3.  ,  

    Katrin Seyr

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© 1999 Springer-Verlag Berlin Heidelberg

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Lukasiewicz, T. (1999). Many-Valued First-Order Logics with Probabilistic Semantics. In: Gottlob, G., Grandjean, E., Seyr, K. (eds) Computer Science Logic. CSL 1998. Lecture Notes in Computer Science, vol 1584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10703163_28

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  • DOI: https://doi.org/10.1007/10703163_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65922-8

  • Online ISBN: 978-3-540-48855-2

  • eBook Packages: Springer Book Archive

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