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A Denotational Semantics for First-Order Logic

  • Krzysztof R. Apt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1861)

Abstract

In Apt and Bezem [AB99] we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic. Additionally, by allowing an assignment of a non-ground term to a variable we introduce in this framework logical variables.

The semantics combines a number of well-known ideas from the areas of semantics of imperative programming languages and logic programming. In the resulting computational view conjunction corresponds to sequential composition, disjunction to “don’t know” nondeterminism, existential quantification to declaration of a local variable, and negation to the “negation as finite failure” rule. The soundness result shows correctness of the semantics with respect to the notion of truth. The proof resembles in some aspects the proof of the soundness of the SLDNF-resolution.

Keywords

Induction Hypothesis Logic Program Logic Programming Operational Semantic Atomic Formula 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Krzysztof R. Apt
    • 1
    • 2
  1. 1.CWIAmsterdamThe Netherlands
  2. 2.University of AmsterdamThe Netherlands

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