2000/05/08 by Krzysztof R. Apt, Apt, Krzysztof R.
Computer Science · Psychology · #Artificial Intelligence (cs.AI) #D.3.2 #F.3.2 #FOS: Computer and information sciences #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Philosophy and Theoretical Science #Programming Languages (cs.PL) #cs.AI #cs.PL
paper · pdf · doi:10.48550/arxiv.cs/0005008
17 pages. Invited talk at the Computational Logic Conference (CL 2000). To appear in Springer-Verlag Lecture Notes in Computer Science
arxiv created 2000/05/08 · openalex publication_date 2000/05/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In Apt and Bezem [AB99] (see cs.LO/9811017) 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.