Axiomatization of a Denotational Semantics for First-order Logic

An axiomatization is presented of the denotational semantics for first order language of Apt [1]. The goal is to obtain a rational reconstruction of the intuitions underlying this semantics. The axiomatization combines ideas about four valued logic with facts about substitutions. Soundness and compl...

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Bibliographic Details
Published in:Logic journal of the IGPL 2004-07, Vol.12 (4), p.277-299
Main Author: Vermeulen, C. F. M.
Format: Article
Language:English
Subjects:
axiomatization
Declarative programming
denotational semantics
first order logic
Online Access:Get full text
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Summary:An axiomatization is presented of the denotational semantics for first order language of Apt [1]. The goal is to obtain a rational reconstruction of the intuitions underlying this semantics. The axiomatization combines ideas about four valued logic with facts about substitutions. Soundness and completeness of the axiomatization are established. From the completeness proof a decision procedure is obtained that shows how four valued logic and order sensitivity of substitution together add up in a natural way to the denotational semantics for the language of first order logic as proposed by Apt.
ISSN:1367-0751
1368-9894
DOI:10.1093/jigpal/12.4.277