A lemma on closures and its application to modularity in logic programming semantics

2020/08/03 by Michael J. Maher, Maher, Michael J.
Computer Science · #Advanced Algebra and Logic #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #acm:68N17 #cs.LO #msc:68N17

paper · pdf · doi:10.48550/arxiv.2008.00724

12 pages

arxiv created 2020/08/03 · arxiv updated 2020/08/04

Abstract

This note points out a lemma on closures of monotonic increasing functions and shows how it is applicable to decomposition and modularity for semantics defined as the least fixedpoint of some monotonic function. In particular it applies to numerous semantics of logic programs. An appendix addresses the fixedpoints of (possibly non-monotonic) functions that are sandwiched between functions with the same fixedpoints.

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