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

TL;DR

This paper introduces a lemma on closures of monotonic functions and demonstrates its application to modularity and decomposition in logic programming semantics, enhancing understanding of fixedpoint-based semantics.

Contribution

It presents a new lemma on closures of monotonic functions and applies it to improve modularity analysis in logic programming semantics.

Findings

Applicable to various logic program semantics

Enhances modularity and decomposition techniques

Addresses fixedpoints of non-monotonic functions

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.