Back and Forth Between Rules and SE-Models (Extended Version)

TL;DR

This paper explores the relationship between rules and SE-model semantics in logic programming, proposing new notions of equivalence that better capture rule interdependencies and their manipulations.

Contribution

It introduces a detailed analysis of rule equivalence classes under SE-model semantics and proposes stronger and weaker notions of equivalence suited for rule dependency considerations.

Findings

Identifies rule equivalence classes induced by SE-models

Characterizes sets of SE-interpretations representable by a single rule

Proposes new notions of equivalence beyond strong and update equivalence

Abstract

Rules in logic programming encode information about mutual interdependencies between literals that is not captured by any of the commonly used semantics. This information becomes essential as soon as a program needs to be modified or further manipulated. We argue that, in these cases, a program should not be viewed solely as the set of its models. Instead, it should be viewed and manipulated as the set of sets of models of each rule inside it. With this in mind, we investigate and highlight relations between the SE-model semantics and individual rules. We identify a set of representatives of rule equivalence classes induced by SE-models, and so pinpoint the exact expressivity of this semantics with respect to a single rule. We also characterise the class of sets of SE-interpretations representable by a single rule. Finally, we discuss the introduction of two notions of equivalence, both stronger than strong equivalence [1] and weaker than strong update equivalence [2], which seem more suitable whenever the dependency information found in rules is of interest.