Minimal founded semantics for disjunctive logic programs and deductive databases

TL;DR

This paper introduces minimal founded semantics, a new interpretative framework for disjunctive logic programs that extends stable model semantics, providing more intuitive meanings for programs with constraints without increasing computational complexity.

Contribution

It proposes minimal founded semantics, a novel semantics for disjunctive logic programs that generalizes stable model semantics and handles programs with constraints more intuitively.

Findings

Minimal founded semantics aligns with stable model semantics on non-disjunctive programs.

It offers more intuitive interpretations for programs with constraints.

The expressive power matches that of disjunctive stable model semantics.

Abstract

In this paper, we propose a variant of stable model semantics for disjunctive logic programming and deductive databases. The semantics, called minimal founded, generalizes stable model semantics for normal (i.e. non disjunctive) programs but differs from disjunctive stable model semantics (the extension of stable model semantics for disjunctive programs). Compared with disjunctive stable model semantics, minimal founded semantics seems to be more intuitive, it gives meaning to programs which are meaningless under stable model semantics and is no harder to compute. More specifically, minimal founded semantics differs from stable model semantics only for disjunctive programs having constraint rules or rules working as constraints. We study the expressive power of the semantics and show that for general disjunctive datalog programs it has the same power as disjunctive stable model semantics.