Parametric Connectives in Disjunctive Logic Programming

TL;DR

This paper extends Disjunctive Logic Programming with parametric connectives, enhancing its ability to naturally express problems with input-dependent disjunction sizes, and demonstrates the formal semantics and practical benefits of this extension.

Contribution

It introduces parametric connectives to DLP, formally defines their semantics, and shows how they improve knowledge representation for input-dependent disjunctions.

Findings

Enhanced expressiveness for input-dependent disjunctions

Formal semantics for $DLP^{igvee,igwedge}$

Practical benefits demonstrated on relevant problems

Abstract

Disjunctive Logic Programming (\DLP) is an advanced formalism for Knowledge Representation and Reasoning (KRR). \DLP is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class $\SigmaP{2}$ ($\NP^{\NP}$). Importantly, the \DLP encodings are often simple and natural. In this paper, we single out some limitations of \DLP for KRR, which cannot naturally express problems where the size of the disjunction is not known ``a priori'' (like N-Coloring), but it is part of the input. To overcome these limitations, we further enhance the knowledge modelling abilities of \DLP, by extending this language by {\em Parametric Connectives (OR and AND)}. These connectives allow us to represent compactly the disjunction/conjunction of a set of atoms having a given property. We formally define the semantics of the new language, named $DLP^{\bigvee,\bigwedge}$ and we show the usefulness of the new constructs on relevant knowledge-based problems. We address implementation issues and discuss related works.