Analyzing Semantics of Aggregate Answer Set Programming Using Approximation Fixpoint Theory

TL;DR

This paper uses Approximation Fixpoint Theory to formalise aggregates in answer set programming, providing a unified framework that relates to existing approaches and aims to clarify their semantics.

Contribution

It introduces an AFT-based formalisation for aggregates in ASP, extending the Gelfond-Lifschitz reduct and analyzing its relation to existing methods.

Findings

AFT formalisation equivalent to Gelfond-Lifschitz reduct for basic ASP

Extension of AFT to handle aggregate constructs

Analysis of how existing approaches relate to the new framework

Abstract

Aggregates provide a concise way to express complex knowledge. The problem of selecting an appropriate formalisation of aggregates for answer set programming (ASP) remains unsettled. This paper revisits it from the viewpoint of Approximation Fixpoint Theory (AFT). We introduce an AFT formalisation equivalent with the Gelfond-Lifschitz reduct for basic ASP programs and we extend it to handle aggregates. We analyse how existing approaches relate to our framework. We hope this work sheds some new light on the issue of a proper formalisation of aggregates. This paper is under consideration for acceptance in TPLP.