Analyzing Semantics of Aggregate Answer Set Programming Using Approximation Fixpoint Theory

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 e...

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Bibliographic Details
Published in:arXiv.org 2022-05
Main Authors: Linde Vanbesien, Bruynooghe, Maurice, Denecker, Marc
Format: Article
Language:English
Subjects:
Aggregates
Approximation
Declarative programming
Logic programming
Mathematical analysis
Mathematical programming
Semantics
Online Access:Get full text
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Summary: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.
ISSN:2331-8422