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Aggregate Semantics for Propositional Answer Set Programs

Published online by Cambridge University Press:  23 February 2022

MARIO ALVIANO Open the ORCID record for MARIO ALVIANO [Opens in a new window] ,
WOLFGANG FABER Open the ORCID record for WOLFGANG FABER [Opens in a new window]  and
MARTIN GEBSER Open the ORCID record for MARTIN GEBSER [Opens in a new window]
MARIO ALVIANO
Affiliation:
University of Calabria, Rende, Italy (e-mail: alviano@mat.unical.it)
WOLFGANG FABER
Affiliation:
University of Klagenfurt, Klagenfurt, Austria (e-mail: wolfgang.faber@aau.at)
MARTIN GEBSER
Affiliation:
University of Klagenfurt, Klagenfurt, Austria Graz University of Technology, Graz, Austria (e-mail: martin.gebser@aau.at@aau.at)
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Abstract

Answer set programming (ASP) emerged in the late 1990s as a paradigm for knowledge representation and reasoning. The attractiveness of ASP builds on an expressive high-level modeling language along with the availability of powerful off-the-shelf solving systems. While the utility of incorporating aggregate expressions in the modeling language has been realized almost simultaneously with the inception of the first ASP solving systems, a general semantics of aggregates and its efficient implementation have been long-standing challenges. Aggregates have been proposed and widely used in database systems, and also in the deductive database language Datalog, which is one of the main precursors of ASP. The use of aggregates was, however, still restricted in Datalog (by either disallowing recursion or only allowing monotone aggregates), while several ways to integrate unrestricted aggregates evolved in the context of ASP. In this survey, we pick up at this point of development by presenting and comparing the main aggregate semantics that have been proposed for propositional ASP programs. We highlight crucial properties such as computational complexity and expressive power, and outline the capabilities and limitations of different approaches by illustrative examples.

Keywords

answer set programmingaggregate expressionssemanticscomplexity and expressiveness
Type
Survey Article
Information
Theory and Practice of Logic Programming , Volume 23 , Issue 1 , January 2023 , pp. 157 - 194
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Footnotes

*

The work of Mario Alviano was partially supported by projects PRIN “Declarative Reasoning over Streams” (CUP: H24I17000080001), PON-MISE MAP4ID “Multipurpose Analytics Platform 4 Industrial Data” (CUP: B21B19000650008), lab LAIA (part of SILA), and GNCS-INdAM. Martin Gebser was partially supported by KWF project 28472, cms electronics GmbH, FunderMax GmbH, Hirsch Armbänder GmbH, incubed IT GmbH, Infineon Technologies Austria AG, Isovolta AG, Kostwein Holding GmbH, and Privatstiftung Kärntner Sparkasse. We are grateful to the reviewers for valuable and constructive comments helping to improve this paper.

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