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ASP ($\mathcal A \mathcal C$): Answer Set Programming with Algebraic Constraints

Published online by Cambridge University Press:  22 September 2020

THOMAS EITER Open the ORCID record for THOMAS EITER [Opens in a new window]  and
RAFAEL KIESEL Open the ORCID record for RAFAEL KIESEL [Opens in a new window]
THOMAS EITER
Affiliation:
Technical University Vienna, Vienna, Austria (e-mail: thomas.eiter@tuwien.ac.at, rafael.kiesel@tuwien.ac.at)
RAFAEL KIESEL
Affiliation:
Technical University Vienna, Vienna, Austria (e-mail: thomas.eiter@tuwien.ac.at, rafael.kiesel@tuwien.ac.at)
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Abstract

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Weighted Logic is a powerful tool for the specification of calculations over semirings that depend on qualitative information. Using a novel combination of Weighted Logic and Here-and-There (HT) Logic, in which this dependence is based on intuitionistic grounds, we introduce Answer Set Programming with Algebraic Constraints (ASP($\mathcal A \mathcal C$)), where rules may contain constraints that compare semiring values to weighted formula evaluations. Such constraints provide streamlined access to a manifold of constructs available in ASP, like aggregates, choice constraints, and arithmetic operators. They extend some of them and provide a generic framework for defining programs with algebraic computation, which can be fruitfully used e.g. for provenance semantics of datalog programs. While undecidable in general, expressive fragments of ASP($\mathcal A \mathcal C$) can be exploited for effective problem solving in a rich framework.

Keywords

Weighted LogicHere-and-There LogicAnswer Set ProgrammingConstraints
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 20 , Issue 6: 36th International Conference on Logic Programming Special Issue II , November 2020 , pp. 895 - 910
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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