ASP ($\mathcal A \mathcal C$): Answer Set Programming with Algebraic Constraints. Issue 6 (November 2020)

• Record Type: Journal Article
• Authors: EITER, THOMAS; KIESEL, RAFAEL
• Is Part Of: Theory and practice of logic programming. Volume 20:Issue 6(2020)
• Page Start: 895
• Page End: 910
• Publication Date: 2020-11
• Subjects: Weighted Logic, -- Here-and-There Logic, -- Answer Set Programming, -- Constraints; Logic programming -- Periodicals; Artificial intelligence -- Computer programs -- Periodicals; Constraint programming (Computer science) -- Periodicals; 005.115
• DOI: 10.1017/S1471068420000393
• Languages: English
• ISSNs: 1471-0684

Abstract

Abstract: 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.