Abstract
AbstractWeighted 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.
Highlights
Answer Set Programming (ASP) is a well-known non-monotonic declarative programming paradigm
As customary for ASP we restrict ourselves to a fragment of First-Order Weighted Here-and-There Logic (FO-WHT) Logic and introduce A C programs that allow for algebraic constraints, i.e. constraints on the values of weighted formulas, in both heads and bodies of rules
To verify that the semantics of algebraic constraints is in line with the intuition of HT logic, we show that the persistence property is maintained for sentences that include algebraic constraints
Summary
Answer Set Programming (ASP) is a well-known non-monotonic declarative programming paradigm. Cabalar et al (2020a; 2020b) recently introduced a general non-monotonic integration of CP into ASP providing aggregates and conditionals for the specification of numeric values that depend on the satisfaction of formulas. An important feature of constraint extensions is the possibility to express (in)equations involving computations on an algebraic structure, whose solutions are accessible by the ASP rules Basic such structures are semirings R = (R, ⊕, ⊗, e⊕, e⊗), where ⊕ and ⊗ are addition and multiplication with neutral elements e⊕ and e⊗, respectively. As customary for ASP we restrict ourselves to a fragment of FO-WHT Logic and introduce A C programs that allow for algebraic constraints, i.e. constraints on the values of weighted formulas, in both heads and bodies of rules. Proof details and more details can be found in the supplementary material corresponding to this paper at the TPLP archives
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