ASP(AC): Answer Set Programming with Algebraic Constraints
This work provides a generic framework for defining programs with algebraic computation in ASP, potentially benefiting researchers in logic programming and knowledge representation, though it appears incremental as it builds on existing Weighted and HT Logic.
The authors tackled the problem of integrating algebraic computations into Answer Set Programming by introducing ASP(AC), which combines Weighted Logic and Here-and-There Logic to allow rules with constraints comparing semiring values to weighted formula evaluations, resulting in a framework that extends constructs like aggregates and choice constraints and can be used for applications such as provenance semantics in datalog programs.
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(AC)), 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(AC) can be exploited for effective problem-solving in a rich framework. This work is under consideration for acceptance in Theory and Practice of Logic Programming.