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Weighted Logic is a powerful tool for the specification of calculations oversemirings that depend on qualitative information. Using a novel combination ofWeighted Logic and Here-and-There (HT) Logic, in which this dependence is basedon intuitionistic grounds, we introduce Answer Set Programming with AlgebraicConstraints (ASP(AC)), where rules may contain constraints that comparesemiring values to weighted formula evaluations. Such constraints providestreamlined access to a manifold of constructs available in ASP, likeaggregates, choice constraints, and arithmetic operators. They extend some ofthem and provide a generic framework for defining programs with algebraiccomputation, which can be fruitfully used e.g. for provenance semantics ofdatalog programs. While undecidable in general, expressive fragments of ASP(AC)can be exploited for effective problem-solving in a rich framework. This workis under consideration for acceptance in Theory and Practice of LogicProgramming.

ASP(AC): Answer Set Programming with Algebraic Constraints