An ASP semantics for Constraints involving Conditional Aggregates

• URL: http://arxiv.org/abs/2002.06911v2
• Date: Sat, 22 Feb 2020 15:37:28 GMT
• Title: An ASP semantics for Constraints involving Conditional Aggregates
• Authors: Pedro Cabalar and Jorge Fandinno and Torsten Schaub and Philipp Wanko
• Abstract summary: We elaborate upon the formal foundations of hybrid Answer Set Programming (ASP) We extend its underlying logical framework with aggregate functions over constraint values and variables. We put some emphasis on logic programs with linear constraints and show how common ASP aggregates can be regarded as particular cases of so-called conditional linear constraints.
• Score: 9.289905977910378
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We elaborate upon the formal foundations of hybrid Answer Set Programming (ASP) and extend its underlying logical framework with aggregate functions over constraint values and variables. This is achieved by introducing the construct of conditional expressions, which allow for considering two alternatives while evaluating constraints. Which alternative is considered is interpretation-dependent and chosen according to an associated condition. We put some emphasis on logic programs with linear constraints and show how common ASP aggregates can be regarded as particular cases of so-called conditional linear constraints. Finally, we introduce a polynomial-size, modular and faithful translation from our framework into regular (condition-free) Constraint ASP, outlining an implementation of conditional aggregates on top of existing hybrid ASP solvers.

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