Axiomatization of Aggregates in Answer Set Programming

Abstract

The paper presents a characterization of logic programs with aggregates based on many-sorted generalization of operator SM that refers neither to grounding nor to fixpoints. This characterization introduces new symbols for aggregate operations and aggregate elements, whose meaning is fixed by adding appropriate axioms to the result of the SM transformation. We prove that for programs without positive recursion through aggregates our semantics coincides with the semantics of the answer set solver Clingo.

External Behavior of a Logic Program and Verification of Refactoring

“…The proof assistant anthem-p2p can be used for verifying the correctness of refactoring an ASP program, and also for comparing alternative solutions to the same programming problem (for instance, in classroom teaching and in ASP programming contests). To make this tool more versatile, we plan to make it applicable to programs with aggregates, along the lines of recent publications (Fandinno et al 2022;Lifschitz 2022).…”

Splitting Answer Set Programs with Respect to Intensionality Statements

“…The Thirty-Seventh AAAI Conference on Artificial Intelligence such as arithmetic operations (Fandinno et al 2020;Lifschitz 2021) and aggregate expressions (Fandinno, Hansen, and Lierler 2022). We follow the presentation by Fandinno and Lifschitz (2022, Appendix A).…”

Strong Equivalence of Logic Programs with Counting

“…Fandinno et al . (2022) defined a translation similar to for an answer set programming language that is in some ways less expressive than mini- gringo with counting (no arithmetic operations), and in some ways more expressive (the aggregate is allowed, besides ). The main difference between that approach to transforming aggregate expressions into formulas and the one described above is that the former employs function symbols in the role that predicate symbols (19) play here.…”

“…This is apparently the reason why the adequacy of the translation due to Fandinno et al . is only guaranteed for programs without positive recursion through aggregates (Fandinno et al 2022, Theorem 3). This assumption is not satisfied, for instance, for program (4), (5).…”