Conditional literals are an expressive Answer Set Programming language construct supported by the solver clingo. Their semantics are currently defined by a translation to infinitary propositional logic, however, we develop an alternative characterization with the SM operator which does not rely on grounding. This allows us to reason about the behavior of a broad class of clingo programs/encodings containing conditional literals, without referring to a particular input/instance of an encoding. We formalize the intuition that conditional literals behave as nested implications, and prove the equivalence of our semantics to those implemented by clingo.
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Axiomatization of Aggregates in Answer Set Programming
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.
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- Award ID(s):
- 1707371
- PAR ID:
- 10379361
- Date Published:
- Journal Name:
- Proceedings of the AAAI Conference on Artificial Intelligence
- Volume:
- 36
- Issue:
- 5
- ISSN:
- 2159-5399
- Page Range / eLocation ID:
- 5634 to 5641
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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