Two New Definitions of Stable Models of Logic Programs with Generalized Quantifiers
This work addresses foundational issues in logic programming semantics, but it appears incremental as it builds on existing stable model theories without introducing a new paradigm.
The paper tackles the problem of defining stable model semantics for logic programs with generalized quantifiers by proposing two alternative definitions based on reducts and an operator similar to the SM operator, and shows that these semantics are interchangeable for a reasonable syntactic class of programs.
We present alternative definitions of the first-order stable model semantics and its extension to incorporate generalized quantifiers by referring to the familiar notion of a reduct instead of referring to the SM operator in the original definitions. Also, we extend the FLP stable model semantics to allow generalized quantifiers by referring to an operator that is similar to the $\sm$ operator. For a reasonable syntactic class of logic programs, we show that the two stable model semantics of generalized quantifiers are interchangeable.