A Functional View of Strong Negation in Answer Set Programming
This work provides a theoretical bridge for logic programming researchers, but it is incremental as it builds on existing semantics without introducing new paradigms.
The paper tackles the problem of integrating strong negation into answer set programming by proposing an alternative account that aligns it with functional stable model semantics, showing equivalence under complete interpretations and enabling computation using existing solvers.
The distinction between strong negation and default negation has been useful in answer set programming. We present an alternative account of strong negation, which lets us view strong negation in terms of the functional stable model semantics by Bartholomew and Lee. More specifically, we show that, under complete interpretations, minimizing both positive and negative literals in the traditional answer set semantics is essentially the same as ensuring the uniqueness of Boolean function values under the functional stable model semantics. The same account lets us view Lifschitz's two-valued logic programs as a special case of the functional stable model semantics. In addition, we show how non-Boolean intensional functions can be eliminated in favor of Boolean intensional functions, and furthermore can be represented using strong negation, which provides a way to compute the functional stable model semantics using existing ASP solvers. We also note that similar results hold with the functional stable model semantics by Cabalar.