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Researcher profile

Michael Bartholomew

Michael Bartholomew contributes to research discovery and scholarly infrastructure.

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Artificial Intelligence

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Published work

2 published item(s)

preprint2026arXiv

Functional Stable Model Semantics and Answer Set Programming Modulo Theories

Recently there has been an increasing interest in incorporating ``intensional'' functions in answer set programming. Intensional functions are those whose values can be described by other functions and predicates, rather than being pre-defined as in the standard answer set programming. We demonstrate that the functional stable model semantics plays an important role in the framework of ``Answer Set Programming Modulo Theories (ASPMT)'' -- a tight integration of answer set programming and satisfiability modulo theories, under which existing integration approaches can be viewed as special cases where the role of functions is limited. We show that ``tight'' ASPMT programs can be translated into SMT instances, which is similar to the known relationship between ASP and SAT.

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preprint2013arXiv

A Functional View of Strong Negation in Answer Set Programming

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.

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