Tight Integration of Non-Ground Answer Set Programming and Satisfiability Modulo Theories

Non-Boolean variables are important primitives in logical modeling. For instance, in Answer Set Programming (ASP), they are used as place holders for constants and more complex ground terms. This is essential for compact and uniform encodings used in ASP although variables are removed in a grounding phase preceding the search for answer sets. On the other hand, in theories in the Satisfiability Modulo Theories (SMT) framework, variables are realized as constants that have a free interpretation over a specific domain such as integers or reals. The goal of this paper is to propose an approach to integrating the languages employed in ASP and SMT so that non-Boolean variables of the kinds above can appear in the same program. The resulting formalism ASP(SMT) is rule-based and extended by theory atoms from SMT dialects. We illustrate the use of the new language and its advantages from the modeling perspective. Moreover, we show how existing off-the-shelf ASP and SMT technology can be used to implement grounding and search for answer sets for this class of programs.