Transition Systems for Model Generators - A Unifying Approach

A fundamental task for propositional logic is to compute models of propositional formulas. Programs developed for this task are called satisfiability solvers. We show that transition systems introduced by Nieuwenhuis, Oliveras, and Tinelli to model and analyze satisfiability solvers can be adapted for solvers developed for two other propositional formalisms: logic programming under the answer-set semantics, and the logic PC(ID). We show that in each case the task of computing models can be seen as "satisfiability modulo answer-set programming," where the goal is to find a model of a theory that also is an answer set of a certain program. The unifying perspective we develop shows, in particular, that solvers CLASP and MINISATID are closely related despite being developed for different formalisms, one for answer-set programming and the latter for the logic PC(ID).