A flexible schema for generating explanations in lazy theory propagation

Theory propagation in Satisfiability Modulo Theories is crucial for the solver´s performance. It is important, however, to pay particular care to the amount of deductions to perform. The risk is in fact to clog the SAT-Solver with too many (and potentially useless clauses). In this paper we review some techniques for generating and communicating clauses to the SAT-Solver. In addition we propose a generic and flexible schema for theory propagation in which explanations for entailed facts are generated by re-using the consistency check procedure that is normally available in a theory solver. We argue that our schema can simplify the design of a theory solver, and allow a flexible form of theory propagation even for inherently hard theories (such as bit-vectors).