Foundations of Satisfiability Modulo Theories

Abstract

Satisfiability Modulo Theories (SMT) studies methods for checking the (un)- satisfiability of first-order formulas with respect to a given logical theory T . Distinguishing features of SMT, as opposed to traditional theorem proving, are that the background theory T need not be finitely or even first-order axiomatizable, and that specialized inference methods are used for each theory of interest. By being theory-specific and restricting their language to certain classes of formulas (such as, typically but not exclusively, quantifier-free formulas), these methods can be implemented into solvers that are more efficient in practice than general-purpose theorem provers.