Ground Logic with Equality (GL) is a subset of First-Order Logic (FOL) in which functions or quantifiers are excluded, but equality is preserved. We argue about GL’s unique position (in terms of expressiveness and ease of decidability) between FOL and Propositional Logic (PL). We aim to solve satisfiability (SAT) problems formulated in GL by converting them into PL using a satisfiability-preser...

In this article we extend BDDs (binary decision diagrams) for plain propositional logic to the fragment of first order logic, consisting of quantifier free logic with equality, zero and successor. We insert equations with zero and successor in BDDs, and call these objects (0, S, =)-BDDs. We extend the notion of Ordered BDDs in the presence of equality, zero and successor. (0, S, =)-BDDs can be ...

Model Evolution is a lifted version of the propositional DPLL procedure for first-order logic with equality. This paper combines and extends the essentials of the latest Model Evolution variants with and without theory reasoning into a new calculus. The new calculus is described in detail. The main results reported here are the calculus’ completeness under (unavoidable) conditions, and its appl...

Suppose that T is an equational theory of groups or of rings. If T is finitely axiomatizable, then there is a least number μ so that T can be axiomatized by μ equations. This μ can depend on the operation symbols that occur in T . In the 1960’s, Alfred Tarski and Thomas C. Green completely determined the values of μ for arbitrary equational theories of groups and of rings. While Tarski and Gree...

Many applications of automated deduction require reasoning modulo backgroundtheories, in particular some form of integer arithmetic. Developing corresponding auto-mated reasoning systems that are also able to deal with quantified formulas has recentlybeen an active area of research. We contribute to this line of research and propose anovel instantiation-based method for a large ...