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 ...

Formal specification language and deduction system for object-oriented models is proposed in this article. It extends ς-calculus introduced by Martín Abadi and Luca Cardelli with propositional connectives, and quantified terms. The first-order type system of ς-calculus serves as typing theory of suggested calculus. Deduction system consists of reduction rules of ς-terms, equality theory of ς-ca...

Many applications of automated deduction require reasoning modulo background theories, in particular some form of integer arithmetic. Developing corresponding automated reasoning systems that are also able to deal with quantified formulas has recently been an active area of research. We contribute to this line of research and propose a novel instantiation-based method for a large fragment of fi...

The logic of equality with uninterpreted functions (EUF) has been proposed for verifying abstract hardware designs. Fast satisfiability checking over this logic is important for such verification to be successful. Our algorithm is based on the Davis-Putman-Logemann-Loveland (DPLL) procedure, one of the most effective methods to check propositional satisfiability. The DPLL procedure returns a sa...