Unification is a fundamental process upon which many methods for automated deduction
are based. Unification theory abstracts from the specific applications of this process: it …

The aim of this chapter is to review the fundamental techniques in paramodulationbased
theorem proving, presenting them in a uniform framework. We start with easier subcases …

Deduction methods for first-order constrained clauses with equality are described within an
abstract framework: constraint strategies, consisting of an inference system, a constraint …

Equational reasoning is fundamental in mathematics, logics, and many applications of
formal methods in computer science. In this chapter we describe the theoretical concepts …

Solving equations in the free algebra T (F, X)(ie, unification) uses the two rules: ƒ (s)= ƒ (t)→
s= t (decomposition) and s [x]= x→⊥(occur-check). These two rules are not correct in …

We define equality constrained equations and clauses and use them to prove the
completeness of what we have called basic superposition: a restricted form of superposition …

In an overlay wireless network, a mobile user can connect to different radio access networks
if it is equipped with appropriate network interfaces. When the mobile user changes its …

The height of a piecewise-testable language L is the maximum length of the words needed
to define L by excluding and requiring given subwords. The height of L is an important …

We consider a constrained equational logic where the constraints are membership
conditions t∈ swheresis interpreted as a regular tree language. Our logic includes a …

In the context of combinations of theories with disjoint signatures, we classify the component
theories according to the decidability of constraint satisfiability problems in arbitrary and in …