Equality elimination for the inverse method and extension procedures

We demonstrate how to handle equality in the inverse method using equality elimination. In the equality elimination method, proofs consist of two parts. In the first part we try to solve equations obtaining so called solution clauses. Solution clauses are obtained by a very refined strategy — basic superposition with selection function. In the second part, we perform the usual sequent proof search by the inverse method. Our approach is called equality elimination because we eliminate all occurrences of equality in the first part of the proof. Unlike the previous approach proposed by Maslov, our method uses most general substitutions, orderin

Visualizing Abduction

info:eu-repo/semantics/publishedVersio

A theory of resolution

We review the fundamental resolution-based methods for first-order theorem proving and present them in a uniform framework. We show that these calculi can be viewed as specializations of non-clausal resolution with simplification. Simplification techniques are justified with the help of a rather general notion of redundancy for inferences. As simplification and other techniques for the elimination of redundancy are indispensable for an acceptable behaviour of any practical theorem prover this work is the first uniform treatment of resolution-like techniques in which the avoidance of redundant computations attains the attention it deserves. In many cases our presentation of a resolution method will indicate new ways of how to improve the method over what was known previously. We also give answers to several open problems in the area