Geoffrey D. Alexander

Proving Equality Theorems with Hyper-Linking

Hyper-linking is an instance-based refutation theorem proving strategy for first-order logic, recently developed by Lee and Plaisted[4]. An implementation of hyper-linking is the theorem prover CLIN[3]. We extend hyper-linking to support equality by using Brands E-modification[1]. We discuss how term rewriting is added to improve performance. We describe a number of other improvements, both in support of equality theorems and on-equality theorems.

Conditional Term Rewriting and First-Order Theorem Proving

We survey some basic issues in first-order theorem proving and their implications for conditional term-rewriting systems. In particular, we discuss the propositional efficiency of theorem proving strategies, goal-sensitivity, and the use of semantics. We give several recommendations for theorem proving strategies to enable them to properly treat these issues. Although few current theorem provers implement these recommendations, we discuss the clause linking theorem proving method and its extension to equality and semantics as examples of methods that satisfy most or all of our recommendations. Implicit induction theorem provers meet our recommendations, to some extent. We also discuss correctness and efficiency issues involved in the use of semantics in first-order theorem proving. Finally, we discuss issues of efficiency and semantics in conditional term-rewriting.