From Search to Computation: Redundancy Criteria and Simplification at Work

The concept of redundancy and simplification has been an ongoing theme in Harald Ganzinger’s work from his first contributions to equational completion to the various variants of the superposition calculus. When executed by a theorem prover, the inference rules of logic calculi usually generate a tremendously huge search space. The redundancy and simplification concept is indispensable for cutting down this search space to a manageable size. For a number of subclasses of firstorder logic appropriate redundancy and simplification concepts even turn the superposition calculus into a decision procedure. Hence, the key to successfully applying first-order theorem proving to a problem domain is to find those simplifications and redundancy criteria that fit this domain and can be effectively implemented. We present Harald Ganzinger’s work in the light of the simplification and redundancy techniques that have been developed for concrete problem areas. This includes a variant of contextual rewriting to decide a subclass of Euclidean geometry, ordered chaining techniques for Church-Rosser and priority queue proofs, contextual rewriting and history-dependent complexities for the completion of conditional rewrite systems, rewriting with equivalences for theorem proving in set theory, soft typing for the exploration of sort information in the context of equations, and constraint inheritance for automated complexity analysis.