Little Engines of Proof [chapter]

Natarajan Shankar
2002 Lecture Notes in Computer Science  
The automated construction of mathematical proof is a basic activity in computing. Since the dawn of the field of automated reasoning, there have been two divergent schools of thought. One school, best represented by Alan Robinson's resolution method, is based on simple uniform proof search procedures guided by heuristics. The other school, pioneered by Hao Wang, argues for problem-specific combinations of decision and semi-decision procedures. While the former school has been dominant in the
more » ... st, the latter approach has greater promise. In recent years, several high quality inference engines have been developed, including propositional satisfiability solvers, ground decision procedures for equality and arithmetic, quantifier elimination procedures for integers and reals, and abstraction methods for finitely approximating problems over infinite domains. We describe some of these "little engines of proof" and a few of the ways in which they can be combined. We focus in particular on combining different decision procedures for use in automated verification. Its great triumph was to prove that the sum of two even numbers is even. Martin Davis [Dav83] (on his Presburger arithmetic procedure) The most interesting lesson from these results is perhaps that even in a fairly rich domain, the theorems actually proved are mostly ones which call on a very small portion of the available resources of the domain.
doi:10.1007/3-540-45614-7_1 fatcat:6my3fmm6xjb4vfj6sxly46xbxa