Parallel theorem proving

Abstract

This chapter surveys the research in parallel or distributed strategies for mechanical theorem proving in first-order logic, and explores some of its connections with the research in the parallelization of decision procedures for satisfiability in propositional logic (SAT). We clarify the key role played by the Clause-Diffusion methodology for distributed deduction in moving parallel reasoning from the parallelization of inferences to the parallelization of search, which is the dominating paradigm today. Since the quest for parallel first-order proof procedures has not been pursued recently, we endeavour to relate lessons learned from investigations of parallel theorem proving and parallel SAT-solving with novel advances in theorem proving, such as SGGS (Semantically-Guided Goal-Sensitive reasoning), a method that lifts the CDCL (Conflict-Driven Clause Learning) procedure for SAT to first-order logic.