Simplification: A General Constraint Propagation Technique for Propositional and Modal Tableaux

Tableau and sequent calculi are the basis for most popular interactive theorem provers for formal veriication. Yet, when it comes to automatic proof search, tableaux are often slower than Davis-Putnam, SAT procedures or other techniques. This is partly due to the absence of a bivalence principle (viz. the cut-rule) but there is another source of ineeciency: the lack of constraint propagation mechanisms. This paper proposes an innovation in this direction: the rule of simpli-cation, which plays for tableaux the role of subsumption for resolution and of unit for the Davis-Putnam procedure. The simplicity and generality of simpliication make possible its extension in a uniform way from propositional logic to a wide range of modal logics. This technique gives an unifying view of a number of tableaux-like calculi such as DPLL, KE, HARP, hyper-tableaux, BCP, KSAT. We show its practical impact with experimental results for random 3-SAT and the industrial IFIP benchmarks for hardware veriication.