Implementing Tableaux by Decision Diagrams

Binary Decision Diagrams (BDDs) are usually thought of as devices engineered specially for classical propositional logic. We show that we can build on one of their variants, Minato's zero-suppressed BDDs, to build compact data structures that encode whole tableaux. We call these structures tableaux decision diagrams (TDDs), and show how tableaux proof search is implemented in this framework. For this to be eecient, we have to restrict to canonical proof formats (in the sense of Galmiche et al.) to be able to take advantage of sharing in TDDs. Sharing is fundamental, not because it reduces memory consumption, but because it allows us to expand or close many tableaux paths in parallel, with corresponding gains in eeciency. We provide some empirical evidence that this is indeed eecient, by illustrating the method on a well-chosen system for propositional intuitionistic logic.