CTL-RP: A computation tree logic resolution prover

Abstract

In this paper, we present a resolution-based calculus R_CTL^>,S for Computation Tree Logic (CTL) as well as an implementation of that calculus in the theorem prover CTL-RP. The calculus R_CTL^>,S requires a transformation of an arbitrary CTL formula to an equi-satisfiable clausal normal form formulated in an extension of CTL with indexed path formulae. The calculus itself consists of a set of resolution rules which can be used for an EXPTIME decision procedure for the satisfiability problem of CTL. We give a formal semantics for the clausal normal form, provide proof sketches for the soundness and completeness of the resolution rules, discuss the complexity of the decision procedure based on R_CTL^>,S, and present an approach to implementing the calculus R_CTL^>,S using first-order techniques. Finally, we give a comparison between CTL-RP and a tableau theorem prover for CTL.