Restrictions for loop-check in sequent calculus for temporal logic with until operator

Abstract

In this paper, we present sequent calculus for branching-time temporal logic with until operator. This sequent calculus uses efficient loop-checktechinque. We prove that we can use not all but only several special sequents from the derivation tree for the loop-check. We use indexes to discover these special sequents in the sequent calculus. These restrictions let us to get efficient decision procedure based on introduced sequent calculus.

Keywords

• sequent calculus
• branchnig-time temporal logic
• until operator
• loop-check