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.

Highlights

  • Usual sequent calculi with cut rule are practically unusable in automated environment

  • One of the possibilities is constructing sequent calculi with an efficient loopcheck, or loop-check free calculi

  • In this paper we concentrate on the branching-time temporal logic with modal operators: ◦ (’’), A(φ ∪ ψ) (’in all futures until’) and E(φ ∪ ψ) (’in at least on future until’)

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Summary

Introduction

Usual sequent calculi with cut rule are practically unusable in automated environment. Sequent calculi with analytic cut, or infinitary rule, or some kind of the loop-check must be used to get a decision procedure. Such a sequent calculi are inefficient and need additional modifications to get more or less usable decision procedure. There is known sequent calculus for linear temporal logic with until which is cut free and invariant free sequent calculus [2]. Another cut free and invariant free sequent calculus for branching-time temporal logic with until operator may be find in [5] (as a special fragment of the presented sequent calculus for BDI logic) Both calculi requires loop-check to get decision procedure.

Birštunas
Restrictions for the loop-check
Conclusion
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