Loop-free verification of termination of derivation for a fragment of dynamic logic

Regimantas Pliuškevičius

doi:10.15388/lmr.2008.18111

Abstract

A fragment of a deterministic propositional dynamic logic (DPDL, in short) is considered The language of considered fragment contains propositional symbols, action constants, action operator (repetition) and logical symbols. For safety fragment of considered DPDL a loop-check-free sequent calculus with invertible rules is presented.

Highlights

In the paper deterministic propositional dynamic logic (DP DL, in short) is considered
DP DL is a generalization of propositional linear temporal logic (P LT L, in short)
An initial sequent calculus GDP DL for considered DP DL is defined by the following postulates: Axiom:, A →, A

Summary

Introduction

In the paper deterministic propositional dynamic logic (DP DL, in short) is considered. DP DL is a generalization of propositional linear temporal logic (P LT L, in short). It is well known (see, e.g., [3], [4]) that with the aim to get termination of derivations in sequent (or tableaux) calculus for DP DL “good loops” (related with induction-like rules) and “bad loops” (related with induction-free parts of derivations) are used. Instead of both types of loop checking special “final” sequents are used. These “final” sequents allow us to verify a termination of derivations without loop checking

Initial sequent calculus for DP DL

Elimination of loop-check for fragment of DP DL