Soundness and Completeness of a Model-Checking Proof System for CTL

TL;DR

This paper introduces a local model-checking proof system for a fragment of CTL, ensuring soundness, completeness, and termination for finite-state models by using tagged sequents.

Contribution

It presents a novel proof system for CTL model checking that guarantees termination and correctness through state tagging and fixed-point based rules.

Findings

Proof system is sound and complete.

Proof search terminates for finite models.

Uses tagged sequents to ensure termination.

Abstract

We propose a local model-checking proof system for a fragment of CTL. The rules of the proof system are motivated by the well-known fixed-point characterisation of CTL based on unfolding of the temporal operators. To guarantee termination of proofs, we tag the sequents of our proof system with the set of states that have already been explored for the respective temporal formula. We define the semantics of tagged sequents, and then state and prove soundness and completeness of the proof system, as well as termination of proof search for finite-state models.