Model Checking Linear Temporal Logic with Standpoint Modalities

TL;DR

This paper introduces a model checking approach for standpoint linear temporal logic ($SLTL$), extending classical $LTL$ with standpoint modalities, analyzing semantics variations, and establishing computational complexity results.

Contribution

It presents a general model checking algorithm for $SLTL$ under multiple semantics and analyzes its computational complexity, showing PSPACE-completeness in several cases.

Findings

Model checking $SLTL$ is feasible under various semantics.

Three semantics cases are PSPACE-complete.

$SLTL$ satisfiability remains EXPSPACE-complete.

Abstract

Standpoint linear temporal logic ($SLTL$) is a recently introduced extension of classical linear temporal logic ($LTL$) with standpoint modalities. Intuitively, these modalities allow to express that, from agent $a$'s standpoint, it is conceivable that a given formula holds. Besides the standard interpretation of the standpoint modalities we introduce four new semantics, which differ in the information an agent can extract from the history. We provide a general model checking algorithm applicable to $SLTL$ under any of the five semantics. Furthermore we analyze the computational complexity of the corresponding model checking problems, obtaining PSPACE-completeness in three cases, which stands in contrast to the known EXPSPACE-completeness of the $SLTL$ satisfiability problem.