Adding the Relation Meets to the Temporal Logic of Prefixes and Infixes makes it EXPSPACE-Complete

TL;DR

This paper investigates the computational complexity of a specific interval temporal logic, showing that adding the 'Meets' relation to a known fragment increases its complexity to EXPSPACE-complete.

Contribution

It proves that incorporating the 'Meets' relation into the BD fragment of HS logic raises its satisfiability problem to EXPSPACE-complete, establishing a new complexity boundary.

Findings

Adding 'Meets' to BD makes the logic EXPSPACE-complete.

The complexity of HS fragments varies with added relations.

The result clarifies the trade-off between expressiveness and complexity.

Abstract

The choice of the right trade-off between expressiveness and complexity is the main issue in interval temporal logic. In their seminal paper, Halpern and Shoham showed that the satisfiability problem for HS (the temporal logic of Allen's relations) is highly undecidable over any reasonable class of linear orders. In order to recover decidability, one can restrict the set of temporal modalities and/or the class of models. In the following, we focus on the satisfiability problem for HS fragments under the homogeneity assumption, according to which any proposition letter holds over an interval if only if it holds at all its points. The problem for full HS with homogeneity has been shown to be non-elementarily decidable, but its only known lower bound is EXPSPACE (in fact, EXPSPACE-hardness has been shown for the logic of prefixes and suffixes BE, which is a very small fragment of it. The logic of prefixes and infixes BD has been recently shown to be PSPACE-complete. In this paper, we prove that the addition of the Allen relation Meets to BD makes it EXPSPACE-complete.