Decidability of the interval temporal logic ABBar over the natural numbers

TL;DR

This paper investigates the interval temporal logic ABBar over natural numbers, demonstrating its expressive power and establishing the decidability and complexity of its satisfiability problem.

Contribution

It introduces ABBar, proves its satisfiability is decidable via a novel contraction method, and shows the problem is EXPSPACE-complete.

Findings

ABBar can model various interval properties and point-based modalities.

Satisfiability for ABBar over natural numbers is decidable.

The problem is EXPSPACE-complete.

Abstract

In this paper, we focus our attention on the interval temporal logic of the Allen's relations "meets", "begins", and "begun by" (ABBar for short), interpreted over natural numbers. We first introduce the logic and we show that it is expressive enough to model distinctive interval properties,such as accomplishment conditions, to capture basic modalities of point-based temporal logic, such as the until operator, and to encode relevant metric constraints. Then, we prove that the satisfiability problem for ABBar over natural numbers is decidable by providing a small model theorem based on an original contraction method. Finally, we prove the EXPSPACE-completeness of the problem