Tractable Fragments of Temporal Sequences of Topological Information

TL;DR

This paper investigates the computational complexity of qualitative topological temporal sequences, identifying tractable subclasses and proposing an alternative semantics for sequences of regions evolving over time.

Contribution

It introduces new tractable subclasses of topological temporal sequences and formalizes an alternative semantics for sequences of regions over time.

Findings

No Cartesian subclass contains all basic and universal relations for satisfiability.

Identified large tractable fragments by excluding certain relations.

Formalized an alternative semantics for temporal sequences of regions.

Abstract

In this paper, we focus on qualitative temporal sequences of topological information. We firstly consider the context of topological temporal sequences of length greater than 3 describing the evolution of regions at consecutive time points. We show that there is no Cartesian subclass containing all the basic relations and the universal relation for which the algebraic closure decides satisfiability. However, we identify some tractable subclasses, by giving up the relations containing the non-tangential proper part relation and not containing the tangential proper part relation. We then formalize an alternative semantics for temporal sequences. We place ourselves in the context of the topological temporal sequences describing the evolution of regions on a partition of time (i.e. an alternation of instants and intervals). In this context, we identify large tractable fragments.