A Cookbook for Temporal Conceptual Data Modelling with Description Logics

TL;DR

This paper develops and analyzes temporal description logics for reasoning about temporal conceptual data models, balancing expressiveness and computational complexity, with practical implications for reasoning tools.

Contribution

It introduces new temporal description logics with various temporal operators and constraints, and characterizes their computational complexity, including decidability results and reductions to propositional temporal logic.

Findings

Most expressive logic is undecidable.

Restricted logics have complexity between PSpace and NLogSpace.

Reductions enable use of propositional temporal provers.

Abstract

We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging from atomic concept inclusions and disjointness to the full Booleans), as well as cardinality constraints and role inclusions. In the temporal dimension, they capture future and past temporal operators on concepts, flexible and rigid roles, the operators `always' and `some time' on roles, data assertions for particular moments of time and global concept inclusions. The logics are interpreted over the Cartesian products of object domains and the flow of time (Z,<), satisfying the constant domain assumption. We prove that the most expressive of our temporal description logics (which can capture lifespan cardinalities and either qualitative or quantitative evolution constraints) turn out to be undecidable. However, by omitting some of the temporal operators on concepts/roles or by restricting the form of concept inclusions we obtain logics whose complexity ranges between PSpace and NLogSpace. These positive results were obtained by reduction to various clausal fragments of propositional temporal logic, which opens a way to employ propositional or first-order temporal provers for reasoning about temporal data models.