Extending SROIQ with Constraint Networks and Grounded Circumscription

TL;DR

This paper extends the expressive power of the description logic SROIQ by integrating constraint networks and grounded circumscription, enabling more complex knowledge modeling for temporal, spatial, and defeasible reasoning.

Contribution

It introduces SROIQc and GC-SROIQ, providing formal syntax, semantics, and algorithms for constraint integration and grounded circumscription in expressive description logics.

Findings

Developed a sound, complete, and terminating tableau algorithm for SROIQc.

Designed an intuitive algorithm for grounded circumscription applicable to various logics.

Enhanced modeling capabilities for temporal, spatial, and defeasible reasoning in ontologies.

Abstract

Developments in semantic web technologies have promoted ontological encoding of knowledge from diverse domains. However, modelling many practical domains requires more expressiveness than what the standard description logics (most prominently SROIQ) support. In this paper, we extend the expressive DL SROIQ with constraint networks (resulting in the logic SROIQc) and grounded circumscription (resulting in the logic GC-SROIQ). Applications of constraint modelling include embedding ontologies with temporal or spatial information, while those of grounded circumscription include defeasible inference and closed world reasoning. We describe the syntax and semantics of the logic formed by including constraint modelling constructs in SROIQ, and provide a sound, complete and terminating tableau algorithm for it. We further provide an intuitive algorithm for Grounded Circumscription in SROIQc, which adheres to the general framework of grounded circumscription, and which can be applied to a whole range of expressive logics for which no such specific algorithm presently exists.