KR2024Proceedings of the 21st International Conference on Principles of Knowledge Representation and ReasoningProceedings of the 21st International Conference on Principles of Knowledge Representation and Reasoning

Hanoi, Vietnam. November 2-8, 2024.

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ISSN: 2334-1033
ISBN: 978-1-956792-05-8

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Copyright © 2024 International Joint Conferences on Artificial Intelligence Organization

Reasoning in SHIQ with Axiom- and Concept-Level Standpoint Modalities

  1. Lucía Gómez Álvarez(Université Grenoble Alpes, Inria, CNRS, Grenoble INP, LIG, France)
  2. Sebastian Rudolph(Computational Logic Group, TU Dresden, Germany, Center for Scalable Data Analytics and Artificial Intelligence Dresden/Leipzig, Germany)

Keywords

  1. Description logics-General
  2. Ontologies and knowledge-enriched data management-General
  3. Reasoning about knowledge, beliefs, and other mental attitudes-General

Abstract

Standpoint logic is a recently proposed modal logic framework that is well-suited for multiperspective reasoning and ontology integration. For this reason, combinations of standpoint logic with description logics (DLs) are of special interest.

Prior work has shown that it is possible to add standpoints to numerous decidable fragments of first-order logics - including very expressive DLs up to SROIQbs - while preserving their reasoning complexity, so long as standpoint modalities are limited to the axiom level. A more expressive tighter modal integration, where standpoint modalities are also allowed to occur in concept expressions, has so far only been investigated for the much less expressive DL EL+.

In this paper, we push this line of research showing that the DL SHIQ allows for a tight modal integration with standpoints without compromising its ExpTime reasoning complexity. The core insight toward this result is that any satisfiable knowledge base admits a model with only polynomially many worlds, an argument which requires a rather elaborate model-theoretic construction. This allows us to establish a polynomial equisatisfiable translation into plain SHIQ which, beyond showing the theoretical result, enables us to use highly optimised OWL reasoners to provide practical reasoning support for ontology languages extended by standpoint modelling. We complement our findings with the observation that our techniques would fail upon adding the modelling feature of nominals to the underlying DL.