Standpoint logic/Logique de point de vue in areas (2024-02-10)

Standpoint extensions of KR formalisms have been recently introduced to incorporate multi-perspective modelling and reasoning capabilities. In such modal extensions, the integration of conceptual modelling and perspective annotations can be more or less tight, with monodic standpoint extensions striking a good balance as they enable advanced modelling while preserving good reasoning complexities. We consider the extension of C2 — the counting two-variable fragment of first-order logic — by monodic standpoints. At the core of our treatise is a polytime translation of formulae in said formalism into standpoint-free C2, requiring elaborate model-theoretic arguments. By virtue of this translation, the NEXPTIME-complete complexity of checking satisfiability in C2 carries over to our formalism. As our formalism subsumes monodic S5 over C2, our result also significantly advances the state of the art in research on first-order modal logics. As a practical consequence, the very expressive description logics SHOIQBs and SROIQBs which subsume the popular W3C-standardized OWL 1 and OWL 2 ontology languages are shown to allow for monodic standpoint extensions without any increase of standard reasoning complexity. We prove that NEXPTIME-hardness already occurs in much less expressive DLs as long as they feature both nominals and monodic standpoints. We also show that, with inverses, functionality, and nominals present, minimally lifting the monodicity restriction leads to undecidability.

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), a popular family of logic-based ontology languages, 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 modeling feature of nominals to the underlying DL.