Logical Reasoning

Representing time is crucial for cyber-physical systems and has been studied extensively in the situation calculus. The most commonly used approach represents time by adding a real-valued function $\mathit{time}(a)$ that attaches a time point to each action and consequently to each situation. We show that in this approach, checking whether there is a reachable situation that satisfies a given formula is undecidable, even when the domain contains only finitely many objects. We present an alternative approach based on well-established results from timed automata theory by introducing clocks as real-valued fluents with restricted successor state axioms and comparison operators. With this restriction, we can show that the reachability problem for finite-domain basic action theories is decidable. Finally, we apply our results to Golog program realization by presenting a decidable procedure for determining an action sequence that is a successful execution of a given program.

In this paper, we explore the issue of inconsistency handling over prioritized knowledge bases (KBs), which consist of an ontology, a set of facts, and a priority relation between conflicting facts. In the database setting, a closely related scenario has been studied and led to the definition of three different notions of optimal repairs (global, Pareto, and completion) of a prioritized inconsistent database. After transferring the notions of globally-, Pareto- and completion-optimal repairs to our setting, we study the data complexity of the core reasoning tasks: query entailment under inconsistency-tolerant semantics based upon optimal repairs, existence of a unique optimal repair, and enumeration of all optimal repairs. Our results provide a nearly complete picture of the data complexity of these tasks for ontologies formulated in common DL-Lite dialects. The second contribution of our work is to clarify the relationship between optimal repairs and different notions of extensions for (set-based) argumentation frameworks. Among our results, we show that Pareto-optimal repairs correspond precisely to stable extensions (and often also to preferred extensions), and we propose a novel semantics for prioritized KBs which is inspired by grounded extensions and enjoys favourable computational properties. Our study also yields some results of independent interest concerning preference-based argumentation frameworks.

Semantic reasoning aims to infer new knowledge from existing knowledge, with OWL ontologies serving as a standardized framework for organizing information. A key challenge in semantic reasoning is verifying ontology consistency. However, state-of-the-art reasoners are computationally expensive, and their efficiency decreases as ontology sizes grow. While classical machine learning models have been explored for consistency checking of A-Box axioms, considering T-Boxes remains unaddressed. Large language models (LLMs) have shown promising results for natural language inference but perform poorly on logical reasoning. The recently introduced Graph Language Model (GLM) offers a way to simultaneously process graph-structured data and text. This paper proposes GLaMoR (Graph Language Model for Reasoning), a reasoning pipeline that transforms OWL ontologies into graph-structured data and adapts the GLM architecture for consistency checking. We evaluate GLaMoR on ontologies from the NCBO BioPortal repository, converting them into triples suitable for model input. Our results show that the GLM outperforms all baseline models, achieving $95\%$ accuracy, and is $20$ times faster than classical reasoners.