Axiom pinpointing has been introduced in description logics (DLs) to help the user to understand the reasons why consequences hold and to remove unwanted consequences by computing minimal (maximal) subsets of the knowledge base that have (do not have) the consequence in question. Most of the pinpointing algorithms described in the DLliterature are obtained as extensions of the standard tableau-based reasoning algorithms for computing consequences from DL knowledge bases. Although these extensions are based on similar ideas, they are all introduced for a particular tableau-based algorithm for a particular DL. The purpose of this article is to develop a general approach for extending a tableau-based algorithm to a pinpointing algorithm. This approach is based on a general definition of ‘tableau algorithms,’ which captures many of the known tableau-based algorithms employed in DLs, but also other kinds of reasoning procedures.

In recent years, there has been a growing interest in the application of foundational ontologies, i.e., formal ontological theories in the philosophical sense, to provide a theoretically sound foundation for improving the theory and practice of conceptual modeling and knowledge representation. This paper addresses one particular foundational theory of events termed UFO-B, which has been successfully employed as a reference model for addressing problems from complex media management, enterprise architecture, software engineering, and modeling of events in petroleum exploration. Despite its success, there is still no formalization of UFO-B in a decidable knowledge representation language that could support reasoning about complex events and event relations. We address this gap by proposing a number of alternative translations from UFO-B’s original axiomatization (in first-order logic and in the Alloy formal language) to the description logic SROIQ , which is the formal underpinning of OWL 2 DL. Additionally, to support practical applications, we translated these SROIQ theories to OWL 2 DL TBoxes, which were validated by showing that all the intended models of UFO-B (the logical models of the UFO-B specification in Alloy) that we generated are consistent with these UFO-B TBoxes. In a sense, the specification in Alloy implements the specification in first-order logic, while the OWL 2 TBoxes implement the SROIQ specifications. Incidentally, the methodology that we designed for the translation from UFO-B’s original axiomatization in FOL and Alloy to SROIQ came to be a key contribution of this work by providing us evidence of the inadequacy of DLs for the specification of comprehensive foundational ontologies.