Automated Synthesis of Tableau Calculi

This paper presents a method for synthesising sound and complete tableau calculi. Given a specification of the formal semantics of a logic, the method generates a set of tableau inference rules that can then be used to reason within the logic. The method guarantees that the generated rules form a calculus which is sound and constructively complete. If the logic can be shown to admit finite filtration with respect to a well-defined first-order semantics then adding a general blocking mechanism provides a terminating tableau calculus. The process of generating tableau rules can be completely automated and produces, together with the blocking mechanism, an automated procedure for generating tableau decision procedures. For illustration we show the workability of the approach for a description logic with transitive roles and propositional intuitionistic logic.Comment: 32 page

Practical Reasoning for Very Expressive Description Logics

Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm that decides satisfiability of the DL ALC extended with transitive and inverse roles and functional restrictions with respect to general concept inclusion axioms and role hierarchies; early experiments indicate that this algorithm is well-suited for implementation. Additionally, we show that ALC extended with just transitive and inverse roles is still in PSPACE. We investigate the limits of decidability for this family of DLs, showing that relaxing the constraints placed on the kinds of roles used in number restrictions leads to the undecidability of all inference problems. Finally, we describe a number of optimisation techniques that are crucial in obtaining implementations of the decision procedures, which, despite the worst-case complexity of the problem, exhibit good performance with real-life problems

A \textsf{C++} reasoner for the description logic \shdlssx (Extended Version)

We present an ongoing implementation of a \ke\space based reasoner for a decidable fragment of stratified elementary set theory expressing the description logic \dlssx (shortly \shdlssx). The reasoner checks the consistency of \shdlssx-knowledge bases (KBs) represented in set-theoretic terms. It is implemented in \textsf{C++} and supports \shdlssx-KBs serialized in the OWL/XML format. To the best of our knowledge, this is the first attempt to implement a reasoner for the consistency checking of a description logic represented via a fragment of set theory that can also classify standard OWL ontologies.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1702.03096, arXiv:1804.1122

Semantic metrics

In the context of the Semantic Web, many ontology-related operations, e.g. ontology ranking, segmentation, alignment, articulation, reuse, evaluation, can be boiled down to one fundamental operation: computing the similarity and?or dissimilarity among ontological entities, and in some cases among ontologies themselves. In this paper, we review standard metrics for computing distance measures and we propose a series of semantic metrics. We give a formal account of semantic metrics drawn from a variety of research disciplines, and enrich them with semantics based on standard Description Logic constructs. We argue that concept-based metrics can be aggregated to produce numeric distances at ontology-level and we speculate on the usability of our ideas through potential areas

What Do Definites Do That Indefinites Definitely Don't?

This paper investigates how (in)definiteness in word order; more specifically, how it in the ordering of objects in the Mittelfeld of German double-object constructions. As a starting point I take what I'll call the Indefinite Puzzle