A survey of current, stand-alone OWL Reasoners

Abstract. We present a survey of the current OWL reasoner landscape. Through literature and web search we have identified 35 OWL reasoners that are, at least to some degree, actively maintained. We conducted a survey directly addressing the respective developers, and collected 33 responses. We present an analysis of the survey, characterising all reasoners across a wide range of categories such as supported expressiveness and reasoning services. We will also provide some insight about ongoing research efforts and a rough categorisation of reasoner calculi

Towards Ranking Geometric Automated Theorem Provers

The field of geometric automated theorem provers has a long and rich history, from the early AI approaches of the 1960s, synthetic provers, to today algebraic and synthetic provers. The geometry automated deduction area differs from other areas by the strong connection between the axiomatic theories and its standard models. In many cases the geometric constructions are used to establish the theorems' statements, geometric constructions are, in some provers, used to conduct the proof, used as counter-examples to close some branches of the automatic proof. Synthetic geometry proofs are done using geometric properties, proofs that can have a visual counterpart in the supporting geometric construction. With the growing use of geometry automatic deduction tools as applications in other areas, e.g. in education, the need to evaluate them, using different criteria, is felt. Establishing a ranking among geometric automated theorem provers will be useful for the improvement of the current methods/implementations. Improvements could concern wider scope, better efficiency, proof readability and proof reliability. To achieve the goal of being able to compare geometric automated theorem provers a common test bench is needed: a common language to describe the geometric problems; a comprehensive repository of geometric problems and a set of quality measures.Comment: In Proceedings ThEdu'18, arXiv:1903.1240

Vitro - ein universell einsetzbarer Editor für Ontologien und Instanzen

In diesem Artikel wird die Open-Source-Software Vitro beschrieben. Vitro ist ein universeller Instanz- und Ontologie-Editor, der hauptsächlich von der VIVO-Community entwickelt und gepflegt wird. Es wird ein Überblick über die Hauptmerkmale der Software geschaffen. Dann werden verschiedene Anwendungen der Software beispielhaft erläutert. Der Artikel schließt mit einem Ausblick auf zukünftige Anwendungsfälle und Entwicklungen von Vitro

Scavenger 0.1: A Theorem Prover Based on Conflict Resolution

This paper introduces Scavenger, the first theorem prover for pure first-order logic without equality based on the new conflict resolution calculus. Conflict resolution has a restricted resolution inference rule that resembles (a first-order generalization of) unit propagation as well as a rule for assuming decision literals and a rule for deriving new clauses by (a first-order generalization of) conflict-driven clause learning.Comment: Published at CADE 201

XQOWL: An Extension of XQuery for OWL Querying and Reasoning

One of the main aims of the so-called Web of Data is to be able to handle heterogeneous resources where data can be expressed in either XML or RDF. The design of programming languages able to handle both XML and RDF data is a key target in this context. In this paper we present a framework called XQOWL that makes possible to handle XML and RDF/OWL data with XQuery. XQOWL can be considered as an extension of the XQuery language that connects XQuery with SPARQL and OWL reasoners. XQOWL embeds SPARQL queries (via Jena SPARQL engine) in XQuery and enables to make calls to OWL reasoners (HermiT, Pellet and FaCT++) from XQuery. It permits to combine queries against XML and RDF/OWL resources as well as to reason with RDF/OWL data. Therefore input data can be either XML or RDF/OWL and output data can be formatted in XML (also using RDF/OWL XML serialization).Comment: In Proceedings PROLE 2014, arXiv:1501.0169

Consistency and Completeness of Rewriting in the Calculus of Constructions

Adding rewriting to a proof assistant based on the Curry-Howard isomorphism, such as Coq, may greatly improve usability of the tool. Unfortunately adding an arbitrary set of rewrite rules may render the underlying formal system undecidable and inconsistent. While ways to ensure termination and confluence, and hence decidability of type-checking, have already been studied to some extent, logical consistency has got little attention so far. In this paper we show that consistency is a consequence of canonicity, which in turn follows from the assumption that all functions defined by rewrite rules are complete. We provide a sound and terminating, but necessarily incomplete algorithm to verify this property. The algorithm accepts all definitions that follow dependent pattern matching schemes presented by Coquand and studied by McBride in his PhD thesis. It also accepts many definitions by rewriting, containing rules which depart from standard pattern matching.Comment: 20 page

A Framework for Reasoning on Probabilistic Description Logics

While there exist several reasoners for Description Logics, very few of them can cope with uncertainty. BUNDLE is an inference framework that can exploit several OWL (non-probabilistic) reasoners to perform inference over Probabilistic Description Logics. In this chapter, we report the latest advances implemented in BUNDLE. In particular, BUNDLE can now interface with the reasoners of the TRILL system, thus providing a uniform method to execute probabilistic queries using different settings. BUNDLE can be easily extended and can be used either as a standalone desktop application or as a library in OWL API-based applications that need to reason over Probabilistic Description Logics. The reasoning performance heavily depends on the reasoner and method used to compute the probability. We provide a comparison of the different reasoning settings on several datasets

Formalising Mathematics in Simple Type Theory

Despite the considerable interest in new dependent type theories, simple type theory (which dates from 1940) is sufficient to formalise serious topics in mathematics. This point is seen by examining formal proofs of a theorem about stereographic projections. A formalisation using the HOL Light proof assistant is contrasted with one using Isabelle/HOL. Harrison's technique for formalising Euclidean spaces is contrasted with an approach using Isabelle/HOL's axiomatic type classes. However, every formal system can be outgrown, and mathematics should be formalised with a view that it will eventually migrate to a new formalism