Unification in the Description Logic EL

The Description Logic EL has recently drawn considerable attention since, on the one hand, important inference problems such as the subsumption problem are polynomial. On the other hand, EL is used to define large biomedical ontologies. Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. The main result of this paper is that unification in EL is decidable. More precisely, EL-unification is NP-complete, and thus has the same complexity as EL-matching. We also show that, w.r.t. the unification type, EL is less well-behaved: it is of type zero, which in particular implies that there are unification problems that have no finite complete set of unifiers.Comment: 31page

Integrating Ontologies and Relational Data

In recent years, an increasing number of scientific and other domains have attempted to standardize their terminology and provide reasoning capabilities through ontologies, in order to facilitate data exchange. This has spurred research into Web-based languages, formalisms, and especially query systems based on ontologies. Yet we argue that DBMS techniques can be extended to provide many of the same capabilities, with benefits in scalability and performance. We present OWLDB, a lightweight and extensible approach for the integration of relational databases and description logic based ontologies. One of the key differences between relational databases and ontologies is the high degree of implicit information contained in ontologies. OWLDB integrates the two schemes by codifying ontologies\u27 implicit information using a set of sound and complete inference rules for SHOIN (the description logic behind OWL ontologies. These inference rules can be translated into queries on a relational DBMS instance, and the query results (representing inferences) can be added back to this database. Subsequently, database applications can make direct use of this inferred, previously implicit knowledge, e.g., in the annotation of biomedical databases. As our experimental comparison to a native description logic reasoner and a triple store shows, OWLDB provides significantly greater scalability and query capabilities, without sacrifcing performance with respect to inference

Business Process Retrieval Based on Behavioral Semantics

This paper develops a framework for retrieving business processes considering search requirements based on behavioral semantics properties; it presents a framework called "BeMantics" for retrieving business processes based on structural, linguistics, and behavioral semantics properties. The relevance of the framework is evaluated retrieving business processes from a repository, and collecting a set of relevant business processes manually issued by human judges. The "BeMantics" framework scored high precision values (0.717) but low recall values (0.558), which implies that even when the framework avoided false negatives, it prone to false positives. The highest pre- cision value was scored in the linguistic criterion showing that using semantic inference in the tasks comparison allowed to reduce around 23.6 % the number of false positives. Using semantic inference to compare tasks of business processes can improve the precision; but if the ontologies are from narrow and specific domains, they limit the semantic expressiveness obtained with ontologies from more general domains. Regarding the perform- ance, it can be improved by using a filter phase which indexes business processes taking into account behavioral semantics propertie

Symbolic modeling of structural relationships in the Foundational Model of Anatomy

The need for a sharable resource that can provide deep anatomical knowledge and support inference for biomedical applications has recently been the driving force in the creation of biomedical ontologies. Previous attempts at the symbolic representation of anatomical relationships necessary for such ontologies have been largely limited to general partonomy and class subsumption. We propose an ontology of anatomical relationships beyond class assignments and generic part-whole relations and illustrate the inheritance of structural attributes in the Digital Anatomist Foundational Model of Anatomy. Our purpose is to generate a symbolic model that accommodates all structural relationships and physical properties required to comprehensively and explicitly describe the physical organization of the human body

Language Model Analysis for Ontology Subsumption Inference

Pre-trained language models (LMs) have made significant advances in various Natural Language Processing (NLP) domains, but it is unclear to what extent they can infer formal semantics in ontologies, which are often used to represent conceptual knowledge and serve as the schema of data graphs. To investigate an LM's knowledge of ontologies, we propose OntoLAMA, a set of inference-based probing tasks and datasets from ontology subsumption axioms involving both atomic and complex concepts. We conduct extensive experiments on ontologies of different domains and scales, and our results demonstrate that LMs encode relatively less background knowledge of Subsumption Inference (SI) than traditional Natural Language Inference (NLI) but can improve on SI significantly when a small number of samples are given. We will open-source our code and datasets

Reasoning with concept diagrams about antipatterns

Ontologies are notoriously hard to define, express and reason about. Many tools have been developed to ease the debugging and the reasoning process with ontologies, however they often lack accessibility and formalisation. A visual representation language, concept diagrams, was developed for expressing and reasoning about ontologies in an accessible way. Indeed, empirical studies show that concept diagrams are cognitively more accessible to users in ontology debugging tasks. In this paper we answer the question of “ How can concept diagrams be used to reason about inconsistencies and incoherence of ontologies?”. We do so by formalising a set of inference rules for concept diagrams that enables stepwise verification of the inconsistency and/or incoherence of a set of ontology axioms. The design of inference rules is driven by empirical evidence that concise (merged) diagrams are easier to comprehend for users than a set of lower level diagrams that offer a one-to-one translation of OWL ontology axioms into concept diagrams. We prove that our inference rules are sound, and exemplify how they can be used to reason about inconsistencies and incoherence. Finally, we indicate how our rules can serve as a foundation for new rules required when representing ontologies in diverse new domains

Knowledge Representation with Ontologies: The Present and Future

Recently, we have seen an explosion of interest in ontologies as artifacts to represent human knowledge and as critical components in knowledge management, the semantic Web, business-to-business applications, and several other application areas. Various research communities commonly assume that ontologies are the appropriate modeling structure for representing knowledge. However, little discussion has occurred regarding the actual range of knowledge an ontology can successfully represent

Evaluating Knowledge Representation and Reasoning Capabilites of Ontology Specification Languages

The interchange of ontologies across the World Wide Web (WWW) and the cooperation among heterogeneous agents placed on it is the main reason for the development of a new set of ontology specification languages, based on new web standards such as XML or RDF. These languages (SHOE, XOL, RDF, OIL, etc) aim to represent the knowledge contained in an ontology in a simple and human-readable way, as well as allow for the interchange of ontologies across the web. In this paper, we establish a common framework to compare the expressiveness of "traditional" ontology languages (Ontolingua, OKBC, OCML, FLogic, LOOM) and "web-based" ontology languages. As a result of this study, we conclude that different needs in KR and reasoning may exist in the building of an ontology-based application, and these needs must be evaluated in order to choose the most suitable ontology language(s)