A Neutrosophic Description Logic

Description Logics (DLs) are appropriate, widely used, logics for managing structured knowledge. They allow reasoning about individuals and concepts, i.e. set of individuals with common properties. Typically, DLs are limited to dealing with crisp, well defined concepts. That is, concepts for which the problem whether an individual is an instance of it is yes/no question. More often than not, the concepts encountered in the real world do not have a precisely defined criteria of membership: we may say that an individual is an instance of a concept only to a certain degree, depending on the individual's properties. The DLs that deal with such fuzzy concepts are called fuzzy DLs. In order to deal with fuzzy, incomplete, indeterminate and inconsistent concepts, we need to extend the fuzzy DLs, combining the neutrosophic logic with a classical DL. In particular, concepts become neutrosophic (here neutrosophic means fuzzy, incomplete, indeterminate, and inconsistent), thus reasoning about neutrosophic concepts is supported. We'll define its syntax, its semantics, and describe its properties.Comment: 18 pages. Presented at the IEEE International Conference on Granular Computing, Georgia State University, Atlanta, USA, May 200

The Complexity of Satisfiability for Sub-Boolean Fragments of ALC

The standard reasoning problem, concept satisfiability, in the basic description logic ALC is PSPACE-complete, and it is EXPTIME-complete in the presence of unrestricted axioms. Several fragments of ALC, notably logics in the FL, EL, and DL-Lite family, have an easier satisfiability problem; sometimes it is even tractable. All these fragments restrict the use of Boolean operators in one way or another. We look at systematic and more general restrictions of the Boolean operators and establish the complexity of the concept satisfiability problem in the presence of axioms. We separate tractable from intractable cases.Comment: 17 pages, accepted (in short version) to Description Logic Workshop 201

On the similarity relation within fuzzy ontology components

Ontology reuse is an important research issue. Ontology merging, integration, mapping, alignment and versioning are some of its subprocesses. A considerable research work has been conducted on them. One common issue to these subprocesses is the problem of defining similarity relations among ontologies components. Crisp ontologies become less suitable in all domains in which the concepts to be represented have vague, uncertain and imprecise definitions. Fuzzy ontologies are developed to cope with these aspects. They are equally concerned with the problem of ontology reuse. Defining similarity relations within fuzzy context may be realized basing on the linguistic similarity among ontologies components or may be deduced from their intentional definitions. The latter approach needs to be dealt with differently in crisp and fuzzy ontologies. This is the scope of this paper.ou

Cognitive context and arguments from ontologies for learning

The deployment of learning resources on the web by different experts has resulted in the accessibility of multiple viewpoints about the same topics. In this work we assume that learning resources are underpinned by ontologies. Different formalizations of domains may result from different contexts, different use of terminology, incomplete knowledge or conflicting knowledge. We define the notion of cognitive learning context which describes the cognitive context of an agent who refers to multiple and possibly inconsistent ontologies to determine the truth of a proposition. In particular we describe the cognitive states of ambiguity and inconsistency resulting from incomplete and conflicting ontologies respectively. Conflicts between ontologies can be identified through the derivation of conflicting arguments about a particular point of view. Arguments can be used to detect inconsistencies between ontologies. They can also be used in a dialogue between a human learner and a software tutor in order to enable the learner to justify her views and detect inconsistencies between her beliefs and the tutor’s own. Two types of arguments are discussed, namely: arguments inferred directly from taxonomic relations between concepts, and arguments about the necessary an

A hybrid approach for modeling uncertainty in terminological logics

This paper proposes a probabilistic extension of terminological logics. The extension maintains the original performance of drawing inferences in a hierarchy of terminological definitions. It enlarges the range of applicability to real world domains determined not only by definitional but also by uncertain knowledge. First, we introduce the propositionally complete terminological language ALC. On the basis of the language construct "probabilistic implication" it is shown how statistical information on concept dependencies can be represented. To guarantee (terminological and probabilistic) consistency, several requirements have to be met. Moreover, these requirements allow one to infer implicitly existent probabilistic relationships and their quantitative computation. By explicitly introducing restrictions for the ranges derived by instantiating the consistency requirements, exceptions can also be handled. In the categorical cases this corresponds to the overriding of properties in non monotonic inheritance networks. Consequently, our model applies to domains where both term descriptions and non-categorical relations between term extensions have to be represented