Fuzzy ontology based knowledge reasoning framework design

Reasoning within expressive fuzzy rough description logics

Bipolarity is an important feature of spatial information, involved in the expression of preferences and constraints about spatial positioning or in pairs of opposite spatial relations such as left and right. Another important feature is imprecision which has to be taken into account to model vagueness, inherent to many spatial relations (as for instance vague expressions such as close to, to the right of), and to gain in robustness in the representations. In previous works, we have shown that fuzzy sets and fuzzy mathematical morphology are appropriate frameworks, on the one hand, to represent bipolarity and imprecision of spatial relations and, on the other hand, to combine qualitative and quantitative reasoning in description logics extended with fuzzy concrete domains. The purpose of this paper is to integrate the bipolarity feature in the latter logical framework based on bipolar and fuzzy mathematical morphology and description logics with fuzzy concrete domains. Two important issues are addressed in this paper: the modeling of the bipolarity of spatial relations at the terminological level and the integration of bipolar notions in fuzzy description logics. At last, we illustrate the potential of the proposed formalism for spatial reasoning on a simple example in brain imaging.

Classical Description Logics (DLs) are not suitable to represent vague pieces of information. The attempts to achieve a solution have lead to the birth of fuzzy DLs and rough DLs. In this work, we provide a simple solution to join these two formalisms and define a fuzzy rough DL. We also show how to extend two reasoning algorithms for fuzzy DLs, which are implemented in the fuzzy DL reasoners fuzzyDL and DeLorean.KeywordsDescription LogicVague ConceptReasoning AlgorithmIndiscernibility RelationLukasiewicz LogicThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Consistency reasoning in lattice-based fuzzy Description Logics

Significant research efforts in the Semantic Web community are recently directed toward the representation and reasoning with fuzzy ontologies. As the theoretical counterpart of fuzzy ontology languages, fuzzy Description Logics (DLs) have attracted a wide range of concerns. With the emergence of a great number of large-scale domain ontologies, the basic reasoning services cannot meet the need of dealing with complex queries (mainly conjunctive queries), which are indispensable in data-intensive applications. Conjunctive queries (CQs), originated from relational databases, play an important role as an expressive reasoning service for ontologies. Since, however, the negation of a role atom in a CQ is not expressible as a part of a knowledge base, existing tableau algorithms cannot be used directly to deal with the issue. In this paper, we thus present a tableau-based algorithm for deciding query entailment of fuzzy conjunctive queries w.r.t. fuzzy \(\mathcal{SHIN}\) ontologies. Moreover, the data complexity problem was still open for answering CQs in expressive fuzzy DLs. We tackle this issue by proving a tight coNP upper bound for the problem in f-\(\mathcal{SHIN}\), as long as only simple roles occur in the query. Regarding combined complexity, we prove that the algorithm for query entailment is co3NExpTime in the size of the knowledge base and the query.

Fuzzy Description Logics are logics which allow to deal with structured knowledge affected by vagueness. Although a relatively important amount of work has been carried out in the last years, fuzzy DLs are open to be extended with several features worked out in the fuzzy logic literature. In this work, we extend fuzzy DLs towards supporting fuzzy spatial reasoning and, thus, offer a framework for modeling spatial relations such as "region a is part of region b, which is connected to region c, a is close to c and b is right over c".

Ontologies represent a method of formally expressing a shared understanding of information, and have paved the way for sharing concepts across applications in an unambiguous way. However, these ontologies are assumed to be hand-crafted, pre-defined structures with crisp concept descriptions and inter-concept relations. Crisp definitions however are not sufficient for real-world applications like ontology-based information extraction from unstructured text. In this paper we propose an enhancement of the ontology structure to a fuzzy ontology, which provides a mechanism to store imprecise concept definitions. The proposed fuzzy ontology framework can also help in ascertaining similarities and dissimilarities of concept definitions across distributed ontologies representing the same domain. Our design of fuzzy ontology is motivated by fuzzy set theoretic representation and reasoning, and is entirely different from other fuzzy ontology designs, which use only co-occurrence of concepts to determine their closeness. We have cited examples from various domains to show the necessity and capability of the structure in representing real-world knowledge.

To satisfy the need of representing and reasoning with fuzzy knowledge and fuzzy data information in the context of the Semantic Web, an expressive fuzzy Description Logic (DL) named f-SROIQ(G) is proposed in this paper. The fuzzy DL f-SROIQ(G) can support not only the representation and reasoning of complex fuzzy OWL 2 concept knowledge, but also fuzzy data information with customized fuzzy data types and predicates. Briefly, the paper makes the following main contributions: (i) we propose a new fuzzy DL f-SROIQ(G), and define its syntax, semantics and knowledge bases. (ii) we propose a tableau algorithm for deciding the reasoning problems of f-SROIQ(G). The work is a step forward in the direction of fuzzy DLs, the representation and reasoning capabilities of f-SROIQ(G) go beyond the existing fuzzy DLs, and it may lay a theoretical foundation for the representation and reasoning of fuzzy data information in the Semantic Web.

Knowledge Representation Using Type-2 Fuzzy Rough Ontologies in Ontology Web Language

Extending fuzzy soft sets with fuzzy description logics

Fuzzy Description Logics (DLs) are a formalism for the representation of structured knowledge that is imprecise or vague by nature. In fuzzy DLs, restricting to a finite set of degrees of truth has proved to be useful, both for theoretical and practical reasons. In this paper, we propose finite fuzzy DLs as a generalization of existing approaches. We assume a finite totally ordered set of linguistic terms or labels, which is very useful in practice since expert knowledge is usually expressed using linguistic terms. Then, we consider fuzzy DLs based on any smooth t-norm defined over this set. Initially we focus on the finite fuzzy DL \(\mathcal{ALCH}\), studying some logical properties, and showing the decidability of the logic by presenting a reasoning preserving reduction to the classical case. Finally, we extend our logic in two directions: by considering non-smooth t-norms and by considering additional DL constructors.

How to construct Web ontologies that meet applications’ needs has become a key technology to enable the Semantic Web. Manual development of ontologies remains a cumbersome and time-consuming task. In real-world applications, however, information is often vague or ambiguous. Thus, developing approaches and tools for constructing fuzzy ontologies by extracting domain knowledge from huge amounts of existing fuzzy databases can facilitate fuzzy ontology development. In this paper, we propose a formal approach and an automated tool for constructing fuzzy ontologies from fuzzy Object-Oriented database (FOOD) models. Firstly, we introduce the fuzzy ontology, which consists of the fuzzy ontology structure and instances. Then, the FOOD models are investigated, and we propose a kind of formal definition of FOOD models. On this basis, we develop a formal approach that can translate the FOOD model and its corresponding database instances into the fuzzy ontology structure and the fuzzy ontology instances, respectively. Furthermore, following the proposed approach, we implement an automated learning tool, which can automatically construct fuzzy ontologies from FOOD models. Case studies show that the approach is feasible and the automated learning tool is efficient.

The distributed fuzzy ontologies play an important role in semantic web. Most current solutions are proposed respectively on one of these two aspects. To represent distributed fuzzy ontology, we combine fuzzy description logics and E-connections, and present distributed extended fuzzy description logic (DEFSHOIN). This novel logical approach couples both fuzzy and distributed features within description logics. The main contribution of this paper is to propose a combined tableau to achieve reasoning within DEFSHOIN.

Fuzzy Description Logics are logics which allow to deal with structured knowledge affected by vagueness. Although a relatively important amount of work has been carried out in the last years, fuzzy DLs are open to be extended with several features worked out in other fields. In this work, we start addressing the problem of incorporating Multi-Criteria Decision Making (MCDM) into fuzzy Description Logics and, thus, start an investigation about offering the possibility of a fuzzy ontology assisted approach to decision making.KeywordsFuzzy NumberDescription LogicDecision MatrixOptimal AlternativeMCDM MethodThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Ontology description can use Description Logic(DL) language, so DL's reasoning service can be used in ontology reasoning. In each kind DL, there is a corresponding tableau algorithm to do the reasoning process. There are some sophisticated software to do DL reasoning, they using tree with conflict to decide whether a problem can be using satisfiability to solve. There are a lot of optimization methods to optimize the reasoning service, their attention on the tree structure with conflict. We propose a new algorithm, Heuristic Skipping Rules Algorithm(HSRA), to simply the rule set called by tableau algorithms, and experimentally proved the effectiveness of the HSRA.