Consistency reasoning in lattice-based fuzzy Description Logics

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.

The existing ontology reasoners are all unilaterally description logic-based or rule-based, and their abilities to deal with fuzzy ontology are limited. It is the diversity of fuzzy ontology representation methods among them that leads to a low processing efficiency of fuzzy ontology. To solve this bottle-neck problem of fuzzy ontology-based knowledge reasoning, fuzzy ontology, fuzzy ontology representation method and fuzzy description logic are investigated, and the existing fuzzy ontology reasoners are comparatively analyzed. By virtue of the advantages of the typical reasoners such as Pellet, JenaAPI and fuzzyDL (fuzzy Description Logic), a method combining rule and description logic reasoning is designed, and a framework about fuzzy ontology based knowledge reasoning is proposed. By reducing fuzzy ontology, checking consistency and repairing inconsistency, the efficiency and accuracy of fuzzy ontology based knowledge reasoning can be improved. Finally, an experiment is given to verify the validity of proposed method.

Extending fuzzy soft sets with fuzzy description logics

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".

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.

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.

Description logics (DLs) are modern knowledge representation formalisms which are used today in many applications for reasoning with structured knowledge. Moreover, they are used in the semantic web (an extension of the current web) through the ontology language OWL. On the other hand fuzzy description logics (fuzzy-DLs) have been proposed as expressive logical formalisms capable of capturing and reasoning with

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.

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.

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.

Description logics are appropriate, widely used, logics for managing strudtured knowledge.

The Internet of Things (IoT) has become one of the most popular technologies in recent years. Advances in computing capabilities, hardware accessibility, and wireless connectivity make possible communication between people, processes, and devices for all kinds of applications and industries. However, the deployment of this technology is confined almost entirely to tech companies, leaving end users with only access to specific functionalities. This paper presents a framework that allows users with no technical knowledge to build their own IoT applications according to their needs. To this end, a framework consisting of two building blocks is presented. A friendly interface block lets users tell the system what to do using simple operating rules such as "if the temperature is cold, turn on the heater." On the other hand, a fuzzy logic reasoner block built by experts translates the ambiguity of human language to specific actions to the actuators, such as "call the police." The proposed system can also detect and inform the user if the inserted rules have inconsistencies in real time. Moreover, a formal model is introduced, based on fuzzy description logic, for the consistency of IoT systems. Finally, this paper presents various experiments using a fuzzy logic reasoner to show the viability of the proposed framework using a smart-home IoT security system as an example.

The article presents refutational resolution theorem proving system for Fuzzy Description Logic (FDL) based on general (non-clausal) resolution rule. It brings several new notions of refutation degree and proves its relation to provability degree in fuzzy predicate logic.