Integrating Bipolar Fuzzy Mathematical Morphology in Description Logics for Spatial Reasoning

Reasoning within expressive fuzzy rough description logics

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

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 (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.

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".

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

The past 25 years have seen many attempts to introduce defeasible-reasoning capabilities into a description logic setting. Many, if not most, of these attempts are based on preferential extensions of description logics, with a significant number of these, in turn, following the so-called KLM approach to defeasible reasoning initially advocated for propositional logic by Kraus, Lehmann, and Magidor. Each of these attempts has its own aim of investigating particular constructions and variants of the (KLM-style) preferential approach. Here our aim is to provide a comprehensive study of the formal foundations of preferential defeasible reasoning for description logics in the KLM tradition.We start by investigating a notion ofdefeasible subsumptionin the spirit of defeasible conditionals as studied by Kraus, Lehmann, and Magidor in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and we investigate KLM-style syntactic properties for bothpreferentialandrationalsubsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. Indeed, we also analyse the problem of non-monotonic reasoning in description logics at the level ofentailmentand present an algorithm for the computation ofrational closureof a defeasible knowledge base. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible knowledge bases is no worse than that of reasoning in the underlying classical DLALC.

Reasoning in Description Logics (DLs) can detect inconsistencies between trusted knowledge and not trusted sources. The proposed method is exemplified on fake news for Covid19. Machine learning is used to generate DL axioms from positive and negative examples using tools such as DL-Learner. The resulted knowledge graph formalised in DL is merged with the trusted ontologies on Covid-19. Reasoning in DL is then performed with the Racer engine, which is responsible to detect inconsistencies within the ontology. When detecting inconsistencies, a "red flag" is raised to signal possible fake news and the corresponding counterspeech is generated.

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

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.

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.