Fuzzy Descriptions Logics with Fuzzy Truth Values (original) (raw)
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1998
Description Logics (DLs, for short) 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 a 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. Concepts of this kind are rather vague than precise. As fuzzy logic directly deals with the notion of vagueness and imprecision, it offers an appealing foundation for a generalisation of DLs to vague concepts. In this paper we present a general fuzzy DL, which combines fuzzy logic with DLs. We define its syntax, semantics and present constraint propagation calculi for reasoning in it.
The fuzzy linguistic description logic ALCFL
Proceedings of the 11th …, 2006
Description Logics (DLs) have been studied and applied successfully in quite a lot of fields (see eg [1]). To deal with vague and imprecise information in real-world applications, fuzzy ALC [7] introduces fuzzy concepts. As a more general case of fuzzy ALC, a DL framework ...
THE FUZZY DESCRIPTION LOGIC ALCFLH
Description Logics, 2000
We present the fuzzy description logic ALC F LH . ALC F LH is based on ALC F H , but linear hedges are used instead of exponential ones. This allows to solve the entailment and the subsumption problem in a fuzzy description logic, where arbitrary concepts and roles may be modified.
Extending Datatype Restrictions in Fuzzy Description Logics
2009 Ninth International Conference on Intelligent Systems Design and Applications, 2009
Fuzzy Description Logics (DLs) are a family of logics which allow the representation of (and the reasoning within) structured knowledge affected by vagueness. Although a relatively important amount of work has been carried out in the last years, little attention has been given to the role of datatypes in fuzzy DLs. This paper presents a fuzzy DL with three kinds of extended datatype restrictions, together with the necessary rules to reason with them.
Fuzzy quantification in fuzzy description logics
Capturing Intelligence, 2006
This chapter introduces reasoning procedures for ALCQ + F (D), a fuzzy description logic with extended qualified quantification [D. Sánchez, A.G.B. Tettamanzi, Generalizing quantification in fuzzy description logics, in: Proceedings 8th Dortmund Fuzzy Days, Dortmund, Germany, 2004]. The language allows for the definition of fuzzy quantifiers of the absolute and relative kind by means of piecewise linear functions on N and Q ∩ [0, 1] respectively. In order to reason about instances, the semantics of quantified expressions is defined by using method GD [M. Delgado, D. Sánchez, M. Vila, Fuzzy cardinality based evaluation of quantified sentences, Int. J. Approximate Reasoning 23 , 23-66], which is based on recently developed measures of the cardinality of fuzzy sets. The main contribution of this chapter is a procedure to calculate the fuzzy satisfiability of a fuzzy concept, which is a very important reasoning task. The procedure considers several different cases and provides direct solutions for the most frequent types of fuzzy concepts. In order to distinguish between these cases, a novel idea of concept independence is also introduced.
Reasoning with very expressive fuzzy description logics
Journal of Artificial …, 2007
It is widely recognized today that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are a family of knowledge representation languages that have gained considerable attention the last decade, mainly due to their decidability and the existence of empirically high performance of reasoning algorithms. In this paper, we extend the well known fuzzy ALC DL to the fuzzy SHIN DL, which extends the fuzzy ALC DL with transitive role axioms (S), inverse roles (I), role hierarchies (H) and number restrictions (N ). We illustrate why transitive role axioms are difficult to handle in the presence of fuzzy interpretations and how to handle them properly. Then we extend these results by adding role hierarchies and finally number restrictions. The main contributions of the paper are the decidability proof of the fuzzy DL languages fuzzy-SI and fuzzy-SHIN , as well as decision procedures for the knowledge base satisfiability problem of the fuzzy-SI and fuzzy-SHIN .
Fuzzy Description Logics and t-norm based fuzzy logics
International journal of …, 2010
Mathematical Fuzzy Logic Propositional and predicate t-norm based fuzzy logics Truth constants a b s t r a c t Description Logics (DLs) are knowledge representation languages built on the basis of classical logic. DLs allow the creation of knowledge bases and provide ways to reason on the contents of these bases. Fuzzy Description Logics (FDLs) are natural extensions of DLs for dealing with vague concepts, commonly present in real applications.
Description Logics with Fuzzy Concrete Domains
2005
We present a fuzzy version of description logics with concrete domains. Main features are: (i) concept constructors are based on t-norm, t-conorm, negation and implication; (ii) concrete domains are fuzzy sets; (iii) fuzzy modifiers are allowed; and (iv) the reasoning algorithm is based on a mixture of completion rules and bounded mixed integer programming.
Fuzzy Description Logic Programs
Uncertainty and Intelligent information Systems, 2008
Description Logic Programs (DLPs), which combine the expressive power of classical description logics and logic programs, are emerging as an important ontology description language paradigm. In this work, we present fuzzy DLPs, which extend DLPs by allowing the representation of vague/imprecise information.
A Fuzzy Description Logic with Product T-norm
2007 IEEE International Fuzzy Systems Conference, 2007
Fuzzy Description Logics (fuzzy DLs) have been proposed as a language to describe structured knowledge with vague concepts. It is well known that the choice of the fuzzy operators may determine some logical properties. However, up to date the study of fuzzy DLs has been restricted to the Łukasiewicz logic and the "Zadeh semantics". In this work, we propose a novel semantics combining the common product t-norm with the standard negation. We show some interesting properties of the logic and propose a reasoning algorithm based on a mixture of tableaux rules and the reduction to Mixed Integer Quadratically Constrained Programming.