Fuzzy Description Logics Research Articles

A dynamic fuzzy description logic

Fuzzy description logics are considered as the logical infrastructure of fuzzy knowledge representation on the semantic Web. To deal with fuzzy and dynamic knowledge on the semantic Web and its applications, a new fuzzy extension of Attribute Language with Complement based on dynamic fuzzy logic called the dynamic fuzzy description logic (DFALC) is presented. The syntax and semantics of DFALC are formally defined, and the forms of axioms and assertions are specified. The DFALC provides more reasonable logic foundation for the semantic Web, and overcomes the insufficiency of using fuzzy description logic FALC to act as logical foundation for the semantic Web. The extended DFALC is more expressive than the existing fuzzy description logics and present more fuzzy information on the semantic Web.

Querying over fuzzy description logic

Description logics (DLs) play an important role in representing and reasoning domain knowledge. Conjunctive queries stemmed from the domain of relational databases, and have attracted more attentions in semantic Web recently. To acquire a tractable DL for query answering, DL-Lite is proposed. Due to the large amount of imprecision and uncertainty in the real world, it is essential to extend DLs to deal with these vague and imprecise information. We thus propose a new fuzzy DL f-DLR-Liteℱ⊓, which allows for the presence of n-ary relations and the occurrence of concept conjunction on the left land of inclusion axioms. We also suggest an improved fuzzy query language, which supports the presence of thresholds and user defined weights. We also show that the query answering algorithm over the extended DL is still FOL reducible and shows polynomial data complexity. DL f-DLR-Liteℱ⊓ can make up for the disadvantages of knowledge representation and reasoning of classic DLs, and the enhanced query language expresses user intentions more precisely and reasonably.

Reasoning with general terminological axioms in fuzzy description logic FALCN

This paper analyzes that the main difficulty in reasoning with general terminological axioms is that the membership degrees of fuzzy interpretations are not discrete, but continous in [0,1]. To remove this obstacle difficulty, this paper proposes a discretization method of fuzzy interpretation to translate membership degrees into discrete values in a finite set. Based on this discretization, it gives a discrete Tableau reasoning technique for FALCN reasoning problems with general terminological axioms, which consists of the definition of discrete Tableaus, a construction algorithm for discrete Tableaus and the proof of soundness, completeness and complexity of this algorithm.

Tightly Coupled Fuzzy Description Logic Programs under the Answer Set Semantics for the Semantic Web

We present a novel approach to fuzzy description logic programs (or simply fuzzy dl-programs) under the answer set semantics, which is a tight integration of fuzzy disjunctive logic programs under the answer set semantics with fuzzy description logics. From a different perspective, it is a generalization of tightly coupled disjunctive dl-programs by fuzzy vagueness in both the description logic and the logic program component. We show that the new formalism faithfully extends both fuzzy disjunctive logic programs and fuzzy description logics, and that under suitable assumptions, reasoning in the new formalism is decidable. We present a polynomial reduction of certain fuzzy dl-programs to tightly coupled disjunctive dl-programs, and we analyze the complexity of consistency checking and query processing for certain fuzzy dl-programs. Furthermore, we provide a special case of fuzzy dl-programs for which deciding consistency and query processing can both be done in polynomial time in the data complexity.

Reasoning within extended fuzzy description logic

An extended fuzzy description logic is proposed to increase expressive power for complex fuzzy information. We introduce cut sets of the fuzzy concepts and fuzzy roles as atomic concepts and atomic roles, and inherit concept constructors of the description logics to support a new logic system for fuzzy knowledge representation. We define the syntax, semantics and knowledge base of the extended fuzzy description logic, and focus on sat-domain and consistency as main reasoning tasks. We also present sound and complete tableau algorithms for these reasoning tasks, and prove the complexity of them is PSPACE-complete. Compared with the other fuzzy description logics, the extended fuzzy description logic can express more wide fuzzy information.

Flexible planning using fuzzy description logics: Theory and application

Description logics (DLs for short) are formalisms for representing knowledge of various domains in a structured and formally well-understood way. Typically, DLs are limited to deal with precise and well-defined concepts. In this paper we first present a fuzzy extension of A L C *, called fuzzy A L C *, combining Zadeh’s fuzzy logic with an expressive DL and define its syntax and semantics. Then we devote to taking advantage of the expressive power and reasoning capabilities of fuzzy A L C * by encoding flexible planning problems within the framework of fuzzy A L C *. Both theory and experimental results have shown that our method is sound and efficient.

Reasoning with Very Expressive Fuzzy Description Logics

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 Logic for Semantics Representation of the Semantic Web

Fuzzy Description Logic for Semantics Representation of the Semantic Web

Computational complexity of t-norm based propositional fuzzy logics with rational truth constants

If a continuous t-norm on [ 0 , 1 ] maps pairs of rationals into rationals then the corresponding fuzzy propositional calculus can be extended by rational truth constants and “bookkeeping” axioms for them. (Łukasiewicz t-norm is the classical example.) Computational complexity of such logics is studied. Consequences for fuzzy description logic are formulated.

A family of Extended Fuzzy Description Logics

Typical description logics are limited to dealing with crisp concepts and crisp roles. However, web applications based on description logics should allow the treatment of the inherent uncertainty. Extended Fuzzy Description Logics (EFDLs), which adopt a special fuzzify-method with more expressive power than the previous fuzzy description logics, are proposed to enable representation and reasoning for complex fuzzy information. They introduce the cut sets of fuzzy concepts and fuzzy roles as atomic concepts and atomic roles, and inherit the concept and role constructors from description logics. The definitions of syntax, semantics, reasoning tasks, reasoning properties, and reasoning algorithm are given for the extended fuzzy description logic.

Fuzzy ER Modeling with Description Logics

The relationship of description logic ALNUI and ER model is analyzed, especially how to translate ER model into ALNUI knowledge bases for reducing the reasoning on ER model to model reasoning on ALNUI knowledge bases is investigated, and the problem of fuzzy ER modeling with description logic is further studied. Aiming at the characteristics and requirement of fuzzy ER model and based on the description logic ALNUI, the description logic ALNUI is generalized through fuzzy logic. And a kind of new description logic, i.e., fuzzy description logic FALNUI (fuzzy ALNUI), is presented. The fuzzy ER modeling with description logic FALNUI is studied to translate fuzzy ER model into FALNUI knowledge bases. The reasoning problem of satisfiability, redundancy, and subsumption relation of fuzzy ER model may reason automatically through reasoning mechanism of fuzzy description logic FALNUI, and the correctness of these reasoning problems is proved.

On Computational Complexity of the Extended Fuzzy Description Logic with Numerical Restriction

Extended fuzzy description logic EFALCN (extended fuzzy attributive concept description language with complements and unqualified number restriction) is the fuzzy extension of the description logic with numerical restriction ALCN (attributive concept description language with complements and unqualified number restriction), but it lacks of reasoning algorithms and complexity analysis for reasoning tasks. In this paper, a constraint-propagation based tableau algorithm is proposed, and it is proved that this algorithm can be executed in PSPACE (polynomial space). For there is a polynomial time reduction that can reduce ALCN reasoning tasks into EFALCN reasoning tasks and ALCN reasoning tasks are PSPACE-complete, EFALCN reasoning tasks are

Making fuzzy description logic more general

A version of fuzzy description logic based on the basic (continuous t-norm based) fuzzy predicate logic BL is presented. Problems of satisfiability, validity and subsumption of concepts are discussed and reduced to problems of fuzzy propositional logic known to be decidable for any continuous t-norm. For Łukasiewicz t-norm some stronger results are obtained.

The Fuzzy Description Logic ALCFH with Hedge Algebras as Concept Modifiers

In this paper we present the fuzzy description logic ALCFH introduced, where primitive concepts are modified by means of hedges taken from hedge algebras. ALCFH is strictly more expressive than Fuzzy-ALC defined in [11]. We show that given a linearly ordered set of hedges primitive concepts can be modified to any desired degree by prefixing them with appropriate chains of hedges. Furthermore, we define a decision procedure for the unsatisfiability problem in ALCFH, and discuss knowledge base expansion when using terminologies, truth bounds, expressivity as well as complexity issues. We extend [8] by allowing modifiers on non-primitive concepts and extending the satisfiability procedure to handle concept definitions.

A model of multimedia information retrieval

Research on multimedia information retrieval (MIR) has recently witnessed a booming interest. A prominent feature of this research trend is its simultaneous but independent materialization within several fields of computer science. The resulting richness of paradigms, methods and systems may, on the long run, result in a fragmentation of efforts and slow down progress. The primary goal of this study is to promote an integration of methods and techniques for MIR by contributing a conceptual model that encompasses in a unified and coherent perspective the many efforts that are being produced under the label of MIR. The model offers a retrieval capability that spans two media, text and images, but also several dimensions: form, content and structure. In this way, it reconciles similarity-based methods with semantics-based ones, providing the guidelines for the design of systems that are able to provide a generalized multimedia retrieval service, in which the existing forms of retrieval not only coexist, but can be combined in any desired manner. The model is formulated in terms of a fuzzy description logic, which plays a twofold role: (1) it directly models semantics-based retrieval, and (2) it offers an ideal framework for the integration of the multimedia and multidimensional aspects of retrieval mentioned above. The model also accounts for relevance feedback in both text and image retrieval, integrating known techniques for taking into account user judgments. The implementation of the model is addressed by presenting a decomposition technique that reduces query evaluation to the processing of simpler requests, each of which can be solved by means of widely known methods for text and image retrieval, and semantic processing. A prototype for multidimensional image retrieval is presented that shows this decomposition technique at work in a significant case.

Reasoning within fuzzy description logics

Description Logics (DLs) are suitable, well-known, logics for managing structured knowledge. They allow reasoning about individuals and well defined concepts, i.e. set of individuals with common pr...

Reasoning within Fuzzy Description Logics

Description Logics (DLs) are suitable, well-known, logics for managing structured knowledge. They allow reasoning about individuals and well defined concepts, i.e., set of individuals with common properties. The experience in using DLs in applications has shown that in many cases we would like to extend their capabilities. In particular, their use in the context of Multimedia Information Retrieval (MIR) leads to the convincement that such DLs should allow the treatment of the inherent imprecision in multimedia object content representation and retrieval. In this paper we will present a fuzzy extension of ALC, combining Zadeh's fuzzy logic with a classical DL. In particular, concepts becomes fuzzy and, thus, reasoning about imprecise concepts is supported. We will define its syntax, its semantics, describe its properties and present a constraint propagation calculus for reasoning in it.