Results 1 - 10
of
22
A fuzzy Description Logic with product t-norm
- In Proceedings of the IEEE International Conference on Fuzzy Systems (FUZZ-IEEE07
, 2007
"... 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, ..."
Abstract
-
Cited by 36 (8 self)
- Add to MetaCart
(Show Context)
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. I.
Mixed integer programming, general concept inclusions and fuzzy description logics
- Mathware & Soft Computing
"... Fuzzy Description Logics (fuzzy DLs) have been proposed as a language to describe structured knowledge with vague concepts. In [23], a solution based on Mixed Integer Linear Programming has been proposed to deal with fuzzy DLs under Łukasiewicz semantics in which typical membership functions, such a ..."
Abstract
-
Cited by 27 (8 self)
- Add to MetaCart
Fuzzy Description Logics (fuzzy DLs) have been proposed as a language to describe structured knowledge with vague concepts. In [23], a solution based on Mixed Integer Linear Programming has been proposed to deal with fuzzy DLs under Łukasiewicz semantics in which typical membership functions, such as triangular and trapezoidal functions, can be explicitly represented in the language. A major theoretical and computational limitation so far is the inability to deal with General Concept Inclusions (GCIs), which is an important feature of classical DLs. In this paper, we address this issue and develop a calculus for fuzzy DLs with GCIs under various semantics: classical logic, “Zadeh semantics”, and Łukasiewicz logic.
Optimizing the crisp representation of the fuzzy description logic SROIQ
- In: Proceedings of the 3rd ISWC Workshop on Uncertainty Reasoning for the Semantic Web (URSW 2007
"... Abstract. Classical ontologies are not suitable to represent imprecise nor uncertain pieces of information. Fuzzy Description Logics were born to represent the former type of knowledge, but they require an appropriate fuzzy language to be agreed and an important number of available resources to be a ..."
Abstract
-
Cited by 23 (6 self)
- Add to MetaCart
(Show Context)
Abstract. Classical ontologies are not suitable to represent imprecise nor uncertain pieces of information. Fuzzy Description Logics were born to represent the former type of knowledge, but they require an appropriate fuzzy language to be agreed and an important number of available resources to be adapted. An alternative is to use classical ontologies to represent fuzzy ontologies. To date, all of the work in this direction has restricted to the Zadeh family of fuzzy operators. In this paper, we generalize existing proposals and propose a reasoning preserving procedure to obtain a crisp representation for a fuzzy extension of the logic ALCHOI under ̷Lukasiewicz semantics. This reduction makes possible to reuse a crisp representation language as well as currently available reasoners under crisp semantics. 1
Supporting Fuzzy Rough Sets in Fuzzy Description Logics
, 2009
"... 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 ..."
Abstract
-
Cited by 13 (2 self)
- Add to MetaCart
(Show Context)
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.
On Qualified Cardinality Restrictions in Fuzzy Description Logics under Łukasiewicz
"... Fuzzy Description Logics have been proposed as a family of languages to describe vague or imprecise structured knowledge. This work deals with one of the less studied constructors, qualified cardinality restrictions, showing some counter-intuitive behaviours under Łukasiewicz semantics, and proposin ..."
Abstract
-
Cited by 10 (3 self)
- Add to MetaCart
(Show Context)
Fuzzy Description Logics have been proposed as a family of languages to describe vague or imprecise structured knowledge. This work deals with one of the less studied constructors, qualified cardinality restrictions, showing some counter-intuitive behaviours under Łukasiewicz semantics, and proposing a new semantics and the corresponding reasoning algorithm.
Representing Uncertain Concepts in Rough Description Logics via Contextual Indiscernibility Relations
"... Abstract. We investigate on modeling uncertain concepts via rough description logics, which are an extension of traditional description logics by a simple mechanism to handle approximate concept definitions through lower and upper approximations of concepts based on a rough-set semantics. This allow ..."
Abstract
-
Cited by 9 (0 self)
- Add to MetaCart
Abstract. We investigate on modeling uncertain concepts via rough description logics, which are an extension of traditional description logics by a simple mechanism to handle approximate concept definitions through lower and upper approximations of concepts based on a rough-set semantics. This allows to apply rough description logics for modeling uncertain knowledge. Since these approximations are ultimately grounded on an indiscernibility relationship, the paper explores possible logical and numerical ways for defining such relationships based on the considered knowledge. In particular, the notion of context is introduced, allowing for the definition of specific equivalence relationships, to be used for approximations as well as for determining similarity measures, which may be exploited for introducing a notion of tolerance in the indiscernibility. 1
An OWL Ontology for Fuzzy OWL 2
"... Abstract. The need to deal with vague information in Semantic Web languages is rising in importance and, thus, calls for a standard way to represent such information. We may address this issue by either extending current Semantic Web languages to cope with vagueness, or by providing an ontology desc ..."
Abstract
-
Cited by 9 (0 self)
- Add to MetaCart
(Show Context)
Abstract. The need to deal with vague information in Semantic Web languages is rising in importance and, thus, calls for a standard way to represent such information. We may address this issue by either extending current Semantic Web languages to cope with vagueness, or by providing an ontology describing how to represent such information within Semantic Web languages. In this work, we follow the latter approach and propose and discuss an OWL ontology to represent important features of fuzzy OWL 2 statements. 1
Multi-criteria decision making in fuzzy Description Logics: A First step",
- In Proceedings of the 13th International Conference on Knowledge-Based & Intelli‐ gent Information & Engineering Systems, Lecture Notes in Artificial Intelligence,
, 2009
"... Abstract. 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, ..."
Abstract
-
Cited by 8 (2 self)
- Add to MetaCart
(Show Context)
Abstract. 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.
DeLorean: A Reasoner for Fuzzy OWL 1.1
"... Abstract. Classical ontologies are not suitable to represent imprecise or vague pieces of information, which has led to fuzzy extensions of Description Logics. In order to support an early acceptance of the OWL 1.1 ontology language, we present DeLorean, the first reasoner that supports a fuzzy exte ..."
Abstract
-
Cited by 6 (1 self)
- Add to MetaCart
(Show Context)
Abstract. Classical ontologies are not suitable to represent imprecise or vague pieces of information, which has led to fuzzy extensions of Description Logics. In order to support an early acceptance of the OWL 1.1 ontology language, we present DeLorean, the first reasoner that supports a fuzzy extension of the Description Logic SROIQ, closely equivalent to it. It implements some interesting optimization techniques, whose usefulness is shown in a preliminary empirical evaluation. 1
Towards Spatial Reasoning in Fuzzy Description Logics
"... Abstract — 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. ..."
Abstract
-
Cited by 6 (1 self)
- Add to MetaCart
(Show Context)
Abstract — 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”. I.
