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A fuzzy description logic for the semantic web
 Fuzzy Logic and the Semantic Web. Capturing Intelligence, Elsevier (2006) 73–90
"... Abstract. In this paper we present a fuzzy version of SHOIN (D), the corresponding ..."
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Cited by 103 (22 self)
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Abstract. In this paper we present a fuzzy version of SHOIN (D), the corresponding
Managing Uncertainty and Vagueness in Description Logics for the Semantic Web
, 2007
"... Ontologies play a crucial role in the development of the Semantic Web as a means for defining shared terms in web resources. They are formulated in web ontology languages, which are based on expressive description logics. Significant research efforts in the semantic web community are recently direct ..."
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Cited by 58 (7 self)
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Ontologies play a crucial role in the development of the Semantic Web as a means for defining shared terms in web resources. They are formulated in web ontology languages, which are based on expressive description logics. Significant research efforts in the semantic web community are recently directed towards representing and reasoning with uncertainty and vagueness in ontologies for the Semantic Web. In this paper, we give an overview of approaches in this context to managing probabilistic uncertainty, possibilistic uncertainty, and vagueness in expressive description logics for the Semantic Web.
A Treatise on ManyValued Logics
 Studies in Logic and Computation
, 2001
"... The paper considers the fundamental notions of many valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with som ..."
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Cited by 53 (3 self)
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The paper considers the fundamental notions of many valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with some hints toward applications which are based upon actual theoretical considerations about infinite valued logics. Key words: mathematical fuzzy logic, algebraic semantics, continuous tnorms, leftcontinuous tnorms, Pavelkastyle fuzzy logic, fuzzy set theory, nonmonotonic fuzzy reasoning 1 Basic ideas 1.1 From classical to manyvalued logic Logical systems in general are based on some formalized language which includes a notion of well formed formula, and then are determined either semantically or syntactically. That a logical system is semantically determined means that one has a notion of interpretation or model 1 in the sense that w.r.t. each such interpretation every well formed formula has some (truth) value or represents a function into
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 tnorm, tconorm, negation and implication; (ii) concrete domains are fuzzy sets; (iii) fuzzy modifiers are allowed; and (iv) the reasoning algorithm is based on a m ..."
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Cited by 43 (18 self)
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We present a fuzzy version of description logics with concrete domains. Main features are: (i) concept constructors are based on tnorm, tconorm, 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.
Reasoning with very expressive fuzzy description logics
 Journal of Artificial Intelligence Research
"... It is widely recognized today that the management of imprecision and vagueness will yield more intelligent and realistic knowledgebased applications. Description Logics (DLs) are a family of knowledge representation languages that have gained considerable attention the last decade, mainly due to th ..."
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Cited by 40 (17 self)
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It is widely recognized today that the management of imprecision and vagueness will yield more intelligent and realistic knowledgebased 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 fuzzySI and fuzzySHIN, as well as decision procedures for the knowledge base satisfiability problem of the fuzzySI and fuzzySHIN. 1.
Hypersequents and the proof theory of intuitionistic fuzzy logic
 Computer Science Logic CSL’2000. Proceedings, LNCS 1862
, 2000
"... Abstract. Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the firstorder Gödel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but no deduction system amenable to prooftheoretic, and ..."
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Cited by 20 (10 self)
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Abstract. Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the firstorder Gödel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but no deduction system amenable to prooftheoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work on hypersequent calculi for propositional Gödel logics by Avron. It is shown that the system is sound and complete, and allows cutelimination. A question by Takano regarding the eliminability of the TakeutiTitani density rule is answered affirmatively. 1
Sequent and Hypersequent Calculi for Abelian and Łukasiewicz Logics
 ACM Transactions on Computational Logic
, 2005
"... We present two embeddings of infinitevalued ̷Lukasiewicz logic ̷L into Meyer and Slaney’s abelian logic A, the logic of latticeordered abelian groups. We give new analytic proof systems for A and use the embeddings to derive corresponding systems for ̷L. These include: hypersequent calculi for A a ..."
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Cited by 19 (6 self)
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We present two embeddings of infinitevalued ̷Lukasiewicz logic ̷L into Meyer and Slaney’s abelian logic A, the logic of latticeordered abelian groups. We give new analytic proof systems for A and use the embeddings to derive corresponding systems for ̷L. These include: hypersequent calculi for A and ̷L and terminating versions of these calculi; labelled single sequent calculi for A and ̷L of complexity coNP; unlabelled single sequent calculi for A and ̷L. 1
Answering Vague Queries in Fuzzy DLLite
"... Fuzzy Description Logics (fuzzy DLs) allow to describe structured knowledge with vague concepts. Unlike classical DLs, in fuzzy DLs an answer is a set of tuples ranked according to the degree they satisfy the query. In this paper, we consider fuzzy DLLite. We show how to compute e#ciently th ..."
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Cited by 19 (9 self)
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Fuzzy Description Logics (fuzzy DLs) allow to describe structured knowledge with vague concepts. Unlike classical DLs, in fuzzy DLs an answer is a set of tuples ranked according to the degree they satisfy the query. In this paper, we consider fuzzy DLLite. We show how to compute e#ciently the topk answers of a complex query (i.e. conjunctive queries) over a huge set of instances.
Basic fuzzy logic and BLalgebras
, 1996
"... The relation of the basic fuzzy logic BL to continuous tnorms is studied and two additional axioms are formulated such that the extended logic is complete with respect to tautologies over all logics given by continuous tnorms. Keywords Basic fuzzy logic, continuous tnorms, residuated lattices. ..."
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Cited by 17 (1 self)
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The relation of the basic fuzzy logic BL to continuous tnorms is studied and two additional axioms are formulated such that the extended logic is complete with respect to tautologies over all logics given by continuous tnorms. Keywords Basic fuzzy logic, continuous tnorms, residuated lattices. 0.1 Introduction. Basic fuzzy logic BL, as developed and investigated in [3], is closely related to continuous tnorms; as summarized bellow, each continuous tnorm determines (1) a semantics of fuzzy propositional logic for which BL is sound, and (2) a particular linearly ordered BLalgebra, BLalgebras from a variety for which BL is sound and complete. Full treatment is found in [3]; bellow we summarize basic facts in Sections 1  3. At the end of Sect. 3 we formulate the main problem of completeness of BL with respect to BLalgebras given by continuous tnorms (talgebras). In Sect. 4 we develop some algebra of linearly ordered BLalgebras. In Sect. 5 we exhibit two additional axioms (B...
fSWRL: A fuzzy extension of SWRL
 Journal on Data Semantics, special issue on Emergent Semantics
"... Abstract. Although the combination of OWL and Horn rules results in the creation of a highly expressive language, i.e. SWRL, there are still many occasions where this language fails to accurately represent knowledge of our world. In particular, SWRL fails at representing vague and imprecise knowledg ..."
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Cited by 17 (5 self)
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Abstract. Although the combination of OWL and Horn rules results in the creation of a highly expressive language, i.e. SWRL, there are still many occasions where this language fails to accurately represent knowledge of our world. In particular, SWRL fails at representing vague and imprecise knowledge and information. Such type of information is apparent in many applications like multimedia processing and retrieval, information fusion, etc. In this paper, we propose fSWRL, a fuzzy extension to SWRL to include fuzzy assertions (such as ‘Mary is tall in the degree of 0.9’) and fuzzy rules (such as ‘being healthy is more important than being rich to determine if one is happy’). 1