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Approximable concepts, Chu spaces, and information systems
"... This paper serves to bring three independent but important areas of computer science to a common meeting point: Formal Concept Analysis (FCA), Chu Spaces, and Domain Theory (DT). Each area is given a perspective or reformulation that is conducive to the flow of ideas and to the exploration of cros ..."
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Cited by 13 (8 self)
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This paper serves to bring three independent but important areas of computer science to a common meeting point: Formal Concept Analysis (FCA), Chu Spaces, and Domain Theory (DT). Each area is given a perspective or reformulation that is conducive to the flow of ideas and to the exploration of crossdisciplinary connections. Among other results, we show that the notion of state in Scott’s information system corresponds precisely to that of formal concepts in FCA with respect to all finite Chu spaces, and the entailment relation corresponds to “association rules”. We introduce, moreover, the notion of approximable concept and show that approximable concepts represent algebraic lattices which are identical to Scott domains except the inclusion of a top element. This notion serves as a stepping stone in the recent work [Hitzler and Zhang, 2004] in which a new notion of morphism on formal contexts results in a category equivalent to (a) the category of complete algebraic lattices and Scott continuous functions, and (b) a category of information systems and approximable mappings.
Sigayret A.: Performances of Galois subhierarchybuilding algorithms
 ICFCA’07, LNCS/LNAI 4390
"... Abstract. The Galois Subhierarchy (GSH) is a polynomialsize representation of a concept lattice which has been applied to several fields, such as software engineering and linguistics. In this paper, we analyze the performances, in terms of computation time, of three GSHbuilding algorithms with ve ..."
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Abstract. The Galois Subhierarchy (GSH) is a polynomialsize representation of a concept lattice which has been applied to several fields, such as software engineering and linguistics. In this paper, we analyze the performances, in terms of computation time, of three GSHbuilding algorithms with very different algorithmic strategies: Ares, Ceres and Pluton. We use Java and C++ as implementation languages and Galicia as our development platform. Our results show that implementations in C++ are significantly faster, and that in most cases Pluton is the best algorithm. Keywords: Galois Subhierarchy, AOCPoset, Performance Analysis. 1
Generalized distance functions in the theory of computation
 Computer Journal
"... We discuss a number of distance functions encountered in the theory of computation, including ..."
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Cited by 11 (0 self)
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We discuss a number of distance functions encountered in the theory of computation, including
ON FIXEDPOINTS OF MULTIVALUED FUNCTIONS ON COMPLETE LATTICES AND THEIR APPLICATION TO GENERALIZED LOGIC PROGRAMS
"... Abstract. Unlike monotone singlevalued functions, multivalued mappings may have none, one or (possibly infinitely) many minimal fixedpoints. The contribution of this work is twofold. At first we overview and investigate about the existence and computation of minimal fixedpoints of multivalued m ..."
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Abstract. Unlike monotone singlevalued functions, multivalued mappings may have none, one or (possibly infinitely) many minimal fixedpoints. The contribution of this work is twofold. At first we overview and investigate about the existence and computation of minimal fixedpoints of multivalued mappings, whose domain is a complete lattice and whose range is its power set. Second, we show how these results are applied to a general form of logic programs, where the truth space is a complete lattice. We show that a multivalued operator can be defined whose fixedpoints are in onetoone correspondence with the models of the logic program. Key words. Fixedpoints; multivalued functions; complete lattices; logic programming AMS subject classifications. 47H10, 06B23 68N17, 68Q55, 1. Introduction. It
A cartesian closed category of approximable concept structures
 Proceedings of the International Conference On Conceptual Structures
, 2004
"... Abstract. Infinite contexts and their corresponding lattices are of theoretical and practical interest since they may offer connections with and insights from other mathematical structures which are normally not restricted to the finite cases. In this paper we establish a systematic connection betwe ..."
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Abstract. Infinite contexts and their corresponding lattices are of theoretical and practical interest since they may offer connections with and insights from other mathematical structures which are normally not restricted to the finite cases. In this paper we establish a systematic connection between formal concept analysis and domain theory as a categorical equivalence, enriching the link between the two areas as outlined in [25]. Building on a new notion of approximable concept introduced by Zhang and Shen [26], this paper provides an appropriate notion of morphisms on formal contexts and shows that the resulting category is equivalent to (a) the category of complete algebraic lattices and Scott continuous functions, and (b) a category of information systems and approximable mappings. Since the latter categories are cartesian closed, we obtain a cartesian closed category of formal contexts that respects both the context structures as well as the intrinsic notion of approximable concepts at the same time. 1
M.: Querying formal contexts with answer set programs
 Proc. ICCS 2006. Volume 4068 of LNAI
, 2006
"... Abstract. Recent studies showed how a seamless integration of formal concept analysis (FCA), logic of domains, and answer set programming (ASP) can be achieved. Based on these results for combining hierarchical knowledge with classical rulebased formalisms, we introduce an expressive commonsense q ..."
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Abstract. Recent studies showed how a seamless integration of formal concept analysis (FCA), logic of domains, and answer set programming (ASP) can be achieved. Based on these results for combining hierarchical knowledge with classical rulebased formalisms, we introduce an expressive commonsense query language for formal contexts. Although this approach is conceptually based on ordertheoretic paradigms, we show how it can be implemented on top of standard ASP systems. Advanced features, such as default negation and disjunctive rules, thus become practically available for processing contextual data. 1
AOCposets: a scalable alternative to Concept Lattices for Relational Concept Analysis
"... Abstract. Relational Concept Analysis (RCA) is a useful tool for classi cation and rule discovery on sets of objects with relations. Based on FCA, it produces more results than the latter but also an increase in complexity. Besides, in numerous applications of FCA, AOCposets are used rather than la ..."
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Abstract. Relational Concept Analysis (RCA) is a useful tool for classi cation and rule discovery on sets of objects with relations. Based on FCA, it produces more results than the latter but also an increase in complexity. Besides, in numerous applications of FCA, AOCposets are used rather than lattices in order to reduce combinatorial problems. An AOCposet is a subset of the concept lattice considering only concepts introducing an object or an attribute. AOCposets are much smaller and easier to compute than concept lattices and still contain the information needed to rebuild the initial data. This paper introduces a modi cation of the RCA process based on AOCposets rather than concept lattices. This work is motivated by a big set of relational data on river streams to be analysed. We show that using AOCposet on these data provides a reasonable concept number. 1
Constructing Lexical Semantic Hierarchies from Binary Semantic Features
"... Abstract. The paper employs and extends methods from Formal Concept Analysis for constructing semantic hierarchies from lexical classifications by binary semantic features. In particular, we show how the dichotomic character of binary features can be captured within an appropriate logical framewo ..."
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Abstract. The paper employs and extends methods from Formal Concept Analysis for constructing semantic hierarchies from lexical classifications by binary semantic features. In particular, we show how the dichotomic character of binary features can be captured within an appropriate logical framework that makes recourse to intuitionistic logic. The investigation is motivated by the use of semantic features in a largescale lexical semantic database. 1
IOS Press A Categorical View on Algebraic Lattices in Formal Concept Analysis
"... Abstract. Formal concept analysis has grown from a new branch of the mathematical field of lattice theory to a widely recognized tool in Computer Science and elsewhere. In order to fully benefit from this theory, we believe that it can be enriched with notions such as approximation by computation or ..."
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Abstract. Formal concept analysis has grown from a new branch of the mathematical field of lattice theory to a widely recognized tool in Computer Science and elsewhere. In order to fully benefit from this theory, we believe that it can be enriched with notions such as approximation by computation or representability. The latter are commonly studied in denotational semantics and domain theory and captured most prominently by the notion of algebraicity, e.g. of lattices. In this paper, we explore the notion of algebraicity in formal concept analysis from a categorytheoretical perspective. To this
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"... We discuss a number of distance functions encountered in the theory of computation, including metrics, ultrametrics, quasimetrics, generalized ultrametrics, partial metrics, dultrametrics, and generalized metrics. We consider their properties, associated fixedpoint theorems, and some general ap ..."
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We discuss a number of distance functions encountered in the theory of computation, including metrics, ultrametrics, quasimetrics, generalized ultrametrics, partial metrics, dultrametrics, and generalized metrics. We consider their properties, associated fixedpoint theorems, and some general applications they have within the theory of computation. We consider in detail the applications of generalized distance functions in giving a uniform treatment of several important semantics for logic programs, including acceptable programs and natural generalizations of them, and also the supported model and the stable model in the context of locally stratified extended disjunctive logic programs and databases.