R. Wille, "Restructuring Lattice Theory: an approach based on hierarchies of concepts". In Ordered Sets, I.Rival Ed., Reidel, Dordrecht-Boston, pp 445-470, 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....meaning of a kind of (2) running (1) event. Memory signs will be alternatively called a prototype. Such signs are specific representations of signs emerging from the recognition of perceived qualities. There is some evidence that such a representation could be generated by a Galois connection ([11]) however this aspect is beyond the scope of the present paper. The collections of qualities generating the semantic qualisigns of the sample phenomenon are defined as follows. a= observed rabbit (the observed continuant qualities of the running rabbit, for example, a grayish form, long ears) ....

Wille, R.: Restructuring lattice theory: An approach based on hierarchies of concepts. In: Rival, I. (ed.): Ordered sets, D. Reidel Publishing Company, DordrechtBoston, (1982) 445--470

.... proposed for ontological engineering in this paper begins with rapid development of a performance system using Multiple Classification Ripple Down Rules (MCRDR) 14] followed by automatic generation of an ontology in the form of an abstraction hierarchy using Formal Concept Analysis (FCA) [45, 46]. MCRDR incrementally and rapidly acquires and validates the knowledge on a case by case basis. Cases are used to motivate and validate the knowledge acquired. Figure 1 shows the process involved. MCRDR use cases found naturally in a domain to assist the user with classification of those cases and ....

Wille, R. (1982) Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts In Ordered Sets (Ed. Rival) pp:445-470, Reidel, Dordrecht, Boston.

....not ensure unique results, the way properties are grouped or the number of classes can be different for two maximally factorized hierarchies. The best compactness can be obtained by using a mathematical structure known in data analysis under the name of Galois lattice [Aig79] or concept lattice [Wil82, Wil89, Wil92]. Galois lattices [Aig79] are used (at least) in domains such that knowledge acquisition and representation, data analysis, information retrieval, data mining and their interest for hierarchy organization was recently highlighted by [GM93] In section 8, we will show that some algorithms produce ....

R. Wille. Restructuring lattice theory: An approach based on hierarchies of concepts. Ordered Sets, in I. Rivals (Eds), 23, 1982.

....a summary of the key results from the Galois lattice theory [3] which provide the basis of our approach towards incremental generation of frequent closed itemsets. 3. 1 Basics The domain focuses on the partially ordered structure 2, known under the names of Galois lattice [3] or concept lattice [20], which is induced by a binary relation R over a pair of sets O (objects) and A (attributes) For example, Figure i on the left shows the binary relation ]C = O, A, R) or context) drawn from the TDB of Table i where transactions are taken as objects, items as attributes, and oRa is to be read as ....

R. Wille. Restructuring the lattice theory: An approach based on hierarchies of concepts. In I. Rival, editor, Ordered sets, pages 445-470, Dordrecht-Boston, 1982. Reidel.

....knowledge rather than single level knowledge as output. Ripple down rules (RDR) 2] are used for manual and incremental acquisition of rules from cases at a rate of approximately 1 rule per minute. The rules are then mined using a set theoretical technique known as Formal Concept Analysis (FCA) [28], 29] to automatically generate a concept lattice. The approach is applicable beyond RDR and can be used on any propositional knowledge based representation. The approach should be highly attractive to other data mining techniques that produce association rules which are low level and simply based ....

Wille, R. (1982) Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts In I. Rival (ed), Ordered Sets Reidel, Dordrecht, Boston, 445-470,.

....framework surrounding ToscanaJ, that will provide an Open Source toolset for programs based on Formal Concept Analysis and the planning for future development. 1 Introduction Grounded on the idea of restructuring lattice theory, the development of Formal Concept Analysis (FCA) was started (cf. [16, 2]) about twenty years ago. FCA is based on the conceptualization of the concept concept and supports in a mathematically founded way the conceptual representation and visualization of data and knowledge. In the context of research and development of this theory, many ideas have been applied ....

Rudolf Wille, `Restructuring lattice theory: an approach based on hierarchies of concepts.', in Ordered sets, ed., Ivan Rival, pp. 445--470, Dordrecht--Boston, (1982). Reidel.

....Visualization, Lattices 1 Introduction Concept Lattices are used to represent conceptual hierarchies which are inherent in data. They are the core of the mathematical theory of Formal Concept Analysis (FCA) Introduced in the early 1980ies as a formalization of the concept of concept [37], FCA has over the years grown to a powerful theory for data analysis, information retrieval, and knowledge discovery [32] In Artificial Intelligence (AI) FCA is used as a knowledge representation mechanism [39] and as conceptual clustering method [38, 7, 23] In database theory, FCA has been ....

....concepts are necessary for expressing human knowledge, any knowledge management process benefits from a comprehensive formalization of concepts. FCA offers such a formalization by mathematizing the concept of concept as a unit of thought constituted of two parts: its extension and its intension [37, 10]. This understanding of concept is first mentioned explicitly in the Logic of Port Royal [3] and has been established in the German standard DIN 2330 and the International Standard ISO 704. We recall the basics of Formal Concept Analysis as far as they are needed for this paper. A more ....

R. Wille. Restructuring lattice theory: an approach based on hierarchies of concepts. In I. Rival, editor, Ordered sets, pages 445--470. Reidel, Dordrecht--Boston, 1982.

....It is convenient to model dependence and causality, and provides a vivid and concise account of the relations between the variables in the universe of discourse. Concept hierarchy is not necessarily a tree structure. Wille et al. propose to build corresponding concept lattice from binary relations [1, 2, 3]. This kind of special lattice and the corresponding Hasse diagram represent a concept hierarchy. Concept lattice reflects entity attribute relationships between objects. In some practical applications such as information management and knowledge discovery, concept lattice has gained good results ....

....Firstly, our method takes only one pass over the database; secondly, it is incremental; finally, it is efficient. 2 Basic Notions of Concept Lattice In this section we recall necessary basic notions of concept lattice briefly, the detail description about concept lattice can be found in [1, 2, 3]. Suppose given the context (O, D, R) describing a set O of objects, a set D of descriptors and a binary relation R, there is a unique corresponding lattice structure, which is known as concept lattice. Each node in lattice L is a couple, noted (X , X) where X P(O) is called extension of the ....

Wille, R.: Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts. In: Rival I (Ed.). Dordrecht Reidel (1982) 445-470

....powerdomain, and extended it to a disjunctive logic programming paradigm [10] A notion of default negation, in the spirit of answer set programming [11] and Reiter s default logic [12] was also added [13] The notion of formal concept evolved out of the philosophical theory of concepts. Wille [14] proposed the main ideas which lead to the development of formal concept analysis as a mathematical field [15] The underlying philosophical rationale is that a concept is determined by its extent, i.e. the collection of objects which fall under this concept, and its intent, i.e. the collection of ....

Wille, R.: Restructuring lattice theory: An approach based on hierarchies of concepts. In Rival, I., ed.: Ordered Sets. Reidel, Dordrecht-Boston (1982) 445--470

....: 2 which satisfy This observation later formed the basis for the correspondence theory between Kripke frames and modal logics. Examples are the approximation operators of rough set theory [24] various generalizations [27, 28, 34, 38] the derivation operator of formal concept analysis [33], or the span content operators of [6] 2 Operators and relations Much of the mathematical background of qualitative data analysis is concerned with set operators, relational structures, and the interplay among them: Closure and interior operators, semi ) lattices, polarities, Galois ....

....R U X xRz and z y yRz xRz and R z X xRz and z 3. follows from 1. and 2. by duality. Observe that Proposition 2 is true for arbitrary R. The following result has been known in a different context for some time [33]: Corollary 1 is a closure operator. Proof. First, R V by duality The claim follows now from Proposition 2. This result is also a direct consequence of Proposition 1; we have taken the route above to emphasize the connection with ....

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Wille, R. (1982). Restructuring lattice theory: An approach based on hierarchies of concepts. In Rival, I., editor, Ordered sets, volume 83 of NATO Advanced Studies Institute, pages 445--470. Reidel, Dordrecht.

....presents a family of algorithms able to produce effective constructions for representing and extracting new knowledge from a set of relevant examples or observed events of a given world. The formal framework utilized to develop the inductive process is the lattice theory. As Wille remarked in [9], the idea is to go back to the origin of lattice concept in nineteenth century attempting to formalize logic, where the fundamental step was the reduction of a concept to its extent. From a computational point of view, lattices can be thought as a mathematical abstraction of a frame system. That ....

....we will not use arrows in the links following the tradition of Hasse diagrams to represent lattices. 1. Concept Lattices In this section we present, in a formal framework, an ordered structure able to capture the dependency of properties in a given world. To this end we define, following Wille [9], concept lattices. Throughout the paper E will be a finite set of examples or observed events of a given world. Each example e of E is described by a set of elements called properties, and P will be the set of all these properties. 1.1) DEFINITION. A context is a pair (E,P) where P is a ....

[Article contains additional citation context not shown here]

R. Wille, Restructuring Lattices Theory: An Approach Based on Hierarchies of Concepts, in: I. Rival, ed., Ordered Sets (Reidel Publishing, 1982) 445-470.

....powerdomain, and extended it to a disjunctive logic programming paradigm [11] A notion of default negation, in the spirit of answer set programming [12] and Reiter s default logic [13] was also added [14] The notion of formal concept evolved out of the philosophical theory of concepts. Wille [15] proposed the main ideas which lead to the development of formal concept analysis as a mathematical field [16] The underlying philosophical rationale is that a concept is determined by its extent, i.e. the collection of objects which fall under this concept, and its intent, i.e. the collection of ....

Wille, R.: Restructuring lattice theory: An approach based on hierarchies of concepts. In Rival, I., ed.: Ordered Sets. Reidel, Dordrecht-Boston (1982) 445--470

....a parametric type in a type declaration, operator preceedence inside an expression, or a procedure or method call inside a statement. 1. 3 Formal Concept Analysis Formal Concept Analysis (FCA) is a technique of data analysis first introduced by Rudolf Wille as a way to restructure latice theory [15]. Since its inception in 1982, FCA has grown into a large field with successful applications in Psychology [16, 17] Social Science [18] Civil Engineering [19] and Software Engineering [20, 21, 22] An exposition of the mathematical foundations of formal concept analysis is beyond the scope of ....

.... operator is used for both S 1 and S 2 , i.e. # 1 : m 1 (G) and # 2 : m 2 (G) G 2 , a new composition operator acting on the object set of the semi product is given by # 1 # # 2 : m 1 (G) 2 (G) 2 , where: # 1 # # 2 (w 1 , w 2 ) # 1 (w 1 ) # 2 (w 2 ) Wille and Ganter in [24, 15] provide a general framework for understanding conceptual scaling of single valued contexts. A scale for a single valued context K = G, M, I) is introduced as a context S = G S , M S , I S ) The two contexts are connected by a special type of map called an S measure. An S measure from K to S is ....

R. Wille, "Restructuring lattice theory: An approach based on hierarchies of concepts," Ordered Sets, pp. 445--470, 1982.

....still another name for these things. An introduction to and a survey of recent work on KR languages, including a good bibliography, can be found in Borgida [B95] Right at the start, let s say what this paper is not about. It is not about the formal concept analysis of R. Wille (see, for example, [W82]) which deals with the derivation, from tables of attributes for individuals, of hierarchies of what are also called concepts. Wille s hierarchies are lattices, but they are not necessarily distributive. There are no clear connections between Wille s work and the contents of this paper. Each ....

Wille, R., "Restructuring lattice theory: an approach based on hierarchies of concepts," in Graphs and Order, edited by I. Rival, NATO ASI Series 147, Reidel, Dordrecht, 1982.

....cepts and capture similarities among a set of elements based on their common properties. Mathematically, concepts are maximal collections of elements sharing common properties. They form a complete partial order, called a concept lattice, which represents the relationships between all the concepts [11, 4]. The advantage of CA is that this technique allows us to infer commonalities between elements based only on the specification of simple properties satisfied by each element. Since the user only needs to specify the properties of interest on each element, he does not need to think about all ....

R. Wille. Restructuring lattice theory: An approach based on hierarchies of concepts. Ordered Sets, Ivan Rival Ed., NATO Advanced Study Institute, pages 445--470, September 1981.

....at least as frequent as the superepisode [51] 5.3 Closed Sets of Episodes In this section, we develop theoretical results that lead to the development of our algorithm for representative episodal association rules (REAR) generation. These results are directly related to formal concept analysis [91] and are an adaptation of the results in [77] to episodes. Our notion of a closed episode is similar to that of a concept. Informally, a concept is a pair of two sets: set of objects (windows or episodes) and set of features (events) common to all the objects. Using the framework of formal concept ....

....This leads to the following definition. Definition 4. An set of episodes Y that satisfies the condition #(#(Y ) Y is called a closed set of episodes. Closed sets of episodes are important because all members of the concept lattice of a data mining context satisfy the condition #(#(Y ) Y [91]. This step of considering only closed sets of episodes can be considered as a first step in pruning the episode set lattice. Example 4. Let Y = B, D . #(#(Y ) Y . Therefore, Y is a closed set of episodes of length one. On the other hand, the set of episodes D given in Example 3 is not ....

Wille, R., "Restructuring Lattice Theory: an Approach Based on Hierarchies of Concepts", Ordered sets , I. Rivali, ed., Reidel, Dordecht-Boston, 1982, pp. 445-470.

....cepts and capture similarities among a set of elements based on their common properties. Mathematically, concepts are maximal collections of elements sharing common properties. They form a complete partial order, called a concept lattice, which represents the relationships between all the concepts [1, 15, 6]. To use the CA technique, one only needs to specify the properties of interest on each element, and does not need to think about all possible combination of these properties, since these groupings are made automatically by the CA algorithm. 2 Applying concept analysis to inheritance hierarchies ....

R. Wille. Restructuring lattice theory: An approach based on hierarchies of concepts. Ordered Sets, Ivan Rival Ed., NATO Advanced Study Institute, pages 445--470, September 1981.

....and extended it to a disjunctive logic programming paradigm [RZ01] A notion of default negation, in the spirit of answer set programming [MT99] and Reiter s default logic [Rei80] was also added [Hit02] The notion of formal concept evolved out of the philosophical theory of concepts. Wille [Wil82] proposed the main ideas which lead to the development of formal concept analysis as a mathematical eld [GW99b] The underlying philosophical rationale is that a concept is determined by its extent, i.e. the collection of objects which fall under this concept, and its intent, i.e. the collection ....

Rudolf Wille. Restructuring lattice theory: An approach based on hierarchies of concepts. In Ivan Rival, editor, Ordered Sets, pages 445-470. Reidel, DordrechtBoston, 1982.

....Concept Analysis Concepts are necessary for expressing human knowledge. Therefore, the process of discovering knowledge in databases benefits from a comprehensive formalization of concepts which can be activated to communicatively represent knowledge coded in databases. Formal Concept Analysis ([27], 28] 5] offers such a formalization by mathematizing concepts that are understood as units of thought constituted by their extension and intension. To allow a mathematical description of 3 A2 5, A8, A9, B1, B3 9 A10 21, A23 A22 B10 B11 16, B30 35, B90, B91, C3, C10, C21 23 B20, B22 28, ....

Wille, R., Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts. In I. Rival (ed.): Ordered Sets. Boston-Dordrecht: Reidel, 1982, 445-- 470.

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R. Wille, "Restructuring Lattice Theory: an approach based on hierarchies of concepts". In Ordered Sets, I.Rival Ed., Reidel, Dordrecht-Boston, pp 445-470, 1982.

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Wille, R. (1982). Restructuring lattice theory: an approach based on hierarchies of concepts. In I. Rival (Ed.), Ordered sets. Reidel, Dordrecht-Boston, 445-470.

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Wille, R.: "Restructuring Lattices Theory: An Approach Based on Hierarchies of Concepts", in: I. Rival, ed., Ordered Sets (Reidel Publishing, 1982) 445-470.

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Wille, R.: "Restructuring Lattices Theory: An Approach Based on Hierarchies of Concepts", in: I. Rival, ed., Ordered Sets (Reidel Publishing, 1982) 445-470.

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Wille, R. Restructuring lattice theory: an approach based on hierarchies of concepts. In: Ivan Rival (ed.), Ordered sets, Reidel, Dordrecht-Boston, 445-470, 1982.

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R. Wille. Restructuring lattice theory: An approach based on hierarchies of concepts. In I. Rival, editor, Ordered sets, pages 445--470. D. Reidel Publishing Company, Dordrecht--Boston, 1982. 16

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R. Wille. Restructuring lattice theory: An approach based on hierarchies of concepts. Ordered Sets, Ivan Rival Ed., NATO Advanced Study Institute, 83:445--470, September 1981.

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R. Wille. Restructuring the lattice theory: An approach based on hierarchies of concepts. In I. Rival, editor, Ordered sets, pages 445--470, Dordrecht-Boston, 1982. Reidel.

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R. Wille. Restructuring lattice theory: An approach based on hierarchies of concepts. Ordered Sets, in I. Rivals (Eds), 23, 1982.

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Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Ordered Sets (ed. I.Rival). Reidel, Dordrecht-Boston 1982, 445-470.

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WILLE R., "Restructuring lattice theory: An approach based on hierarchies of concepts ", Ordered Sets, Ivan Rival Ed., NATO Advanced Study Institute, , 1981, p. 445-470.

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R. Wille. Restructuring lattice theory: An approach based on hierarchies of concepts. In I. Rival, editor, Ordered Sets, pages 445--470. Reidel, 1982.

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R. Wille. Restructuring lattice theory: an approach based on hierarchies of concepts. In: I. Rival (eds.), Ordered Sets, Reidel, Dordrecht, 1982. pp. 445-470

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R. Wille. Restructuring lattice theory: An approach based on hierarchies of concepts. In I. Rival, editor, Ordered Sets, pages 445--470. Reidel, 1982.

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R. Wille, Restructuring lattice theory: an approach based on hierarchies of concepts. In: I. Rival (ed.): Ordered Sets. Reidel, Dordrecht-Boston (1982), 445--470.

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Wille, R., (1982). Restructuring lattice theory: an approach based on hierarchies of concepts. In I. Rival, (Ed.), Ordered sets (pp. 445-470). Dordrecht: Reidel.

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R. Wille. Restructuring lattice theory: An approach based on hierarchies of concepts. Ordered Sets, Ivan Rival Ed., NATO Advanced Study Institute, 83:445--470, September 1981. 10

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R. Wille. Restructuring lattice theory: an approach based on hierarchies of concepts. In I. Rival, editor, Ordered sets, pages 445--470, Dordrecht-Boston, 1982. Reidel.

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Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In Ivan Rival, editor, Ordered sets, Reidel, Dordrecht-Boston(1982), 445--470.

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R. Wille. Restructuring lattice theory: An approach based on hierarchies of concepts. In I. Rival, editor, Ordered sets, pages 445--470, Dordrecht-Boston, 1982. Reidel.

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R. Wille. Restructuring lattice theory: an approach based on hierarchies of concepts. In Ordered Sets. I. Rival, ed. pp. 445--470. Reidel, Dordrecht, Boston, 1982.

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R. Wille. Restructuring lattice theory: An approach based on hierarchies of concepts. In I. Rival, editor, Ordered sets, pages 445--470. D. Reidel Publishing Company, Dordrecht--Boston, 1982.

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R. Wille. Restructuring the lattice theory: An approach based on hierarchies of concepts. In I. Rival, editor, Ordered sets, pages 445--470, Dordrecht-Boston, 1982. Reidel.

No context found.

Wille, R. (1982). Restructuring lattice theory: an approach based on hierarchies of concepts, In: Ivan Rival (ed.), Ordered sets, Reidel, Dordrecht-Boston, 445-470.

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R. Wille. Restructuring lattice theory: An approach based on hierarchies of concepts. In I. Rival, editor, Ordered Sets, pages 445--470. Reidel, 1982.

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R. Wille. Restructuring lattice theory: An approach based on hierarchies of concepts. Ordered Sets, Ivan Rival Ed., NATO Advanced Study Institute, 83:445--470, September 1981. 10

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R. Wille. Restructuring lattice theory: An approach based on hierarchies of concepts. In I. Rival, ed., Ordered Sets, pp. 445--470. Reidel, 1982.

No context found.

Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Ordered Sets (ed. I.Rival). Reidel, Dordrecht-Boston 1982, 445-470.

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R. Wille. Restructuring lattice theory: An approach based on hierarchies of concepts. In I. Rival, editor, Ordered sets, pages 445--470, Dordrecht-Boston, 1982. Reidel.

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R. Wille. Restructuring the lattice theory: An approach based on hierarchies of concepts. In I. Rival, editor, Ordered sets, pages 445--470, Dordrecht-Boston, 1982. Reidel.

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Wille, R.: Restructuring lattice theory: An approach based on hierarchies of concepts. In Rival, I., ed.: Ordered Sets. Reidel, Dordrecht-Boston (1982) 445--470

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