Introduction to logical information systems

Ferré, Sébastien; Ridoux, Olivier

doi:10.1016/s0306-4573(03)00018-9

Cited by 64 publications

(53 citation statements)

References 26 publications

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“…Note that, any Galois connection between two lattices may be rewritten as the connection between two powersets and therefore there is no strict gain in expressive power in the more general setting. However, the direct formulation as sets of closed elements of the lattice T is often useful [9,10,3]. Proposition 3 follows from, for instance, theorem 2 in [3].…”

Section: Proposition 4 Intmentioning

confidence: 99%

Closed Patterns and Abstraction Beyond Lattices

Soldano¹

2014

Formal Concept Analysis

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Abstract. Recently pattern mining has investigated closure operators in families of subsets of an attribute set that are not lattices. In particular, various authors have investigated closure operators starting from a context, in the Formal Concept Analysis (FCA) sense, in which objects are described as usual according to their relation to attributes, and in which a closed element is a maximal element of the equivalence class of elements sharing the same support, i.e. occurring in the same objects. The purpose of this paper is twofold. First we thoroughly investigate this framework and relate it to FCA, defining in particular a structure called a preconfluence, weaker than a lattice, in which we can define a closure operator with respect to a set of objects. Second, we show that the requirements allowing us to define abstract concept lattices also allow us to define corresponding abstract Galois pre-confluences.

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Section: Proposition 4 Intmentioning

confidence: 99%

Closed Patterns and Abstraction Beyond Lattices

Soldano¹

2014

Formal Concept Analysis

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“…A first way is to use scale contexts [12] when the set of values is finite and fixed. A second way is to define logics as in Logical Concept Analysis (LCA, [10]), which works well for infinite domains (e.g., integers, dates, geographic shapes), and allows for the dynamic and automatic insertion of new values in the hierarchy.…”

Section: Definition 2 (Value Domain)mentioning

confidence: 99%

“…In the following, we assume a multi-valued context K = (O, A, V, T ) together with value domains D a for each a ∈ A, and its derived feature context K F = (O, F, I F ). In this paper, we start from the framework of Logical Information Systems (LIS, [10]) with a restriction to conjunctive queries, whereas disjunction and negation are generally available in LIS. For the sake of simplicity, we will stick in this paper to this restriction, but the following results easily extent to Boolean queries.…”

Section: Lemma 1 the Following Equations Holds For Every Multi-valuementioning

confidence: 99%

“…They extend manyvalued contexts by allowing several values for the attribute of an object, rather than only one. The advantages of using multi-valued contexts are (1) more general results that directly apply to many-valued contexts and binary contexts, and (2) a data model close to databases [4], OLAP [5,20], the Semantic Web [2], and Logical Information Systems [10].…”

Section: Introductionmentioning

confidence: 99%

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Cubes of Concepts: Multi-dimensional Exploration of Multi-valued Contexts

Ferré

Allard

Ridoux

2012

Formal Concept Analysis

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Abstract. A number of information systems offer a limited exploration in that users can only navigate from one object to another object, e.g. navigating from folder to folder in file systems, or from page to page on the Web. An advantage of conceptual information systems is to provide navigation from concept to concept, and therefore from set of objects to set of objects. The main contribution of this paper is to push the exploration capability one step further, by providing navigation from set of concepts to set of concepts. Those sets of concepts are structured along a number of dimensions, thus forming a cube of concepts. We describe a number of representations of concepts, such as sets of objects, multisets of values, and aggregated values. We apply our approach to multi-valued contexts, which stand at an intermediate position between many-valued contexts and logical contexts. We explain how users can navigate from one cube of concepts to another. We show that this navigation includes and extends both conceptual navigation and OLAP operations on cubes.

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“…The algorithm is implemented into LISFS [PR03], a file system based on Logical Concept Analysis (LCA) [FR04], a version of FCA.…”

Section: Introductionmentioning

confidence: 99%

An Algorithm to Find Frequent Concepts of a Formal Context with Taxonomy

Cellier

Ferré

Ridoux

et al. 2008

Lecture Notes in Computer Science

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Abstract. Formal Concept Analysis (FCA) considers attributes as a non-ordered set. This is appropriate when the data set is not structured. When an attribute taxonomy exists, existing techniques produce a completed context with all attributes deduced from the taxonomy. Usual algorithms can then be applied on the completed context for finding frequent concepts, but the results systematically contain redundant information. This article describes an algorithm which allows the frequent concepts of a formal context with taxonomy to be computed. It works on a non-completed context and uses the taxonomy information when needed. The results avoid the redundancy problem with equivalent performance.

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Introduction to logical information systems

Cited by 64 publications

References 26 publications

Closed Patterns and Abstraction Beyond Lattices

Closed Patterns and Abstraction Beyond Lattices

Cubes of Concepts: Multi-dimensional Exploration of Multi-valued Contexts

An Algorithm to Find Frequent Concepts of a Formal Context with Taxonomy

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