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Induction of Classifications from Linguistic Data
, 2002
"... We present a flexible approach for extracting hierarchical classifications from linguistic data. To this end, the framework of observational logic is introduced, which extends the logic that underlies standard Formal Concept Analysis by allowing disjunctive rules and exclusions. We give a rigorous m ..."
Abstract

Cited by 4 (2 self)
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We present a flexible approach for extracting hierarchical classifications from linguistic data. To this end, the framework of observational logic is introduced, which extends the logic that underlies standard Formal Concept Analysis by allowing disjunctive rules and exclusions. We give a rigorous mathematical characterization of how the chosen rule type affects the structure of the induced hierarchy. The framework is applied to the induction of hierarchical classifications from linguistic databases. The pros and cons of several types of hierarchies are discussed in detail with respect to criteria such as compactness of representation, suitability for inference tasks, and intelligibility for the human user.
Localic Completion Of Quasimetric Spaces
, 1997
"... We give a constructive localic account of the completion of quasimetric spaces. In the context of Lawvere's approach, using enriched categories, the points of the completion are flat left modules over the quasimetric space. The completion is a triquotient surjective image of a space of Cauchy s ..."
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We give a constructive localic account of the completion of quasimetric spaces. In the context of Lawvere's approach, using enriched categories, the points of the completion are flat left modules over the quasimetric space. The completion is a triquotient surjective image of a space of Cauchy sequences and can also be embedded in a continuous dcpo, the "ball domain". Various examples and constructions are given, including the lower, upper and Vietoris powerlocales, which are completions of finite powerspaces. The exposition uses the language of locales as "topologyfree spaces". Keywords topology, locale, topos, geometric theory, metric, quasimetric, completion, enriched category, triquotient, powerlocale. AMS Subject Code Classifications: Primary  26E40. Secondary  03G30, 54E50, 54B20, 18D20. 2 1.