Visible to the public Towards Concept Analysis in Categories: Limit Inferior as Algebra, Limit Superior as CoalgebraConflict Detection Enabled

TitleTowards Concept Analysis in Categories: Limit Inferior as Algebra, Limit Superior as Coalgebra
Publication TypeConference Paper
Year of Publication2015
AuthorsToshiki Kataoka, Dusko Pavlovic
Secondary AuthorsLawrence S. Moss, Pawel Sobocinski
Conference Name6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)
PublisherSchloss Dagstuhl–Leibniz-Zentrum fuer Informatik
Conference LocationDagstuhl, Germany
ISBN Number978-3-939897-84-2
Keywordsalgebra, category, completion, concept analysis, Resilient Monitoring and Control, semantic indexing, SURE Project
Abstract

While computer programs and logical theories begin by declaring the concepts of interest, be it as data types or as predicates, network computation does not allow such global declarations, and requires concept mining and concept analysis to extract shared semantics for different network nodes. Powerful semantic analysis systems have been the drivers of nearly all paradigm shifts on the web. In categorical terms, most of them can be described as bicompletions of enriched matrices, generalizing the Dedekind-MacNeille-style completions from posets to suitably enriched categories. Yet it has been well known for more than 40 years that ordinary categories themselves in general do not permit such completions. Armed with this new semantical view of Dedekind-MacNeille completions, and of matrix bicompletions, we take another look at this ancient mystery. It turns out that simple categorical versions of the limit superior and limit inferior operations characterize a general notion of Dedekind-MacNeille completion, that seems to be appropriate for ordinary categories, and boils down to the more familiar enriched versions when the limits inferior and superior coincide. This explains away the apparent gap among the completions of ordinary categories, and broadens the path towards categorical concept mining and analysis, opened in previous work.

URLhttp://drops.dagstuhl.de/opus/volltexte/2015/5531
DOIhttp://dx.doi.org/10.4230/LIPIcs.CALCO.2015.130
Citation Keykataoka_et_al:LIPIcs:2015:5531