Book Chapter10.1007/978-3-642-29892-9_25
Some notes on managing closure operators
Sebastian Rudolph
- 07 May 2012
- pp 278-291
TL;DR: This paper surveys known results and presents new findings concerning time and space requirements of diverse tasks for managing closure operators, given in contextual, implicational, or black-box representation.
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Abstract: It is widely known that closure operators on finite sets can be represented by sets of implications (also known as inclusion dependencies) as well as by formal contexts. In this paper we survey known results and present new findings concerning time and space requirements of diverse tasks for managing closure operators, given in contextual, implicational, or black-box representation. These tasks include closure computation, size minimization, finer-coarser-comparison, modification by "adding" closed sets or implications, and conversion from one representation into another.
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Citations
•Book
Conceptual structures: leveraging semantic technologies : 17th International Conference on Conceptual Structures, ICCS 2009, Moscow, Russia, July 26-31, 2009 : proceedings
Sebastian Rudolph,Frithjof Dau,Sergei O. Kuznetsov +2 more
- 01 Jan 2009
TL;DR: The Maturing Semantic Web: Lessons in Web-Scale Knowledge Representation and another Reason Why Conceptual Graphs Need Actors.
14
Direct-optimal basis computation by means of the fusion of simplification rules
TL;DR: A new method, named SLgetdo, is proposed, to calculate the direct-optimal basis, providing the full integration of simplification paradigm, providing a limited rise of the implicational set throughout its execution.
10
•Proceedings Article
From an implicational system to its corresponding D-basis
Estrella Rodr ´ iguez-Lorenzo,Kira Adaricheva,Pablo Cordero,Manuel Enciso,Angel Mora +4 more
- 30 Oct 2015
TL;DR: An open problem is to obtain an arbitrary implicational system by means of minimal generators calculated using the Simplification Logic for implications of the D-basis, which is ordered-direct.
Succinctness and tractability of closure operator representations
TL;DR: This article considers extended implication sets and context families, as well as generalizations of them, and discusses the mutual succinctness of these four representations and the tractability of certain operations used to compare and modify closure operators.
8
Canonical dichotomous direct bases
TL;DR: This work introduces a new paradigm based on the bipartition of the implicational sets into two components, according to their behavior wrt the closure, and presents the notions of two new direct bases, named DD-basis and canonical DD-Basis, providing two methods to compute each of them.
7
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