Fast Computation of Proper Premises

This work is motivated by an application related to refactor- ing of model variants. In this application an implicational base needs to be computed, and runtime is more crucial than minimal cardinality. Since the usual stem base algorithms have proven to be too costly in terms of runtime, we have developed a new algorithm for the fast computation of proper premises. It is based on a known link between proper premises and minimal hypergraph transversals. Two further improvements are made, which reduce the number of proper premises that are obtained multiple times and redundancies within the set of proper premises. We provide heuristic evidence that an approach based on proper premises will also be beneficial for other applications.

[1]  Georg Gottlob,et al.  New results on monotone dualization and generating hypergraph transversals , 2002, STOC '02.

[2]  Felix Distel Hardness of Enumerating Pseudo-intents in the Lectic Order , 2010, ICFCA.

[3]  Vincent Duquenne,et al.  Attribute-incremental construction of the canonical implication basis , 2007, Annals of Mathematics and Artificial Intelligence.

[4]  Bernhard Ganter,et al.  Two Basic Algorithms in Concept Analysis , 2010, ICFCA.

[5]  Klaus Kabitzsch,et al.  Extraction of feature models from formal contexts , 2011, SPLC '11.

[6]  Vincent Duquenne,et al.  Familles minimales d'implications informatives résultant d'un tableau de données binaires , 1986 .

[7]  Sebastian Rudolph Some Notes on Pseudo-closed Sets , 2007, ICFCA.

[8]  Vladimir Gurvich,et al.  An Efficient Incremental Algorithm for Generating All Maximal Independent Sets in Hypergraphs of Bounded Dimension , 2000, Parallel Process. Lett..

[9]  Heikki Mannila,et al.  Algorithms for Inferring Functional Dependencies from Relations , 1994, Data Knowl. Eng..

[10]  Bernhard Ganter,et al.  Formal Concept Analysis: Mathematical Foundations , 1998 .

[11]  Karell Bertet,et al.  The multiple facets of the canonical direct unit implicational basis , 2010, Theor. Comput. Sci..

[12]  Sergei O. Kuznetsov,et al.  Recognizing Pseudo-intents is coNP-complete , 2010, CLA.

[13]  Sergei O. Kuznetsov,et al.  On the Intractability of Computing the Duquenne?Guigues Bas , 2004, J. Univers. Comput. Sci..

[14]  Leonid Khachiyan,et al.  On the Complexity of Dualization of Monotone Disjunctive Normal Forms , 1996, J. Algorithms.

[15]  Klaus Kabitzsch,et al.  Automatic variation-point identification in function-block-based models , 2010, GPCE '10.