Modeling Preferences over Attribute Sets in Formal Concept Analysis

In this paper, we consider two types of preferences from preference logic and propose their interpretation in terms of formal concept analysis. We are concerned only with preferences between sets of attributes, or, viewed logically, between conjunctions of atomic formulas. We provide inference systems for the two types of preferences and study their relation to implications.

[1]  Diego Calvanese,et al.  The Description Logic Handbook: Theory, Implementation, and Applications , 2003, Description Logic Handbook.

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

[3]  Henry Rouanet,et al.  Algèbre linéaire et formalisation de la notion de comparaison , 1968 .

[4]  Harry S. Delugach,et al.  Conceptual Structures at Work , 2004, Lecture Notes in Computer Science.

[5]  Bernhard Ganter,et al.  Implications in Triadic Formal Contexts , 2004, ICCS.

[6]  W. W. Armstrong,et al.  Dependency Structures of Data Base Relationships , 1974, IFIP Congress.

[7]  Amedeo Napoli,et al.  A Proposal for Combining Formal Concept Analysis and Description Logics for Mining Relational Data , 2007, ICFCA.

[8]  Sheila Pantry,et al.  Changing for the Better , 2004 .

[9]  Bernhard Ganter,et al.  Formal Concept Analysis , 2013 .

[10]  Felix Distel,et al.  On the complexity of enumerating pseudo-intents , 2011, Discret. Appl. Math..

[11]  Sergei O. Kuznetsov,et al.  Some decision and counting problems of the Duquenne-Guigues basis of implications , 2008, Discret. Appl. Math..

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

[13]  Fenrong Liu,et al.  Changing for the better : preference dynamics and agent diversity , 2008 .

[14]  J.F.A.K. van Benthem,et al.  Modal Logic for Open Minds , 2010 .

[15]  Bernhard Ganter,et al.  Attribute Exploration with Background Knowledge , 1999, Theor. Comput. Sci..

[16]  D. Angluin.  Queries and Concept Learning , 1988 .

[17]  N. Rescher.  The Logic of Preference , 1968 .