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Journal of Logic and Computation Advance Access published online on April 5, 2008
Journal of Logic and Computation, doi:10.1093/logcom/exn006
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© The Author, 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original papers

Synthesizing Monadic Predicates

Carlo Meghini

Consiglio Nazionale delle Ricerche, Istituto della Scienza e delle Tecnologie della Informazione, Pisa, Italy E-mail: carlo.meghini{at}isti.cnr.it

Nicolas Spyratos

Université Paris-Sud, Laboratoire de Recherche en Informatique, Orsay Cedex, France E-mail: spyratos{at}lri.fr

Received 8 September 2007.


  Abstract

We study the problem of determining a concise, quantifier-free monadic predicate for a given set of objects in a given interpretation. We address both DNF and CNF predicates, as well as important sub-languages thereof. The problem is formalized as the search of a minimal element in a set of predicates equipped with a binary relation. We show that the problem has always a solution, that finding a minimal solution is always hard, but much harder when neither the given set of objects nor its complement are the extent of a formal concept (in the sense of Formal Concept Analysis).

Keywords: CNF/DNF monadic predicates; complexity; formal concept analysis


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