Minimum implicational basis for ∧-semidistributive lattices

Authors:
Philippe Janssen;Lhouari Nourine
Affiliations:
LIRMM, Université Montpellier II, Montpellier cedex, France;LIMOS, Université Blaise Pascal, Aubiere, France
Venue:
Information Processing Letters
Year:
2006

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Abstract

For a ∧-semidistributive lattice L, we study some particular implicational systems and show that the cardinality of a minimum implicational basis is polynomial in the size of join-irreducible elements of the lattice L. We also provide a polynomial time algorithm to compute a minimum implicational basis for L.