Minimum implicational basis for $$\wedge$$-semidistributive lattices.(English)Zbl 1185.06009

Summary: For a $$\wedge$$-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 $$L$$.

MSC:

 06D75 Other generalizations of distributive lattices 03G10 Logical aspects of lattices and related structures 68Q25 Analysis of algorithms and problem complexity
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References:

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