Algebraicity and the tensor product of concept lattices

Bogdan Chornomaz (1)

1 NASU - National Academy of Sciences of Ukraine

In this paper we prove that the tensor product of complete lattices, as it is defined in formal context analysis, preserves algebraicity. The proof of this fact is based on the compactness of propositional logic. We use this property to show that the box product of join-semilattices with zero, introduced by G.Gratzer and F.Wehrung in 1999, can be obtained from the tensor product of concept lattices in a manner similar to how it is done in the definition of tensor product in "general" lattice theory.

Mots clés: lattice; semilattice; formal concept analysis; tensor product; box product

Domaines: Mathématiques générales [math.GM]

Bogdan Chornomaz. Algebraicity and the tensor product of concept lattices. 2014. ⟨hal-00983199v1⟩