Let V be a variety of monotone bounded lattice expansions, that is, bounded lattices endowed with additional operations, each of which is order preserving or reversing in each coordinate. We prove that if V is closed under MacNeille completions, then it is also closed under canonical extensions. As a corollary we show that in the case of Boolean algebras with operators, any such variety V is ge...

Abstract. Studied is the issue of similarity relations in fuzzy concept lattices. Fuzzy concepts and fuzzy concept lattices represent a formal approach to the modeling of non-sharp (fuzzy) concepts and conceptual structures in the sense of traditional (PortRoyal) logic. Applications of concept lattices are in representation of conceptual knowledge and in conceptual analysis of (fuzzy) data. Sim...

We show that the variety of ortholattices has the strong amalgamation property and that the variety of orthomodular lattices has the strong Boolean amalgamation property, i.e. that two orthomodular lattices can be strongly amalgamated over a common Boolean subalgebra. We give examples to show that the variety orthomodular lattices does not have the amalgamation property and that the variety of ...

2014 We formulate a conjecture concerning the critical frontiers of q-state Potts ferromagnets on d-dimensional lattices (d > 1) which generalize a recent one stated for planar lattices. The present conjecture is verified within satisfactory accuracy (exactly in some cases) for all the lattices or arrays whose critical points are known. Its use leads to the prediction of : a) a considerabl...

This paper studies the issue of similarity relations in fuzzy concept lattices. Fuzzy concepts and fuzzy concept lattices represent a formal approach to the modelling of non-sharp (fuzzy) concepts and conceptual structures in the sense of traditional (Port-Royal) logic. Applications of concept lattices are in representation of conceptual knowledge and in conceptual analysis of (fuzzy) data. Sim...

Discretizations of the Laplacian operator on non-hypercubical lattices are discussed in a systematic approach. It is shown that order a2 errors always exist for discretizations involving only nearest neighbors. Among all lattices with the same density of lattice sites, the hypercubical lattices always have errors smaller than other lattices with the same number of spacetime dimensions. On the o...