This paper deals with join-semilattices whose sections, i.e. principal filters, are pseudocomplemented lattices. The pseudocomplement of a∨b in the section [b,1] is denoted by a → b and can be considered as connective implication certain kind intuitionistic logic. Contrary to case Brouwerian semilattices, sections need not distributive essentially allows possible applications non-classical logi...

A variety V has tolerances permutable with factor congruences if for any A1, A2 of V and every tolerance T on A1 × A2 we have T ◦ Π1 = Π1 ◦ T and T ◦ Π2 = Π2 ◦ T , where Π1,Π2 are factor congruences. If B is a subalgebra of A1×A2, the congruences Θi = Πi∩B are called decomposing congruences. V has tolerances permutable with decomposing congruences if T ◦ Θi = Θi ◦ T (i = 1, 2) for each A1, A2 ∈...