Join-semilattices whose principal filters are pseudocomplemented lattices

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 logics. We present connection semilattices mentioned beginning so-called which converted into I-algebras having everywhere defined operations. Moreover, we relate our structures sectionally relatively residuated means that logical closely connected substructural show form congruence distributive, 3-permutable weakly regular variety.