Intuitionistic Modal Algebras

Abstract Recent research on algebraic models of quasi-Nelson logic has brought new attention to a number classes algebras which result from enriching (subreducts of) Heyting with special modal operator, known in the literature as nucleus . Among these various structures, for we employ umbrella term intuitionistic , some have been studied since at least 1970s, usually within framework topology and sheaf theory. Others may seem more exotic, their primitive operations arise terms language not previously considered. We shall instance investigate variety weak implicative semilattices whose members are (non-necessarily distributive) meet endowed an implication operation is relative pseudo-complement but satisfies postulates Celani Jansana’s strict implication. For each establish representation topological duality generalize ones enriched nucleus.