Abstract

To generalize as in [7] the constructions of [2] and [5], let L be a nondegenerate join-semilattice with unit. With A · B = {x ∨ y ∈ L : x ∈ A, y ∈ B} and A⊥ = {y ∈ L : x ∨ y = 1 for all x ∈ A}, the structure , ·,∪, ⊥ , L, ∅) is the algebra of subsets for L. Let R be the maximal ideals of L. Interpreting L as the totality of elementary situations, and 1 ∈ L as the impossible one , the members of R will be called realizations, and R itself – the logical space associated with L