Completeness theorem for dummett's LC quantified and some of its extensions

AbstractDummett's logic LC quantified, Q-LC, is shown to be characterized by the extended frame 〈Q+, ≤,D〉, where Q+ is the set of non-negative rational numbers, ≤is the numerical relation “less or equal then” and D is the domain function such that for all v, w ∈ Q+, Dv ≠ φ and if v ≤ w, then Dv. Dv $$ \subseteq $$ Dw. Moreover, simple completeness proofs of extensions of Q-LC are given.