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

Abstract

Dummett'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 D v . D v \( \subseteq \)D w . Moreover, simple completeness proofs of extensions of Q-LC are given.