 If M = &lt;W, ≤, v+, v− &gt; is a C-model, then M ⊨ A (“A is valid in M”) iff for every t ∈ W, M, t ⊨+ A. F ⊨ A (“A is valid on F”) iff M ⊨ A for every model M based on F. A formula is C-valid iff it is valid on every frame. Support of truth and support of falsity for arbitrary formulas are persistent with respect to the relation ≤ of possible expansion of information states. That is, for any C-model M = &lt;W, ≤, v+, v− &gt; and formula A, if s ≤ t, then M, s ⊨+ A implies M, t ⊨+ A and M, s ⊨− A implies M, t ⊨− A. It can easily be shown that a negation normal form theorem holds. The logic C is characterized by the class of all C-frames: for any L-formula A, ⊢C A iff A is C-valid. Moreover, C satisfies the disjunction property and the constructible falsity property. If ⊢C A ∨ B, then ⊢C A or ⊢C B. If ⊢C ~(A ∧ B), then ⊢C ~ A or ⊢C ~B. Decidability of C follows from a faithful embedding into positive intuitionistic propositional logic.