Quick completeness proofs for some logics of conditionals.
John P. Burgess · Notre Dame Journal of Formal Logic · 1981
Vx e W\/y e W x RxyyVx e W Vj/, z, w e W x (Rxyz & Rxzw D Rxyw).A model-class is any 71/ C. Tfty closed under isomorphism; the interesting examples are obtained by imposing certain characteristic restrictions on R.Next, we fix a notion of satisfaction/validity.A valuation in(W, R)e7ft/ is a map F assigning each variable p, a subset of W. K can be extended to all of Ji by treating truth-functions in the usual way (e.g.,and defining V(a -• j8) as the set of all x e W such that: VyeW x Γ) Via) 3z e W x Π F(α) [Λxzy & Vr e H/ x Π F(α)(Λx^z D t e V(β))]