Kripke completeness of some intermediate predicate logics with the axiom of constant domain and a variant of canonical formulas

Abstract

For each intermediate propositional logicJ, J* denotes the least predicate extension ofJ. By the method of canonical models, the strongly Kripke completeness ofJ*+D(=∀x(p(x)∨q)⊃∀xp(x)∨q) is shown in some cases including: 1. J is tabular, 2. J is a subframe logic.