We generalize the incompleteness proof of the modal predicate logic Q-S4+ âœ·âœ¸p âŠƒ âœ¸âœ·p + BF described in Hughes-Cresswell [6]. As a corollary, we show that, for every subframe logic L containing S4, Kripke completeness of Q-L+BF implies the finite embedding property of L.

In the previous papers [4], [5], the author gave several completeness and incompleteness results on some predicate extensions with the constant domain of intermediate and modal propositional logics by means of the theory of canonical formulas (cf. [1]). However, these results are on subframe and cofinal subframe logics, and little is known for non cofinalâ€¦ (More)

Kripke frame semantics is used as a concise and convenient apparatus for the study of non-classical predicate logics, but it is well-known that there exist a great many important logics which cannot be complete with respect to this semantics. Logicians have been introducing many kinds of new semantics to get rid of this difficulty. (cf. [1], [3]) Hence itâ€¦ (More)

Let Q-L be the least predicate extension of a normal extension L of S4 and BF be the Barcan formula âˆ€x2A(x) âŠƒ 2âˆ€xA(x). Ghilardi [3] showed that it is rare that Q-L is complete with respect to Kripke semantics. On the other hand, if L is a subframe logic with the finite embedding property, we can show the completeness of Q-L + BF by the method of canonicalâ€¦ (More)