Some Super-intuitionistic Logics as the Logical Fragments of Equational Theories
نویسندگان
چکیده
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 it is important to find a non-trivial example of the logics complete with respect to these new semantics. The second author [4] found finitely axiomatizable and Kripke-frame incomplete super-intuitionistic predicate logics each of which is complete with respect to Kripke sheaf semantics, which is an extended version of Kripke frame semantics introduced by V. B. Shehtman and D. P. Skvortsov [3]. In this article, we discuss a generalization of this result. By a careful reading of [4], the proof turns out to consist of the following two parts:
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