On Universal Character of the Primitive Logic

Abstract

The PRIMITIVE LOGIC LO introduced in my former work is a logic having only two logical constants IMPLICATION → and UNIVERSAL QUANTIFICATION ( ) with their usual inference rules which are admitted even in the INTUITIONISTIC PREDICATE LOGIC LJ. LO is really a very simple logic, maybe the simplest possible logic as one can imagine, but it is very important because of its universal character. In fact, popular logics such as the LOWER CLASSICAL PREDICATE LOGIC LK, the INTUITIONISTIC PREDICATE LOGIC LJ, the MINIMAL PREDICATE .LOGIC LM, etc. can be faithfully interpreted in it. Speaking frankly, I am further expecting that all the important logics would be interpreted faithfully in it and would disclose their intrinsic characteristics by being interpreted in it. Main purpose of this paper is to show the universal character of the primitive logic LO by pointing out that a series of typical logics are faithfully interpretable in LO.