On the Minimal Non-Fregean Grzegorczyk Logic

Abstract

The paper concerns Grzegorczyk’s non-Fregean logics that are intended to be a formal representation of the equimeaning relation defined on descriptions. We argue that the main Grzegorczyk logics discussed in the literature are too strong and we propose a new logical system, (Formula presented.) , which satisfies Grzegorczyk’s fundamental requirements. We present a sound and complete semantics for (Formula presented.) and we prove that it is decidable. Finally, we show that many non-classical logics are extensions of (Formula presented.) , which makes it a generic non-Fregean logic.