Grzegorczyk Logic Unlocked
Wojciech Aleksander Wo{\l}oszyn
TL;DR
This paper presents a simplified axiomatization of Grzegorczyk logic and extends the analysis to its modal extensions, developing a control statement theory and characterizing one extension with finite Boolean algebras.
Contribution
It introduces a new simplified axiomatization of Grz and develops a control statement framework for its modal extensions, providing new insights into their algebraic structures.
Findings
Grz.2 characterized by finite Boolean algebras
Developed control statement theory for Grzegorczyk logics
Extended analysis to modal extensions Grz.2 and Grz.3
Abstract
The article offers a fresh perspective on Grzegorczyk logic Grz, introducing a simplified axiomatization and extending the analysis to its natural modal extensions, Grz.2 and Grz.3. I develop a control statement theory for these logics, utilizing concepts such as buttons, switches, and ratchets. Through this framework, I establish that Grz.2 is characterized by finite Boolean algebras.
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Taxonomy
TopicsHistory and Theory of Mathematics