Rasiowa-Sikorski Style Relational Elementary Set Theory

摘要

A Rasiowa-Sikorski proof system is presented for an elementary set theory which can act as a target language for translating prepositional modal logics. The proposed system permits a modular analysis of (modal) axioms in terms of deductive rules for the relational apparatus. Such an analysis is possible even in the case when the starting modal logic does not possess a first-order correspondent. Moreover, the formalism enables a fine-tunable and uniform analysis of modal deductions in a simple and purely set-theoretic language.