Sequent Calculi for the Propositional Logic of HYPE

Abstract In this paper we discuss sequent calculi for the propositional fragment of logic HYPE. The HYPE was recently suggested by Leitgeb ( Journal Philosophical Logic 48:305–405, 2019) as a hyperintensional contexts. On one hand introduce simple $$\mathbf{G1}$$ G 1 -system employing rules contraposition. other present $$\mathbf{G3}$$ 3 with an admissible rule Both systems are equivalent well sound and complete proof-system order to provide cut-elimination procedure, expand calculus connections introduced in Kashima Shimura Mathematical Quarterly 40:153–172, 1994).