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Reports on Mathematical Logic

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No. 31

C.J. VAN ALTEN, J.G. RAFTERY:

On Quasivariety Semantics of fragments of
Intuitionistic Propositional Logic without Exchange and Contraction
Rules
A b s t r a c t.
Let $H$ be the Hilbert-style intuitionistic propositional calculus
without exchange and contraction rules (as given by Ono and
Komori). An axiomatization of H with the separation property is
provided. Of the superimplicational fragments of H, it is proved
that just two fail to be finitely axiomatized, and that all are
algebraizable. The paper is a study of these fragments, their
equivalent algebraic (quasivariety) semantics and their axiomatic
extensions.

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