On the Undecidability of some Sub-Classical First-Order Logics

A general criterion for the undecidabily of sub-classical first-order logics and important fragments thereof is established. It is applied, among others, to Urquart's (original version of) C and the closely related logic C*. In addition, hypersequent systems for (first-order) C and C* are introduced and shown to enjoy cut-elimination.

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