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A mechanism for combining any two substructural logics (e.g. linear and intuitionistic logics) is studied from a proof-theoretic point of view. The main results presented are cut-elimination and simulation results for these combined logics called synthesized substructural logics. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The logic just corresponding to (non-commutative) involutive quantales, which was introduced by Wendy MacCaull, is reconsidered in order to obtain a cut-free sequent calculus formulation, and the completeness theorem (with respect to the involutive quantale model ) for this logic is proved using a new admissible rule. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

A spatial modal logic (SML) is introduced as an extension of the modal logic S4 with the addition of certain spatial operators. A sound and complete Kripke semantics with a natural space (or location) interpretation is obtained for SML. The finite model property with respect to the semantics for SML and the cut-elimination theorem for a modified subsystem of SML are also presented. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Variants of classical linear logics are presented based on the modal version of new structural rule !?mingle instead of the known rules !weakening and ?weakening. The cut-elimination theorems, the completeness theorems (with respect to Girard's phase models) and a characteristic property named the mix separation principle are proved for these logics. [ABSTRACT FROM AUTHOR]