Conserving involution in residuated structures

Mathematical Logic Quarterly 53 (6):583-609 (2007)
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This paper establishes several algebraic embedding theorems, each of which asserts that a certain kind of residuated structure can be embedded into a richer one. In almost all cases, the original structure has a compatible involution, which must be preserved by the embedding. The results, in conjunction with previous findings, yield separative axiomatizations of the deducibility relations of various substructural formal systems having double negation and contraposition axioms. The separation theorems go somewhat further than earlier ones in the literature, which either treated fewer subsignatures or focussed on the conservation of theorems only



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Citations of this work

Admissible Rules and the Leibniz Hierarchy.James G. Raftery - 2016 - Notre Dame Journal of Formal Logic 57 (4):569-606.
Contextual Deduction Theorems.J. G. Raftery - 2011 - Studia Logica 99 (1-3):279-319.

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References found in this work

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Models for entailment.Kit Fine - 1974 - Journal of Philosophical Logic 3 (4):347 - 372.
Star and perp: Two treatments of negation.J. Michael Dunn - 1993 - Philosophical Perspectives 7:331-357.
Foreword. [REVIEW]J. Font, R. Jansana & D. Pigozzi - 2003 - Studia Logica 74 (1-2):3-12.

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