Logic and Logical Philosophy 16 (2-3):105-146 (2007)

Abstract
Varieties of natural deduction systems are introduced for Wansing’s paraconsistent non-commutative substructural logic, called a constructive sequential propositional logic (COSPL), and its fragments. Normalization, strong normalization and Church-Rosser theorems are proved for these systems. These results include some new results on full Lambek logic (FL) and its fragments, because FL is a fragment of COSPL
Keywords constructive sequential propositional logic (COSPL)   (strong) normalization  full Lambek logic (FL), natural deduction
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DOI 10.12775/LLP.2007.005
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A Normalizing System of Natural Deduction for Intuitionistic Linear Logic.Sara Negri - 2002 - Archive for Mathematical Logic 41 (8):789-810.
Introduction: Paraconsistent Logics.Graham Priest & Richard Routley - 1984 - Studia Logica 43 (1-2):3 - 16.
Varieties of Linear Calculi.Sara Negri - 2002 - Journal of Philosophical Logic 31 (6):569-590.
Proof Theory and Formal Grammars: Applications of Normalization.Hans-Jörg Tiede - 2003 - In Benedikt Löwe, Thoralf Räsch & Wolfgang Malzkorn (eds.), Foundations of the Formal Sciences Ii. Kluwer Academic Publishers. pp. 235--256.
Sequent Calculus in Natural Deduction Style.Sara Negri & Jan von Plato - 2001 - Journal of Symbolic Logic 66 (4):1803-1816.

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