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V. Michele Abrusci (1991). Phase Semantics and Sequent Calculus for Pure Noncommutative Classical Linear Propositional Logic.

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  1.  1
    Substructural Logics, Pragmatic Enrichment, and the Inferential Role of Logical Constants.Pilar Terrés Villalonga - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy:1-27.
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  2.  13
    Contrary-to-Duty Reasoning: A Categorical Approach.Clayton Peterson - 2015 - Logica Universalis 9 (1):47-92.
    This paper provides an analysis of contrary-to-duty reasoning from the proof-theoretical perspective of category theory. While Chisholm’s paradox hints at the need of dyadic deontic logic by showing that monadic deontic logics are not able to adequately model conditional obligations and contrary-to-duties, other arguments can be objected to dyadic approaches in favor of non-monotonic foundations. We show that all these objections can be answered at one fell swoop by modeling conditional obligations within a deductive system defined as an instance of (...)
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    Strong Negation in Intuitionistic Style Sequent Systems for Residuated Lattices.Michał Kozak - 2014 - Mathematical Logic Quarterly 60 (4-5):319-334.
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  4.  11
    Cut Elimination and Strong Separation for Substructural Logics: An Algebraic Approach.Nikolaos Galatos & Hiroakira Ono - 2010 - Annals of Pure and Applied Logic 161 (9):1097-1133.
    We develop a general algebraic and proof-theoretic study of substructural logics that may lack associativity, along with other structural rules. Our study extends existing work on substructural logics over the full Lambek Calculus [34], Galatos and Ono [18], Galatos et al. [17]). We present a Gentzen-style sequent system that lacks the structural rules of contraction, weakening, exchange and associativity, and can be considered a non-associative formulation of . Moreover, we introduce an equivalent Hilbert-style system and show that the logic associated (...)
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  5.  74
    Symmetric Categorial Grammar.Michael Moortgat - 2009 - Journal of Philosophical Logic 38 (6):681-710.
    The Lambek-Grishin calculus is a symmetric version of categorial grammar obtained by augmenting the standard inventory of type-forming operations (product and residual left and right division) with a dual family: coproduct, left and right difference. Interaction between these two families is provided by distributivity laws. These distributivity laws have pleasant invariance properties: stability of interpretations for the Curry-Howard derivational semantics, and structure-preservation at the syntactic end. The move to symmetry thus offers novel ways of reconciling the demands of natural language (...)
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  6.  46
    Proper Semantics for Substructural Logics, From a Stalker Theoretic Point of View.Sato Kentaro - 2008 - Studia Logica 88 (2):295-324.
    We study filters in residuated structures that are associated with congruence relations (which we call -filters), and develop a semantical theory for general substructural logics based on the notion of primeness for those filters. We first generalize Stone’s sheaf representation theorem to general substructural logics and then define the primeness of -filters as being “points” (or stalkers) of the space, the spectrum, on which the representing sheaf is defined. Prime FL-filters will turn out to coincide with truth sets under various (...)
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    2005 Summer Meeting of the Association for Symbolic Logic. Logic Colloquium'05.Stan S. Wainer - 2006 - Bulletin of Symbolic Logic 12 (2):310-361.
  8.  4
    Linear Läuchli Semantics.R. F. Blute & P. J. Scott - 1996 - Annals of Pure and Applied Logic 77 (2):101-142.
    We introduce a linear analogue of Läuchli's semantics for intuitionistic logic. In fact, our result is a strengthening of Läuchli's work to the level of proofs, rather than provability. This is obtained by considering continuous actions of the additive group of integers on a category of topological vector spaces. The semantics, based on functorial polymorphism, consists of dinatural transformations which are equivariant with respect to all such actions. Such dinatural transformations are called uniform. To any sequent in Multiplicative Linear Logic (...)
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