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V. Michele Abrusci & Paul Ruet (1999). Non-Commutative Logic I: The Multiplicative Fragment.

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  1.  1
    On Vidal's Trivalent Explanations for Defective Conditional in Mathematics.Yaroslav Petrukhin & Vasily Shangin - forthcoming - Journal of Applied Non-Classical Logics:1-14.
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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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  3.  22
    Non-Normal Modalities in Variants of Linear Logic.D. Porello & N. Troquard - 2015 - Journal of Applied Non-Classical Logics 25 (3):229-255.
    This article presents modal versions of resource-conscious logics. We concentrate on extensions of variants of linear logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have shown that the results scale up to logics with multiple non-minimal modalities. Here, we start with the language of propositional intuitionistic linear logic without the additive disjunction, to which we add a modality. We provide an interpretation of this language on a class of Kripke resource models (...)
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  4.  5
    A Logical Calculus for Controlled Monotonicity.Marcello D'Agostino, Mario Piazza & Gabriele Pulcini - 2014 - Journal of Applied Logic 12 (4):558-569.
  5.  2
    A Geometrical Procedure for Computing Relaxation.Gabriele Pulcini - 2009 - Annals of Pure and Applied Logic 158 (1-2):80-89.
    Permutative logic is a non-commutative conservative extension of linear logic suggested by some investigations on the topology of linear proofs. In order to syntactically reflect the fundamental topological structure of orientable surfaces with boundary, permutative sequents turn out to be shaped like q-permutations. Relaxation is the relation induced on q-permutations by the two structural rules divide and merge; a decision procedure for relaxation has been already provided by stressing some standard achievements in theory of permutations. In these pages, we provide (...)
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  6.  17
    Applying Pregroups to Italian Statements and Questions.Claudia Casadio - 2007 - Studia Logica 87 (2-3):253-268.
    We know from the literature in theoretical linguistics that interrogative constructions in Italian have particular syntactic properties, due to the liberal word order and the rich inflectional system. In this paper we show that the calculus of pregroups represents a flexible and efficient computational device for the analysis and derivation of Italian sentences and questions. In this context the distinction between direct vs. indirect statements and questions is explored.
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    Non-Commutative Proof Construction: A Constraint-Based Approach.Jean-Marc Andreoli, Roberto Maieli & Paul Ruet - 2006 - Annals of Pure and Applied Logic 142 (1):212-244.
    This work presents a computational interpretation of the construction process for cyclic linear logic and non-commutative logic sequential proofs. We assume a proof construction paradigm, based on a normalisation procedure known as focussing, which efficiently manages the non-determinism of the construction. Similarly to the commutative case, a new formulation of focussing for NL is used to introduce a general constraint-based technique in order to dealwith partial information during proof construction. In particular, the procedure develops through construction steps propagating constraints in (...)
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  8.  17
    Modularity of Proof-Nets.Roberto Maieli & Quintijn Puite - 2004 - Archive for Mathematical Logic 44 (2):167-193.
    When we cut a multiplicative proof-net of linear logic in two parts we get two modules with a certain border. We call pretype of a module the set of partitions over its border induced by Danos-Regnier switchings. The type of a module is then defined as the double orthogonal of its pretype. This is an optimal notion describing the behaviour of a module: two modules behave in the same way precisely if they have the same type.In this paper we define (...)
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