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41
Quantum Logic and NonCommutative Geometry
, 2004
"... We propose a general scheme for the “logic ” of elementary propositions of physical systems, encompassing both classical and quantum cases, in the framework given by Non Commutative Geometry. It involves Baire*algebras, the noncommutative version of measurable functions, arising as envelope of the ..."
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We propose a general scheme for the “logic ” of elementary propositions of physical systems, encompassing both classical and quantum cases, in the framework given by Non Commutative Geometry. It involves Baire*algebras, the noncommutative version of measurable functions, arising as envelope
Relating Natural Deduction and Sequent Calculus for Intuitionistic NonCommutative Linear Logic
, 1999
"... We present a sequent calculus for intuitionistic noncommutative linear logic (INCLL) , show that it satisfies cut elimination, and investigate its relationship to a natural deduction system for the logic. We show how normal natural deductions correspond to cutfree derivations, and arbitrary natura ..."
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Cited by 29 (16 self)
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We present a sequent calculus for intuitionistic noncommutative linear logic (INCLL) , show that it satisfies cut elimination, and investigate its relationship to a natural deduction system for the logic. We show how normal natural deductions correspond to cutfree derivations, and arbitrary
Entropic hopf algebras and models of noncommutative linear logic
 THEORY AND APPLICATIONS OF CATEGORIES 10
, 2002
"... We give a definition of categorical model for the multiplicative fragment of noncommutative logic. We call such structures entropic categories. We demonstrate the soundness and completeness of our axiomatization with respect to cutelimination. We then focus on several methods of building entropic ..."
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Cited by 6 (3 self)
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We give a definition of categorical model for the multiplicative fragment of noncommutative logic. We call such structures entropic categories. We demonstrate the soundness and completeness of our axiomatization with respect to cutelimination. We then focus on several methods of building entropic
Proof nets Construction and Automated Deduction in NonCommutative Linear Logic (Extended Abstract)
 Electronic Notes in Theoretical Computer Science
, 1998
"... Proof nets can be seen as a multiple conclusion natural deduction system for Linear Logic (LL) and form a good formalism to analyze some computation mechanisms, for instance in typetheoretic interpretations. This paper presents an algorithm for automated proof nets construction in the noncommutati ..."
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Cited by 6 (5 self)
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Proof nets can be seen as a multiple conclusion natural deduction system for Linear Logic (LL) and form a good formalism to analyze some computation mechanisms, for instance in typetheoretic interpretations. This paper presents an algorithm for automated proof nets construction in the noncommutative
MFPS XV Preliminary Version Relating Natural Deduction and Sequent Calculus for Intuitionistic NonCommutative Linear Logic
"... We present a sequent calculus for intuitionistic noncommutative linear logic (INCLL), show that it satisfies cut elimination, and investigate its relationship to a natural deduction system for the logic. We show how normal natural deductions correspond to cutfree derivations, and arbitrary natura ..."
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We present a sequent calculus for intuitionistic noncommutative linear logic (INCLL), show that it satisfies cut elimination, and investigate its relationship to a natural deduction system for the logic. We show how normal natural deductions correspond to cutfree derivations, and arbitrary
Twisted (2+1) κAdS Algebra, Drinfel’d Doubles and NonCommutative Spacetimes?
"... Abstract. We construct the full quantum algebra, the corresponding Poisson–Lie structure and the associated quantum spacetime for a family of quantum deformations of the isometry algebras of the (2+1)dimensional antide Sitter (AdS), de Sitter (dS) and Minkowski spaces. These deformations correspon ..."
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Cited by 1 (0 self)
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 and timelike κAdS and dS quantum algebras; their flat limit Λ → 0 leads to a twisted quantum Poincare ́ algebra. The resulting noncommutative spacetime is a nonlinear Λdeformation of the κMinkowski one plus an additional contribution generated by the twist. For the AdS case, we relate this quantum
An Open Logical Framework
"... The LFP Framework is an extension of the HarperHonsellPlotkin’s Edinburgh Logical Framework LF with external predicates, hence the name Open Logical Framework. This is accomplished by defining lock type constructors, which are a sort of ⋄modality constructors, releasing their argument under the ..."
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of logical systems which would otherwise be awkwardly encoded in LF, e.g. sideconditions in the application of rules in Modal Logics, and substructural rules, as in noncommutative Linear Logic. The idea of LFP is that these conditions need only to be specified, while their verification can be delegated
LFP  A Logical Framework with External Predicates
, 2012
"... The LFP Framework is an extension of the HarperHonsellPlotkin’s Edinburgh Logical Framework LF with external predicates. This is accomplished by defining lock type constructors, which are a sort of ⋄modality constructors, releasing their argument under the condition that a possibly external predi ..."
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Cited by 5 (1 self)
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, would be awkwardly encoded in LF, e.g. sideconditions in the application of rules in Modal Logics, and substructural rules, as in noncommutative Linear Logic. The idea of LFP is that these conditions need only to be specified, while their verification can be delegated to an external proof engine
The Logic of Linear Functors
 Math. Structures Comput. Sci
, 2002
"... This paper describes a family of logics whose categorical semantics is based on functors with structure rather than on categories with structure. This allows the consideration of logics which contain possibly distinct logical subsystems whose interactions are mediated by functorial mappings. For exa ..."
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Cited by 9 (4 self)
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. For example, within one unified framework, we shall be able to handle logics as diverse as modal logic, ordinary linear logic, and the "noncommutative logic" of Abrusci and Ruet, a variant of linear logic which has both commutative and noncommutative connectives. Although this paper
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