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A Categorical Semantics of Quantum Protocols
 In: Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LiCS‘04), IEEE Computer Science
"... Quantum information and computation is concerned with the use of quantummechanical systems to carry out computational and informationprocessing tasks [16]. In the few short years that this approach has been studied, a ..."
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Cited by 254 (47 self)
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Quantum information and computation is concerned with the use of quantummechanical systems to carry out computational and informationprocessing tasks [16]. In the few short years that this approach has been studied, a
Categorical semantics of linear logic
 In: Interactive Models of Computation and Program Behaviour, Panoramas et Synthèses 27, Société Mathématique de France 1–196
, 2009
"... Proof theory is the result of a short and tumultuous history, developed on the periphery of mainstream mathematics. Hence, its language is often idiosyncratic: sequent calculus, cutelimination, subformula property, etc. This survey is designed to guide the novice reader and the itinerant mathematic ..."
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Cited by 9 (0 self)
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rewarding: to date, no language (either formal or informal) has been studied by mathematicians as thoroughly as the language of proofs. We start the survey by a short introduction to proof theory (Chapter 1) followed by an informal explanation of the principles of denotational semantics (Chapter 2) which we
Attribute grammars and categorical semantics
 In: ICALP
"... Abstract. We give a new formulation of attribute grammars (AG for short) called monoidal AGs in traced symmetric monoidal categories. Monoidal AGs subsume existing domaintheoretic, graphtheoretic and relational formulations of AGs. Using a 2categorical aspect of monoidal AGs, we also show that ev ..."
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Cited by 3 (1 self)
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Abstract. We give a new formulation of attribute grammars (AG for short) called monoidal AGs in traced symmetric monoidal categories. Monoidal AGs subsume existing domaintheoretic, graphtheoretic and relational formulations of AGs. Using a 2categorical aspect of monoidal AGs, we also show
A Monadic Categorical Semantics for Threads
"... Rather than relegating threads to be a machinelevel concept, it is possible to describe thread semantics at the programminglanguage level. Here, a categorical semantics is given for a potentially multithreaded programming language. The thread behavior is packaged as a monad, and the semantics is d ..."
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Rather than relegating threads to be a machinelevel concept, it is possible to describe thread semantics at the programminglanguage level. Here, a categorical semantics is given for a potentially multithreaded programming language. The thread behavior is packaged as a monad, and the semantics
Categorical Semantics Of Parallel Program Design
, 1997
"... We formalise, using Category Theory, modularisation techniques for parallel and distributed systems based on the notion of superposition, showing that parallel program design obeys the "universal laws" formulated by J.Goguen for General Systems Theory, as well as other algebraic propertie ..."
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Cited by 34 (12 self)
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properties of modularity formulated for Specification Theory. The resulting categorical formalisation unifies the different notions of superposition that have been proposed in the literature and clarifies their algebraic properties with respect to modularisation. It also suggests ways of extending
A categorical semantics for polarized mall
 Ann. Pure Appl. Logic
"... In this paper, we present a categorical model for Multiplicative Additive Polarized Linear Logic MALLP, which is the linear fragment (without structural rules) of Olivier Laurent’s Polarized Linear Logic. Our model is based on an adjunction between reflective/coreflective full subcategories C−/C+ of ..."
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Cited by 4 (1 self)
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In this paper, we present a categorical model for Multiplicative Additive Polarized Linear Logic MALLP, which is the linear fragment (without structural rules) of Olivier Laurent’s Polarized Linear Logic. Our model is based on an adjunction between reflective/coreflective full subcategories C
Categorical Semantics of Linear Logic For All
"... This paper is a survey of results on categorical modeling of linear ..."
On the categorical semantics of Elementary Linear Logic
, 2009
"... We introduce the notion of elementary Seely category as a notion of categorical model of Elementary Linear Logic (ELL) inspired from Seely’s definition of models of Linear Logic (LL). In order to deal with additive connectives in ELL, we use the approach of Danos and Joinet [DJ03]. From the catego ..."
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Cited by 1 (0 self)
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We introduce the notion of elementary Seely category as a notion of categorical model of Elementary Linear Logic (ELL) inspired from Seely’s definition of models of Linear Logic (LL). In order to deal with additive connectives in ELL, we use the approach of Danos and Joinet [DJ03]. From
Convexity, Categorical Semantics and the Foundations of Physics
"... We consider symmetric monoidal categories of convex operational models, and adduce necessary and sufficient conditions for these to be compactclosed or daggercompact. Compact closure amounts to the condition that all processes be implementable by means of a “remote evaluation ” protocol (generalizi ..."
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We consider symmetric monoidal categories of convex operational models, and adduce necessary and sufficient conditions for these to be compactclosed or daggercompact. Compact closure amounts to the condition that all processes be implementable by means of a “remote evaluation ” protocol (generalizing standard conclusive quantum teleportation protocols), which amounts to a form of classical conditioning. This requires the existence, for each system, of a bipartite state involving a further system, whose corresponding conditioning map is an isomorphism, and an an effect whose corresponding map is the inverse of this isomorphism. Degenerate compact closure, in which systems act as their own duals in the compact structure, means that one may take this extension to be the system itself, so the isomorphism implies that systems are weakly selfdual as ordered vector spaces. Degenerate dagger compact categories emerge from a further restriction, namely, that the bipartite “isomorphism ” state and effect be symmetric. It is natural to model physical theories as categories, with objects representing physical
HOMOTOPICAL EQUIVALENCE OF COMBINATORIAL AND CATEGORICAL SEMANTICS OF PROCESS ALGEBRA
, 711
"... Abstract. It is possible to translate a modified version of K. Worytkiewicz’s combinatorial semantics of CCS (Milner’s Calculus of Communicating Systems) in terms of labelled precubical sets into a categorical semantics of CCS in terms of labelled flows using a geometric realization functor. It turn ..."
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Abstract. It is possible to translate a modified version of K. Worytkiewicz’s combinatorial semantics of CCS (Milner’s Calculus of Communicating Systems) in terms of labelled precubical sets into a categorical semantics of CCS in terms of labelled flows using a geometric realization functor
Results 1  10
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2,187