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29
Presheaf Models for Concurrency
, 1999
"... In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their wo ..."
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Cited by 45 (19 self)
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In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their work inspired this thesis by suggesting that presheaf categories could provide abstract models for concurrency with a builtin notion of bisimulation. We show how
Pseudo limits, biadjoints, and pseudo algebras: categorical foundations of conformal field theory
 Mem. Amer. Math. Soc
"... The purpose of this paper is to work out the categorical basis for the foundations of Conformal Field Theory. The definition of Conformal Field Theory was outlined in Segal [45] and recently given in [24] and [25]. Concepts of 2category theory, such as versions of algebra, limit, colimit, and adjun ..."
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Cited by 18 (8 self)
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The purpose of this paper is to work out the categorical basis for the foundations of Conformal Field Theory. The definition of Conformal Field Theory was outlined in Segal [45] and recently given in [24] and [25]. Concepts of 2category theory, such as versions of algebra, limit, colimit, and adjunction, are necessary for this
Profunctors, open maps and bisimulation
 Mathematical Structures in Computer Science, To appear. Available from the Glynn Winskelâ€™s web
, 2000
"... ..."
Homotopy theory of simplicial sheaves in completely decomposable topologies
, 2000
"... decomposable topologies ..."
Logic Programming in Tau Categories
 in Computer Science Logic '94 , LNCS 933
, 1995
"... Many features of current logic programming languages are not captured by conventional semantics. Their fundamentally nonground character, and the uniform way in which such languages have been extended to typed domains, subject to constraints, suggest that a categorical treatment of constraint domai ..."
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Cited by 8 (4 self)
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Many features of current logic programming languages are not captured by conventional semantics. Their fundamentally nonground character, and the uniform way in which such languages have been extended to typed domains, subject to constraints, suggest that a categorical treatment of constraint domains, of programming syntax and of semantics may be closer in spirit to what declarative programming is really about, than conventional settheoretic semantics. We generalize the notion of a (manysorted) logic program and of a resolution proof, by defining them both over a (not necessarily free) category C , a category with products enriched with a mechanism for canonically manipulating nary relations [8]. Computing over this domain includes computing over the Herbrand Universe, and over equationally presented constraint domains as special cases. We give a categorical treatment of the fixpoint semantics of Kowalski and van Emden, which establishes completeness in a very general setting. 1 In...
Categorical Models for Concurrency: Independence, Fairness and Dataflow
 BRICS DISSERTATION SERIES DS001
, 2000
"... This thesis is concerned with formal semantics and models for concurrent computational systems, that is, systems consisting of a number of parallel computing sequential systems, interacting with each other and the environment. A formal semantics gives meaning to computational systems by describing t ..."
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Cited by 6 (4 self)
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This thesis is concerned with formal semantics and models for concurrent computational systems, that is, systems consisting of a number of parallel computing sequential systems, interacting with each other and the environment. A formal semantics gives meaning to computational systems by describing their behaviour in a mathematical model. For concurrent systems the interesting aspect of their computation is often how they interact with the environment during a computation and not in which state they terminate, indeed they may not be intended to terminate at all. For this reason they are often referred to as reactive systems, to distinguish them from traditional calculational systems, as e.g. a program calculating your income tax, for which the interesting behaviour is the answer it gives when (or if) it terminates, in other words the (possibly partial) function it computes between input and output. Church's thesis tells us that regardless of whether we choose the lambda calculus, Turing machines, or almost any modern programming language such as C or Java to describe calculational systems, we are able to describe exactly the same class of functions. However, there is no agreement on observable behaviour for concurrent reactive systems, and consequently there is no correspondent to Church's thesis. A result of this fact is that an overwhelming number of different and often competing notions of observable behaviours, primitive operations, languages and mathematical models for describing their semantics, have been proposed in the litterature on concurrency. The work
Worytkiewicz: A model category for local pospaces
 Homology, Homotopy and Applications
, 506
"... Abstract. Locally partialordered spaces (local pospaces) have been used to model concurrent systems. We provide equivalences for these spaces by ..."
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Cited by 6 (2 self)
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Abstract. Locally partialordered spaces (local pospaces) have been used to model concurrent systems. We provide equivalences for these spaces by
Towards a General Approach for Modeling Actions and Change in Cooperating Agents Scenarios
 Journal of the IGPL
, 1995
"... . The ultimate aim of this work is to find a semantics for reasoning about actions and change in cooperating agent scenarios based on the concept of so called logical fiberings. As a first step in this direction we describe a small but nontrivial 3agentrobotics scenario using two different method ..."
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Cited by 4 (1 self)
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. The ultimate aim of this work is to find a semantics for reasoning about actions and change in cooperating agent scenarios based on the concept of so called logical fiberings. As a first step in this direction we describe a small but nontrivial 3agentrobotics scenario using two different methods, viz. resourceoriented deductive planning and the mathematical framework of logical fiberings. By means of this scenario both methods are illustrated, compared and the correspondences between the basic notions for both methods are clarified. The fiberings method is found to be very useful in modeling communication and interaction between cooperating agents, due to the possibility to switch between a local/global point of view which is inherent to this framework. We formulate a generic modeling principle using this notion. Furthermore, possible extensions of the framework, like formulas depending on space and/or time, are discussed. 1 Introduction The objective of this work is to provide ...
Ind and pro definable sets
, 2006
"... Abstract. We describe the ind and pro categories of the category of definable sets, in some first order theory, in terms of points in a sufficiently saturated model. 1. ..."
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Cited by 4 (0 self)
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Abstract. We describe the ind and pro categories of the category of definable sets, in some first order theory, in terms of points in a sufficiently saturated model. 1.
A Note On The Exact Completion Of A Regular Category, And Its Infinitary Generalizations
, 1999
"... A new description of the exact completion C ex/reg of a regular category C is given, using a certain topos Shv(C) of sheaves on C; the exact completion is then constructed as the closure of C in Shv(C) under finite limits and coequalizers of equivalence relations. An infinitary generalization is ..."
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Cited by 4 (1 self)
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A new description of the exact completion C ex/reg of a regular category C is given, using a certain topos Shv(C) of sheaves on C; the exact completion is then constructed as the closure of C in Shv(C) under finite limits and coequalizers of equivalence relations. An infinitary generalization is proved, and the classical description of the exact completion is derived.