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Chu I: cofree equivalences, dualities and *autonomous categories
, 1993
"... ing from the technique of dual pairs in functional analysis (Kelley, Nanmioka et al. 1963, ch. 5), they defined the objects of their category to be the triples hA; B; A\Omega B OE !?i, where A and B are arbitrary objects of an autonomous category V, and ? is a fixed object, chosen to become duali ..."
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ing from the technique of dual pairs in functional analysis (Kelley, Nanmioka et al. 1963, ch. 5), they defined the objects of their category to be the triples hA; B; A\Omega B OE !?i, where A and B are arbitrary objects of an autonomous category V, and ? is a fixed object, chosen to become dualizing. A morphism from hA; B; OEi to hC; D; fli was defined as a pair hu : A ! C; B / D : vi of Varrows, making the square A\Omega D A\Omega B C\Omega D ? u\Omega D<Fnan><Fnan> fflffl A\Omega v<Fnan><Fnan> // OE<Fnan><Fnan> fflffl fl<Fnan><Fnan> (1) Cofree equivalences, dualities and autonomous categories 3 commute. This is the setting in which the autonomous structure of a Chu category was originally discovered. The starting point of the present paper is the fact that the category described by Chu is isomorphic to the comma category V=? ? , induced by the homming functor ? ? : V op \Gamma! V : A 7\Gamma! A ? = A \Gammaffi? : (2) By definition, the objects of V=? ? (i.e. Id V =?...
Rational mechanics and natural mathematics
 In TAPSOFT'95
, 1995
"... Chu spaces have found applications in computer science, mathematics, and physics. They enjoy a useful categorical duality analogous to that of lattice theory and projective geometry. As natural mathematics Chu spaces borrow ideas from the natural sciences, particularly physics, while as rational mec ..."
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Chu spaces have found applications in computer science, mathematics, and physics. They enjoy a useful categorical duality analogous to that of lattice theory and projective geometry. As natural mathematics Chu spaces borrow ideas from the natural sciences, particularly physics, while as rational mechanics they cast Hamiltonian mechanics in terms of the interaction of body and mind. This paper addresses the chief stumbling block for Descartes ’ 17thcentury philosophy of mindbody dualism, how can the fundamentally dissimilar mental and physical planes causally interact with each other? We apply Cartesian logic to reject not only divine intervention, preordained synchronization, and the eventual mass retreat to monism, but also an assumption Descartes himself somehow neglected to reject, that causal interaction within these planes is an easier problem than between. We use Chu spaces and residuation to derive all causal interaction, both between and within the two planes, from a uniform and algebraically rich theory of betweenplane interaction alone. Lifting the twovalued Boolean logic of binary relations to the complexvalued fuzzy logic of quantum mechanics transforms residuation into a natural generalization of the inner product operation of a Hilbert space and demonstrates that this account of causal interaction is of essentially the same form as the HeisenbergSchrödinger quantummechanical solution to analogous problems of causal interaction in physics. 1 Cartesian Dualism The Chu construction [Bar79] strikes us as extraordinarily useful, more so with every passing month. Elsewhere we have described the application of Chu spaces to process algebra [GP93], metamathematics [Pra93, Pra94a], and physics [Pra94b]. Here we make a first attempt at applying them to philosophy. It might seem that traditional philosophical questions would be beyond the scope of TAPSOFT. Bear in mind however that Boolean logic as the basis for
Configuration Structures, Event Structures and Petri Nets
"... In this paper the correspondence between safe Petri nets and event structures, due to Nielsen, Plotkin and Winskel, is extended to arbitrary nets without selfloops, under the collective token interpretation. To this end we propose a more general form of event structure, matching the expressive powe ..."
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In this paper the correspondence between safe Petri nets and event structures, due to Nielsen, Plotkin and Winskel, is extended to arbitrary nets without selfloops, under the collective token interpretation. To this end we propose a more general form of event structure, matching the expressive power of such nets. These new event structures and nets are connected by relating both notions with configuration structures, which can be regarded as representations of either event structures or nets that capture their behaviour in terms of action occurrences and the causal relationships between them, but abstract from any auxiliary structure. A configuration structure can also be considered logically, as a class of propositional models, or—equivalently— as a propositional theory in disjunctive normal from. Converting this theory to conjunctive normal form is the key
The Impact of Hardware Models on Shared Memory Consistency Conditions
 In Ugo Montanari and Vladimiro Sassone, editors, CONCUR '96
, 1996
"... . Shared memory systems provide a contract to the programmer in the form of a consistency condition. The conditions of atomic memory and sequential consistency provide the illusion of a single memory module, as in the uniprocessor case. Weaker conditions improve performance by sacrificing the simple ..."
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. Shared memory systems provide a contract to the programmer in the form of a consistency condition. The conditions of atomic memory and sequential consistency provide the illusion of a single memory module, as in the uniprocessor case. Weaker conditions improve performance by sacrificing the simple programming model. Consistency conditions are formulated without reference to details of the hardware on which programs execute. We define the notion of a hardware model, a set of limitations on the communication network (e.g., message delay assumptions) and processing nodes (e.g., amount of available memory). We examine the effects of several models on a representative set of consistency conditions. In each model, we show how the conditions are related, and show that some are not appropriate for that model. Our study is carried out through relatively complete implementations, state machines which exactly capture the possible behaviors of all implementations in a given model. In addition t...
EventState Duality: The Enriched Case
"... Enriched categories have been applied in the past to both eventoriented true concurrency models and stateoriented information systems, with no evident relationship between the two. Ordinary Chu spaces expose a natural duality between partially ordered temporal spaces (pomsets, event structures), a ..."
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Enriched categories have been applied in the past to both eventoriented true concurrency models and stateoriented information systems, with no evident relationship between the two. Ordinary Chu spaces expose a natural duality between partially ordered temporal spaces (pomsets, event structures), and partially ordered information systems.
Types as Processes, via Chu spaces
 EXRESS'97 Proceedings
, 1997
"... We match up types and processes by putting values in correspondence with events, coproduct with (noninteracting) parallel composition, and tensor product with orthocurrence. We then bring types and processes into closer correspondence by broadening and unifying the semantics of both using Chu spaces ..."
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We match up types and processes by putting values in correspondence with events, coproduct with (noninteracting) parallel composition, and tensor product with orthocurrence. We then bring types and processes into closer correspondence by broadening and unifying the semantics of both using Chu spaces and their transformational logic. Beyond this point the connection appears to break down; we pose the question of whether the failures of the corrrespondence are intrinsic or cultural. 1 Introduction Typesasprocesses modernizes dataasprograms. It is the CurryHoward propositionsastypes correspondence with propositions replaced by processes. To the extent that types and processes are both part of the working programmer 's toolkit, even more than propositions, the typesasprocesses correspondence is more central to the practice of programming than propositionsastypes. Moreover the connection works out very well mathematically, at least up to a point. The similarities and differences ...
Strategic Directions in Computing Research Concurrency Working Group Report
 BULLETIN OF THE EUROPEAN ASSOCIATION FOR THEORETICAL COMPUTER SCIENCE
, 1996
"... This report focuses on research into models and logics for concurrency and their application in specifying, verifying, and implementing concurrent systems. This general area has become known as concurrency theory , and its roots may be traced back to the 1960s [Dij68, Pet62]. Our aim is to survey th ..."
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This report focuses on research into models and logics for concurrency and their application in specifying, verifying, and implementing concurrent systems. This general area has become known as concurrency theory , and its roots may be traced back to the 1960s [Dij68, Pet62]. Our aim is to survey the rich collection of mature theories and models for concurrency that exist; to review the powerful specification, design, and verification methods and tools that have been developed; and to highlight ongoing active areas of research and suggest fruitful directions for future investigation. By focusing on concurrency theory and its use in verification, we necessarily omit consideration of other concurrencyrelated topics such as concurrency control in database systems, concurrent program debugging, operating systems, distributed system architecture, and realtime systems. The interested reader is referred to other working group reports, which address many of these topics.
A Generic Tool for Modelling and Simulating the Behaviour of Concurrent Systems
, 1998
"... This report summarises the development of a portable, persistent and generic tool for modelling, exploring and analysing the behaviour of concurrent systems. The design is based on the general Action language theory for nondeterministic concurrent programming languages, and hence the tool is called ..."
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This report summarises the development of a portable, persistent and generic tool for modelling, exploring and analysing the behaviour of concurrent systems. The design is based on the general Action language theory for nondeterministic concurrent programming languages, and hence the tool is called the Action language workbench. It has been developed using an algebraic style and implemented in the algebraic programming system APS. The generic algebraicbased approach enables workbench to be applied to many languages by means of rapid prototyping and generation of action languages. A number of applications of the workbench to concurrent constraint and coordination languages, as well as its probabilistic extension are reported. Currently the functionality of the tool is restricted to simulation. Further development of both the underlying theory and the tool is planned regarding the description of distributed systems and the ehnancement of the kinds of analyses which can be performed. 1 I...
Languages for Concurrency
"... This essay offers an overview of basic aspects and central development in Concurrency Theory based on formal languages. In particular, it focuses on the theory of Process Calculi. 1 ..."
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This essay offers an overview of basic aspects and central development in Concurrency Theory based on formal languages. In particular, it focuses on the theory of Process Calculi. 1
Chu Spaces: Towards New Justification for Fuzzy Heuristics
, 2000
"... We show that Chu spaces, a new formalism used to describe parallelism and information flow, provide uniform explanations for different choices of fuzzy methodology, such as choices of fuzzy logical operations, of membership functions, of defuzzification, etc. 1 What Are Chu Spaces? 1.1 World Acc ..."
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We show that Chu spaces, a new formalism used to describe parallelism and information flow, provide uniform explanations for different choices of fuzzy methodology, such as choices of fuzzy logical operations, of membership functions, of defuzzification, etc. 1 What Are Chu Spaces? 1.1 World According to Classical Physics It is well known that measurements can change the measured object: e.g., most methods of chemical analysis destroy a part of the analyzed substance; testing a car often means damaging it, etc. However, in classical (prequantum) physics it was assumed that in principle, we can make this adverse influence as small as possible. Therefore, ideally, each measurement can be described as a function r(x) from the set of all objects X to the set K of all measurement results. These measurements lead to a complete knowledge in the sense that an object x can be uniquely reconstructed from the results r(x) of all such measurements. 1.2 NonDeterminism in Modern Physics: En...