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A Logical View Of Concurrent Constraint Programming
, 1995
"... . Concurrent Constraint Programming (CCP) has been the subject of growing interest as the focus of a new paradigm for concurrent computation. Like logic programming it claims close relations to logic. In fact CCP languages are logics in a certain sense that we make precise in this paper. In recent ..."
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. Concurrent Constraint Programming (CCP) has been the subject of growing interest as the focus of a new paradigm for concurrent computation. Like logic programming it claims close relations to logic. In fact CCP languages are logics in a certain sense that we make precise in this paper. In recent work it was shown that the denotational semantics of determinate concurrent constraint programming languages forms a fibred categorical structure called a hyperdoctrine, which is used as the basis of the categorical formulation of firstorder logic. What this shows is that the combinators of determinate CCP can be viewed as logical connectives. In this paper we extend these ideas to the operational semantics of such languages and thus make available similar analogies for a much broader variety of languages including indeterminate CCP languages and concurrent blockstructured imperative languages. CR Classification: F3.1, F3.2, D1.3, D3.3 Key words: Concurrent constraint programming, simula...
Countable Lawvere Theories and Computational Effects
, 2006
"... Lawvere theories have been one of the two main category theoretic formulations of universal algebra, the other being monads. Monads have appeared extensively over the past fifteen years in the theoretical computer science literature, specifically in connection with computational effects, but Lawvere ..."
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Cited by 17 (3 self)
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Lawvere theories have been one of the two main category theoretic formulations of universal algebra, the other being monads. Monads have appeared extensively over the past fifteen years in the theoretical computer science literature, specifically in connection with computational effects, but Lawvere theories have not. So we define the notion of (countable) Lawvere theory and give a precise statement of its relationship with the notion of monad on the category Set. We illustrate with examples arising from the study of computational effects, explaining how the notion of Lawvere theory keeps one closer to computational practice. We then describe constructions that one can make with Lawvere theories, notably sum, tensor, and distributive tensor, reflecting the ways in which the various computational effects are usually combined, thus giving denotational semantics for the combinations.
Content Selfawareness in Distributed Multimedia Publishing: the Need for a Unifying Theory
, 1997
"... A distributed publishing system is like the pages of a book floating in the breeze: hypertext pulls these together with a nonlinear thread but still leaves the pages like a book withou an index. When the pages belong to multimedia documents, the indexing has not only to be dynamic but to cope als ..."
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Cited by 4 (2 self)
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A distributed publishing system is like the pages of a book floating in the breeze: hypertext pulls these together with a nonlinear thread but still leaves the pages like a book withou an index. When the pages belong to multimedia documents, the indexing has not only to be dynamic but to cope also with the heterogeneous data structures. A survey of current research projects shows the need for unifying principles. A formal abstract theory of indexing for multimedia objects leads to the concept of machine awareness, presented here in the context of constructive database models and drawing on the latest results using category theory. Geometric logic can provide a universal representation in mathematics of concepts such as objects, limits, adjunctions and Heyting implications, all needed to deal with closure over open document contexts in hypermedia.
A Hyperdoctrinal View of Constraint Systems
 In Lecture Notes in Computer Science 666
, 1993
"... We study a relationship between logic and computation via concurrent constraint programming. In previous papers it has been shown how a simple language for specifying asynchronous concurrent processes can be interpreted in terms of constraints. In the present paper we show that the programming inter ..."
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We study a relationship between logic and computation via concurrent constraint programming. In previous papers it has been shown how a simple language for specifying asynchronous concurrent processes can be interpreted in terms of constraints. In the present paper we show that the programming interpretation via closure operators is intimately related to the logic of the constraints. More precisely we show how the usual hyperdoctrinal description of first order logic can be functorially related to another hyperdoctrine built out of closure operators. The logical connectives map onto constructions on closure operators that turn out to model programming constructs, specifically conjunction becomes parallel composition and existential quantification becomes hiding of local variables. 1 Introduction In this paper we develop a category theoretic view of the relationship between concurrent constraint programming and logic. One may think of this as an explication of the relationship between ...
A generalization of Dijkstra’s calculus to typed program specifications
 In Proc. FCT ’99, volume 1684 of LNCS
, 1999
"... ..."
Locality, Weak or Strong Anticipation and Quantum Computing. I. Nonlocality in Quantum Theory
"... Abstract The universal Turing machine is an anticipatory theory of computability by any digital or quantum machine. However the ChurchTuring hypothesis only gives weak anticipation. The construction of the quantum computer (unlike classical computing) requires theory with strong anticipation. Categ ..."
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Abstract The universal Turing machine is an anticipatory theory of computability by any digital or quantum machine. However the ChurchTuring hypothesis only gives weak anticipation. The construction of the quantum computer (unlike classical computing) requires theory with strong anticipation. Category theory provides the necessary coordinatefree mathematical language which is both constructive and nonlocal to subsume the various interpretations of quantum theory in one pullback/pushout Dolittle diagram. This diagram can be used to test and classify physical devices and proposed algorithms for weak or strong anticipation. Quantum Information Science is more than a merger of ChurchTuring and quantum theories. It has constructively to bridge the nonlocal chasm between the weak anticipation of mathematics and the strong anticipation of physics.
CONDITIONS FOR INTEROPERABILITY
"... Abstract: Interoperability for information systems remains a challenge both at the semantic and organisational levels. The original threelevel architecture for local databases needs to be replaced by a categorical fourlevel one based on concepts, constructions, schema types and data together with ..."
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Abstract: Interoperability for information systems remains a challenge both at the semantic and organisational levels. The original threelevel architecture for local databases needs to be replaced by a categorical fourlevel one based on concepts, constructions, schema types and data together with the mappings between them. Such an architecture provides natural closure as further levels are superfluous even in a global environment. The architecture is traversed by means of the Godement calculus: arrows may be composed at any level as well as across levles. The necessary and sufficient conditions for interoperability are satisfied by composable (formal) diagrams both for intension and extension in categories that are cartesian closed and locally cartesian closed. Methods like partial categories and sketches in schema design can benefit from Freyd’s punctured diagrams to identify precisely typeforcing natural transformations. Closure is better achieved in standard full categories. Global interoperability of extension can be achieved through semantic annotation but only if applied at run time. 1 Classical Data Structures Classical information systems employ some suitable model to mediate between data and
2. Given A f
, 2012
"... These are brief informal notes based on lectures I gave at McGill. There is nothing original about them. 1 Basic definitions A category consists of two “collections ” of things called objects and morphisms or arrows or maps. We write C for a category, C0 for the objects and C1 for the morphisms. The ..."
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These are brief informal notes based on lectures I gave at McGill. There is nothing original about them. 1 Basic definitions A category consists of two “collections ” of things called objects and morphisms or arrows or maps. We write C for a category, C0 for the objects and C1 for the morphisms. They satisfy the following conditions: 1. Every morphism f is associated with two objects (which may be the same) called the domain and codomain of f. One can view a morphism as an arrow from one object to another thus forming a directed graph. We sometimes write cod(f) and dom(f) to denote these objects, more often we give them names like A and B. We write f: A − → B or A f −− → B.
Towards a Definition of an Algorithm
, 2005
"... 1 Introduction In their excellent text Introduction to Algorithms, Second Edition [5], Corman,Leiserson, Rivest, and Stein begin Section 1.1 with a definition of an algorithm: Informally, an algorithm is any welldefined computational procedure that takes some value, or set of values, as ..."
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1 Introduction In their excellent text Introduction to Algorithms, Second Edition [5], Corman,Leiserson, Rivest, and Stein begin Section 1.1 with a definition of an algorithm: Informally, an algorithm is any welldefined computational procedure that takes some value, or set of values, as
Geometric Theory of Machine Awareness for Legal Information Retrieval and Reasoning
, 1995
"... This report 1 considers that links in hypertext are representable as links in thought by covariant arrows between categories. Taken in dynamic context, the rightexactness of the Heyting implication A ) B corresponds to inference and the next document in a nonlinear trail through hypermedia. Aw ..."
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This report 1 considers that links in hypertext are representable as links in thought by covariant arrows between categories. Taken in dynamic context, the rightexactness of the Heyting implication A ) B corresponds to inference and the next document in a nonlinear trail through hypermedia. Awareness is provided by the dual contravariant arrows with the important special case of the intensionextension relationship. The corresponding leftexactness is the closure limit that invokes consciousness. About the author Michael Heather is senior lecturer in law where he has been responsible for computers and law since 1979. Nick Rossiter is lecturer in the Department of Computing Science with particular interests in databases and systems analysis. Suggested Keywords hypertext, legal reasoning, information retrieval, category theory, adjoints, Heyting algebra. 1 The work on geometric logic and law in this report was presented at the 17th IVR World Congress June 16th21st 1995 Chall...