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Interaction Categories and the Foundations of Typed Concurrent Programming
 In Deductive Program Design: Proceedings of the 1994 Marktoberdorf Summer School, NATO ASI Series F
, 1995
"... We propose Interaction Categories as a new paradigm for the semantics of functional and concurrent computation. Interaction categories have specifications as objects, processes as morphisms, and interaction as composition. We introduce two key examples of interaction categories for concurrent compu ..."
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Cited by 123 (19 self)
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We propose Interaction Categories as a new paradigm for the semantics of functional and concurrent computation. Interaction categories have specifications as objects, processes as morphisms, and interaction as composition. We introduce two key examples of interaction categories for concurrent computation and indicate how a general axiomatisation can be developed. The upshot of our approach is that traditional process calculus is reconstituted in functorial form, and integrated with type theory and functional programming.
Bisimulation for Probabilistic Transition Systems: A Coalgebraic Approach
, 1998
"... . The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a ..."
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Cited by 75 (15 self)
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. The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a continuous setting involving Borel probability measures. Under reasonable conditions, generalized probabilistic bisimilarity can be characterized categorically. Application of the final coalgebra paradigm then yields an internally fully abstract semantical domain with respect to probabilistic bisimulation. Keywords. Bisimulation, probabilistic transition system, coalgebra, ultrametric space, Borel measure, final coalgebra. 1 Introduction For discrete probabilistic transition systems the notion of probabilistic bisimilarity of Larsen and Skou [LS91] is regarded as the basic process equivalence. The definition was given for reactive systems. However, Van Glabbeek, Smolka and Steffen s...
A Typed Calculus of Synchronous Processes
 In Proceedings of IEEE Symposium on Logic in Computer Science
, 1995
"... We propose a typed calculus of synchronous processes based on the structure of interaction categories. Our aim has been to develop a calculus for concurrency that is canonical in the sense that the typed calculus is canonical for functional computation. We show strong connections between syntax, lo ..."
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Cited by 56 (4 self)
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We propose a typed calculus of synchronous processes based on the structure of interaction categories. Our aim has been to develop a calculus for concurrency that is canonical in the sense that the typed calculus is canonical for functional computation. We show strong connections between syntax, logic and semantics, analogous to the familiar correspondence between the typed calculus, intuitionistic logic and cartesian closed categories. 1 Introduction T ypes are fundamental to the study of functional computation, for both theoretical and practical reasons. On the foundational side there are elegant connections between the typed calculus, intuitionistic logic and cartesian closed categories, leading to the Propositions as Types paradigm [14] and the development of categorical logic [9,17]. From a practical point of view, compiletime type reconstruction is a boon to the programmer in languages such as Standard ML and Haskell. Turning to concurrency, the situation is much less sati...
A Formalization of Viewpoints
 FUNDAMENTA INFORMATICAE
, 1995
"... We present a formalisation for the notion of viewpoint , a construct meant for expressing several varieties of relativised truth. The formalisation consists in a logic which extends first order predicate calculus through an axiomatization of provability and with the addition of proper reflection rul ..."
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Cited by 34 (3 self)
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We present a formalisation for the notion of viewpoint , a construct meant for expressing several varieties of relativised truth. The formalisation consists in a logic which extends first order predicate calculus through an axiomatization of provability and with the addition of proper reflection rules. The extension is not conservative, but consistency is granted. Viewpoints are defined as set of reified metalevel sentences. A proof theory for viewponts is developed which enables to carry out proofs of sentences involving several viewpoints. A semantic account of viewpoints is provided, dealing with issues of self referential theories and paradoxes, and exploiting the notion of contextual entailment . Notions such as beliefs, knowledge, truth and situations can be uniformly modeled as provability in specialised viewpoints, obtained by imposing suitable constraints on viewpoints.
Intuitionistic Sets and Ordinals
 Journal of symbolic Logic
, 1996
"... Transitive extensional well founded relations provide an intuitionistic notion of ordinals which admits transfinite induction. However these ordinals are not directed and their successor operation is poorly behaved, leading to problems of functoriality. We show how to make the successor monotone by ..."
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Cited by 8 (1 self)
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Transitive extensional well founded relations provide an intuitionistic notion of ordinals which admits transfinite induction. However these ordinals are not directed and their successor operation is poorly behaved, leading to problems of functoriality. We show how to make the successor monotone by introducing plumpness, which strengthens transitivity. This clarifes the traditional development of successors and unions, making it intuitionistic; even the (classical) proof of trichotomy is made simpler. The definition is, however, recursive, and, as their name suggests, the plump ordinals grow very rapidly. Directedness must be defined hereditarily. It is orthogonal to the other four conditions, and the lower powerdomain construction is shown to be the universal way of imposing it. We treat ordinals as ordertypes, and develop a corresponding set theory similar to Osius’ transitive set objects. This presents Mostowski’s theorem as a reflection of categories, and settheoretic union is a corollary of the adjoint functor theorem. Mostowski’s theorem and the rank for some of the notions of ordinal are formulated and proved without the axiom of replacement, but this seems to be unavoidable for the plump rank. The comparison between sets and toposes is developed as far as the identification of replacement with completeness and there are some suggestions for further work in this area. Each notion of set or ordinal defines a free algebra for one of the theories discussed by Joyal and Moerdijk, namely joins of a family of arities together with an operation s satisfying conditions such as x ≤ sx, monotonicity or s(x ∨ y) ≤ sx ∨ sy. Finally we discuss the fixed point theorem for a monotone endofunction s of a poset with least element and directed joins. This may be proved under each of a variety of additional hypotheses. We explain why it is unlikely that any notion of ordinal obeying the induction scheme for arbitrary predicates will prove the pure result.
Modelling SIGNAL in Interaction Categories
 THEORY AND FORMAL METHODS 1993: PROCEEDINGS OF THE FIRST IMPERIAL COLLEGE DEPARTMENT OF COMPUTING WORKSHOP ON THEORY AND FORMAL METHODS. SPRINGERVERLAG WORKSHOPS IN COMPUTER SCIENCE
, 1993
"... Abramsky has recently proposed Interaction Categories as a new paradigm for the semantics of sequential and parallel computation. Working with the category SProc of synchronous processes, which is a key example of an Interaction Category, we study synchronous dataflow as part of a programme of gain ..."
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Cited by 3 (1 self)
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Abramsky has recently proposed Interaction Categories as a new paradigm for the semantics of sequential and parallel computation. Working with the category SProc of synchronous processes, which is a key example of an Interaction Category, we study synchronous dataflow as part of a programme of gaining experience in the use of Interaction Categories. After making some general points about representing dataflow in SProc, we present a detailed model of the synchronous dataflow language Signal. We demonstrate that dataflow is a model of concurrency which can easily be treated in a typed framework, and that the structure of Interaction Categories is appropriate for describing real concurrent languages.
Perspectives and the Referential Use of Definite Descriptions in Dialogue
"... This is an investigation into the pragmatics of the referential use of de nite descriptions. We examine situations where a speaker uses a description to induce a hearer to pick out a certain object from a set of mutually given objects, in order to state some proposition about this object. ..."
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Cited by 2 (1 self)
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This is an investigation into the pragmatics of the referential use of de nite descriptions. We examine situations where a speaker uses a description to induce a hearer to pick out a certain object from a set of mutually given objects, in order to state some proposition about this object.
Why sets?
 PILLARS OF COMPUTER SCIENCE: ESSAYS DEDICATED TO BORIS (BOAZ) TRAKHTENBROT ON THE OCCASION OF HIS 85TH BIRTHDAY, VOLUME 4800 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2008
"... Sets play a key role in foundations of mathematics. Why? To what extent is it an accident of history? Imagine that you have a chance to talk to mathematicians from a faraway planet. Would their mathematics be setbased? What are the alternatives to the settheoretic foundation of mathematics? Besi ..."
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Cited by 2 (0 self)
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Sets play a key role in foundations of mathematics. Why? To what extent is it an accident of history? Imagine that you have a chance to talk to mathematicians from a faraway planet. Would their mathematics be setbased? What are the alternatives to the settheoretic foundation of mathematics? Besides, set theory seems to play a significant role in computer science; is there a good justification for that? We discuss these and some related issues.
Abstract Refactored Characteristics of Intelligent Computing Systems
"... We have discussed the following measurable characteristics of intelligent behavior in computing systems: (1) speed and scope of adaptibility to unforeseen situations; (2) rate of effective learning of observations; (3) accurate modeling and prediction of the relevant external environment; (4) speed ..."
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Cited by 1 (0 self)
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We have discussed the following measurable characteristics of intelligent behavior in computing systems: (1) speed and scope of adaptibility to unforeseen situations; (2) rate of effective learning of observations; (3) accurate modeling and prediction of the relevant external environment; (4) speed and clarity of problem identification and formulation; (5) effective association and evaluation of disparate information; (6) identification of more important assumptions and prerequisites; (7) creation and use of symbolic language. In this paper, we isolate some common underlying capabilities for these characteristics, and show how they can all be produced using those capabilities. We describe the architecture of a system that has all of these underlying capabilities, using our Wrapping integration infrastructure to coordinate and organize a large collection of models and other computational resources. In particular, these models include complete models of the system’s resources and processing strategies, and therefore a model of its own behavior, which it can use to affect that behavior.
Dynamische Symbolsysteme (Dynamic Symbol Systems)
, 1994
"... This thesis introduces dynamic symbol systems (DSS). The approach combines a symbolic format of information with a selforganizing dynamics. It is primarily intended for the modeling of intelligent, situated agents. The basic information processing module is a selforganizing stream. In computation ..."
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This thesis introduces dynamic symbol systems (DSS). The approach combines a symbolic format of information with a selforganizing dynamics. It is primarily intended for the modeling of intelligent, situated agents. The basic information processing module is a selforganizing stream. In computational terms, this is an anytimealgorithm for the processing of information that comes in a quite general stream format. In terms of thermodynamic systems, it is an open, dissipative, rapidly selforganizing system. In terms of cognitive science, a selforganizing stream is a module that can appear at any place from the peripheric sensomotoric interface to the central conceptual level, performing tasks of pattern completion, noise filtering, and gestalt formation. Different selforganizing streams can be coupled, yielding complex, selforganizing information processing systems. These associeties can span the entire peripherycentre axis of an agent. Topdown and bottomup influences mutually su...