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45
Linearity in Process Languages
"... The meaning and mathematical consequences of linearity (managing without a presumed ability to copy) are studied for a pathbased model of processes which is also amodel of affinelinear logic. This connection yields an affinelinear language for processes, automatically respecting openmap bisim ..."
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Cited by 13 (10 self)
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The meaning and mathematical consequences of linearity (managing without a presumed ability to copy) are studied for a pathbased model of processes which is also amodel of affinelinear logic. This connection yields an affinelinear language for processes, automatically respecting openmap bisimulation, in which a range of process operations can be expressed. An operational semantics isprovided for the tensor fragment of the language. Different ways to make assemblies of processes lead to differentchoices of exponential, some of which respect bisimulation.
Information Systems for Continuous Posets
, 1993
"... The method of information systems is extended from algebraic posets to continuous posets by taking a set of tokens with an ordering that is transitive and interpolative but not necessarily reflexive. This develops results of Raney on completely distributive lattices and of Hoofman on continuous S ..."
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Cited by 11 (2 self)
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The method of information systems is extended from algebraic posets to continuous posets by taking a set of tokens with an ordering that is transitive and interpolative but not necessarily reflexive. This develops results of Raney on completely distributive lattices and of Hoofman on continuous Scott domains, and also generalizes Smyth's "Rstructures". Various constructions on continuous posets have neat descriptions in terms of these continuous information systems; here we describe HoffmannLawson duality (which could not be done easily with Rstructures) and Vietoris power locales. 2 We also use the method to give a partial answer to a question of Johnstone's: in the context of continuous posets, Vietoris algebras are the same as localic semilattices.
A Linear Metalanguage for Concurrency
 Handbook of Logic in Computer Science
, 1998
"... A metalanguage for concurrent process languages is introduced. ..."
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Cited by 11 (4 self)
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A metalanguage for concurrent process languages is introduced.
Continuous Functionals of Dependent and Transfinite Types
, 1995
"... this paper we study some extensions of the KleeneKreisel continuous functionals [7, 8] and show that most of the constructions and results, in particular the crucial density theorem, carry over from nite to dependent and transnite types. Following an approach of Ershov we dene the continuous functi ..."
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Cited by 10 (2 self)
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this paper we study some extensions of the KleeneKreisel continuous functionals [7, 8] and show that most of the constructions and results, in particular the crucial density theorem, carry over from nite to dependent and transnite types. Following an approach of Ershov we dene the continuous functionals as the total elements in a hierarchy of ErshovScottdomains of partial continuous functionals. In this setting the density theorem says that the total functionals are topologically dense in the partial ones, i.e. every nite (compact) functional has a total extension. We will extend this theorem from function spaces to dependent products and sums and universes. The key to the proof is the introduction of a suitable notion of density and associated with it a notion of codensity for dependent domains with totality. We show that the universe obtained by closing a given family of basic domains with totality under some quantiers has a dense and codense totality provided the totalities on the basic domains are dense and codense and the quantiers preserve density and codensity. In particular we can show that the quantiers and have this preservation property and hence, for example, the closure of the integers and the booleans (which are dense and codense) under and has a dense and codense totality. We also discuss extensions of the density theorem to iterated universes, i.e. universes closed under universe operators. From our results we derive a dependent continuous choice principle and a simple ordertheoretic characterization of extensional equality for total objects. Finally we survey two further applications of density: Waagb's extension of the KreiselLacombeShoeneldTheorem showing the coincidence of the hereditarily eectively continuous hierarchy...
Domain Theory Meets Default Logic
, 1995
"... We present a development of the theory of default information structures, combining ideas from domain theory with ideas from nonmonotonic logic. Conceptually, our treatment is distinguished from standard default logic in that we view default structures as generating models rather than theories. Re ..."
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Cited by 8 (6 self)
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We present a development of the theory of default information structures, combining ideas from domain theory with ideas from nonmonotonic logic. Conceptually, our treatment is distinguished from standard default logic in that we view default structures as generating models rather than theories. Reiter's default rules are viewed as nondeterministic algorithms for generating preferred partial models. Using domaintheoretical notions, we improve the standard definition of extensions in default logic, by introducing the notion of dilation. We prove the existence of such dilations for a new, natural class of default information structures, properly including the socalled seminormal ones. This class, called the class of rational structures, is a robust generalization of the usual kind of default rule system.
Density and Choice for Total Continuous Functionals
 About and Around Georg Kreisel
, 1996
"... this paper is to give complete proofs of the density theorem and the choice principle for total continuous functionals in the natural and concrete context of the partial continuous functionals [Ers77], essentially by specializing more general treatments in the literature. The proofs obtained are rel ..."
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Cited by 8 (3 self)
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this paper is to give complete proofs of the density theorem and the choice principle for total continuous functionals in the natural and concrete context of the partial continuous functionals [Ers77], essentially by specializing more general treatments in the literature. The proofs obtained are relatively short and hopefully perspicious, and may contribute to redirect attention to the fundamental questions Kreisel originally was interested in. Obviously this work owes much to other sources. In particular I have made use of work by Scott [Sco82] (whose notion of an information system is taken as a basis to introduce domains), Roscoe [Ros87], Larsen and Winskel [LW84] and Berger [Ber93]. The paper is organized as follows. Section 1 treats information systems, and in section 2 it is shown that the partial orders defined by them are exactly the (Scott) domains with countable basis. Section 3 gives a characterization of the continuous functions between domains, in terms of approximable mappings. In section 4 cartesian products and function spaces of domains and information systems are introduced. In section 5 the partial and total continuous functionals are defined. Section 6 finally contains the proofs of the two theorems above; it will be clear that the same proofs also yield effective versions of these theorems.
Recursion on the partial continuous functionals
 Logic Colloquium ’05
, 2006
"... We describe a constructive theory of computable functionals, based on the partial continuous functionals as their intendend domain. Such a task had long ago been started by Dana Scott [28], under the wellknown abbreviation ..."
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Cited by 7 (5 self)
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We describe a constructive theory of computable functionals, based on the partial continuous functionals as their intendend domain. Such a task had long ago been started by Dana Scott [28], under the wellknown abbreviation
Configuration Structures (Extended Abstract)
 Proceedings 10 th Annual IEEE Symposium on Logic in Computer Science, LICS’95
, 1995
"... Configuration structures provide a model of concurrency generalising the families of configurations of event structures. They can be considered logically, as classes of propositional models; then subclasses can be axiomatised by formulae of simple prescribed forms. Several equivalence relations for ..."
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Cited by 7 (7 self)
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Configuration structures provide a model of concurrency generalising the families of configurations of event structures. They can be considered logically, as classes of propositional models; then subclasses can be axiomatised by formulae of simple prescribed forms. Several equivalence relations for event structures are generalised to configuration structures, and also to general Petri nets. Every configuration structure is shown to be STbisimulation equivalent to a prime event structure with binary conflict; this fails for the tighter history preserving bisimulation. Finally, Petri nets without selfloops under the collective token interpretation are shown behaviourally equivalent to configuration structures, in the sense that there are translations in both directions respecting history preserving bisimulation. This fails for nets with selfloops. 1 Introduction The aim of this paper is to connect several models of concurrency, by providing translations between them and studying whi...
Disjunctive Systems and LDomains
 Proceedings of the 19th International Colloquium on Automata, Languages, and Programming (ICALP’92
, 1992
"... . Disjunctive systems are a representation of Ldomains. They use sequents of the form X ` Y , with X finite and Y pairwise disjoint. We show that for any disjunctive system, its elements ordered by inclusion form an Ldomain. On the other hand, via the notion of stable neighborhoods, every Ldomain ..."
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Cited by 6 (2 self)
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. Disjunctive systems are a representation of Ldomains. They use sequents of the form X ` Y , with X finite and Y pairwise disjoint. We show that for any disjunctive system, its elements ordered by inclusion form an Ldomain. On the other hand, via the notion of stable neighborhoods, every Ldomain can be represented as a disjunctive system. More generally, we have a categorical equivalence between the category of disjunctive systems and the category of Ldomains. A natural classification of domains is obtained in terms of the style of the entailment: when jXj = 2 and jY j = 0 disjunctive systems determine coherent spaces; when jY j 1 they represent Scott domains; when either jXj = 1 or jY j = 0 the associated cpos are distributive Scott domains; and finally, without any restriction, disjunctive systems give rise to Ldomains. 1 Introduction Discovered by Coquand [Co90] and Jung [Ju90] independently, Ldomains form one of the maximal cartesian closed categories of algebraic cpos. Tog...