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39
A powerdomain construction
 SIAM J. of Computing
, 1976
"... Abstract. We develop a powerdomain construction, [.], which is analogous to the powerset construction and also fits in with the usual sum, product and exponentiation constructions on domains. The desire for such a construction arises when considering programming languages with nondeterministic featu ..."
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Abstract. We develop a powerdomain construction, [.], which is analogous to the powerset construction and also fits in with the usual sum, product and exponentiation constructions on domains. The desire for such a construction arises when considering programming languages with nondeterministic features or parallel features treated in a nondeterministic way. We hope to achieve a natural, fully abstract semantics in which such equivalences as (pparq)=(qparp) hold. The domain (D Truthvalues) is not the right one, and instead we take the (finitely) generable subsets of D. When D is discrete they are ordered in an elementwise fashion. In the general case they are given the coarsest ordering consistent, in an appropriate sense, with the ordering given in the discrete case. We then find a restricted class of algebraic inductive partial orders which is closed under [. as well as the sum, product and exponentiation constructions. This class permits the solution of recursive domain equations, and we give some illustrative semantics using 5[.]. It remains to be seen if our powerdomain construction does give rise to fully abstract semantics, although such natural equivalences as the above do hold. The major deficiency is the lack of a convincing treatment of the fair parallel construct. 1. Introduction. When one follows the ScottStrachey approach to the
Universal Profinite Domains
 Information and Computation
, 1987
"... . We introduce a bicartesian closed category of what we call profinite domains. Study of these domains is carried out through the use of an equivalent category of preorders in a manner similar to the information systems approach advocated by Dana Scott and others. A class of universal profinite dom ..."
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. We introduce a bicartesian closed category of what we call profinite domains. Study of these domains is carried out through the use of an equivalent category of preorders in a manner similar to the information systems approach advocated by Dana Scott and others. A class of universal profinite domains is defined and used to derive sufficient conditions for the profinite solution of domain equations involving continuous operators. As a special instance of this construction, a universal domain for the category SFP is demonstrated. Necessary conditions for the existence of solutions for domain equations over the profinites are also given and used to derive results about solutions of some equations. A new universal bounded complete domain is also demonstrated using an operator which has bounded complete domains as its fixed points. 1 Introduction. For our purposes a domain equation has the form X ¸ = F (X) where F is an operator on a class of semantic domains (typically, F is an endof...
A Complete Characterization of Complete IntersectionType Theories (Extended Abstract)
 ACM TOCL
, 2000
"... M. DEZANICIANCAGLINI Universita di Torino, Italy F. HONSELL Universita di Udine, Italy F. ALESSI Universita di Udine, Italy Abstract We characterize those intersectiontype theories which yield complete intersectiontype assignment systems for lcalculi, with respect to the three canonical ..."
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M. DEZANICIANCAGLINI Universita di Torino, Italy F. HONSELL Universita di Udine, Italy F. ALESSI Universita di Udine, Italy Abstract We characterize those intersectiontype theories which yield complete intersectiontype assignment systems for lcalculi, with respect to the three canonical settheoretical semantics for intersectiontypes: the inference semantics, the simple semantics and the Fsemantics. Keywords Lambda Calculus, Intersection Types, Semantic Completeness, Filter Structures. 1 Introduction Intersectiontypes disciplines originated in [6] to overcome the limitations of Curry 's type assignment system and to provide a characterization of strongly normalizing terms of the lcalculus. But very early on, the issue of completeness became crucial. Intersectiontype theories and filter lmodels have been introduced, in [5], precisely to achieve the completeness for the type assignment system l" BCD W , with respect to Scott's simple semantics. And this result, ...
A knowledge representation based on the Belnap's fourvalued logic
, 1993
"... Introduction Much recent work in artificial intelligence has required formal techniques for working with incomplete knowledge. The new approach clearly necessitated that a distinction be made between logic and the action (i.e. two components of intelligence: the epistemological and the heuristic; c ..."
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Introduction Much recent work in artificial intelligence has required formal techniques for working with incomplete knowledge. The new approach clearly necessitated that a distinction be made between logic and the action (i.e. two components of intelligence: the epistemological and the heuristic; cf. [MCC 69]). However, certain new inference procedures associated with the new approach (for example the familiar example of default logic) have, like classical logic, been based on an underlying consistent ontology. (Cf. [GIN 87a]: "It is precisely this `absence of information to the contrary' that makes the inference nonmonotonic...") 1 Philosophers were the first to call attention to the new situation. (Cf. [RES 79]: "...we can live with the prospect of inconsistency  not only in epistemology, but even in ontology"; and further: "The invocation of ontology here is significant... Thus if t(P ) were to be construed not as `P
From Partial Orders with Projections to Domains (Extended Abstract)
 Mathematical Foundations of Programming Semantics, Fifteenth Conference, volume 20 of Electronic Notes in Theoretical Computer Science
, 1999
"... Ralph Kummetz 1 Institut fur Algebra Technische Universitat Dresden D01062 Dresden, Germany Abstract We study approximating partial orders with projections (approximating pop's). These are triples (D; ; P) consisting of a poset (D; ) and a directed set P of projections such that the supremum ..."
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Ralph Kummetz 1 Institut fur Algebra Technische Universitat Dresden D01062 Dresden, Germany Abstract We study approximating partial orders with projections (approximating pop's). These are triples (D; ; P) consisting of a poset (D; ) and a directed set P of projections such that the supremum of P exists and sup P = id D . We derive a canonical uniformity U on D and relate properties of U such as completeness and compactness to properties of the poset and the projection set. We show that each monotone net in D is convergent if and only if (D; ) is an algebraic domain such that the images of the projections are precisely the compact elements of (D; ). Furthermore, the bifinite domains arise exactly as approximating pop's where U is compact. 1 Introduction In the theory of denotational semantics of programming languages, various classes of domains and their approximations have been intensively investigated. Scott [11] constructed a domaintheoretic model of the typefree calculus ...
A Lambda Model Characterizing Computational Behaviours of Terms
 PROCEEDINGS OF THE AND LIKAVEC INTERNATIONAL WORKSHOP REWRITING IN PROOF AND COMPUTATION
, 2001
"... We build a lambda model which characterizes completely (persistently) normalizing, (persistently) head normalizing, and (persistently) weak head normalizing terms. ..."
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We build a lambda model which characterizes completely (persistently) normalizing, (persistently) head normalizing, and (persistently) weak head normalizing terms.
The Logic of the Partial λCalculus With Equality
"... We investigate the logical aspects of the partial λcalculus with equality, exploiting an equivalence between partial λtheories and partial cartesian closed categories (pcccs) established here. The partial λcalculus with equality provides a fullblown intuitionistic higher order logic, which in a ..."
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We investigate the logical aspects of the partial λcalculus with equality, exploiting an equivalence between partial λtheories and partial cartesian closed categories (pcccs) established here. The partial λcalculus with equality provides a fullblown intuitionistic higher order logic, which in a precise sense turns out to be almost the logic of toposes, the distinctive feature of the latter being unique choice. We give a linguistic proof of the generalization of the fundamental theorem of toposes to pcccs with equality; type theoretically, one thus obtains that the partial λcalculus with equality encompasses a MartinLöfstyle dependent type theory. This work forms part of the semantical foundations for the higher order algebraic specification language HasCasl.
Time, Imaginary Value, Paradox, Sign and Space
 in Computing Anticipatory Systems, CASYS  Fifth International Conference, Liege, Belgium (2001) ed. by Daniel Dubois, AIP Conference Proceedings Volume 627
, 2002
"... This paper discusses paradox and imaginary values in relation to the mutuality of sign and space. ..."
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Cited by 3 (3 self)
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This paper discusses paradox and imaginary values in relation to the mutuality of sign and space.
Domains with Approximating Projections
 Institute of Algebra, Dresden University of Technology
, 1999
"... We investigate approximating posets with projections (approximating pop's). These are triples (D; ; P) consisting of a poset (D; ) and a directed set P of projections with sup P = id D . They carry a canonical uniformity and thus a topology. We relate their properties such as completeness ..."
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We investigate approximating posets with projections (approximating pop's). These are triples (D; ; P) consisting of a poset (D; ) and a directed set P of projections with sup P = id D . They carry a canonical uniformity and thus a topology. We relate their properties such as completeness and compactness to properties of the poset and the projection set. We show that each monotone net in D is convergent if and only if (D; ) is an algebraic domain such that the images of the projections are precisely the compact elements of (D; ). We call these domains Pdomains and characterize them as inverse limits of posets satisfying the ascending chain condition. Moreover, we describe Pdomains by a certain system of socalled "complete" subsets. We prove that if the set of compact elements of an algebraic domain is mubcomplete, then it is a Pdomain if and only if the mubclosure of every finite set of compact elements fulfils the ascending chain condition. Furthermore, we characte...