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18
A Semantics for Complex Objects and Approximate Queries
 In Seventh Symposium on the Principles of Database Systems
, 1988
"... A new definition of complex objects is introduced which provides a denotation for incomplete tuples as well as partially described sets. Set values are "sandwiched" between "complete" and "consistent" descriptions (representing the Smyth and Hoare powerdomains respectiv ..."
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Cited by 26 (0 self)
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A new definition of complex objects is introduced which provides a denotation for incomplete tuples as well as partially described sets. Set values are "sandwiched" between "complete" and "consistent" descriptions (representing the Smyth and Hoare powerdomains respectively), allowing the maximal values to be arbitrary subsets of maximal elements in the domain of the set. We also examine the use of rules in defining queries over such objects. 1 Introduction A characteristic of "complexobject" [1, 2] databases and "higherorder" relations [3, 4] is that the components of tuples are not restricted to taking only atomic values, but may be other tuples or even sets of tuples. A second property of complex objects and related information structures is that there is a natural ordering on the domain of values with an associated algebra [5, 6, 7]. For example, in Bancilhon and Khoshafian's ordering on tuples [1] [Name) 0 J.Doe 0 ] v [Name) 0 J.Doe 0 ;Age)21] This research was suppor...
Domain theory for concurrency
, 2003
"... Concurrent computation can be given an abstract mathematical treatment very similar to that provided for sequential computation by domain theory and denotational semantics of Scott and Strachey. ..."
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Cited by 23 (6 self)
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Concurrent computation can be given an abstract mathematical treatment very similar to that provided for sequential computation by domain theory and denotational semantics of Scott and Strachey.
Clausal Logic And Logic Programming In Algebraic Domains
 Information and Computation
, 2001
"... . We introduce a domaintheoretic foundation for disjunctive logic programming. This foundation is built on clausal logic, a representation of the Smyth powerdomain of any coherent algebraic dcpo. We establish the completeness of a resolution rule for inference in such a clausal logic; we introdu ..."
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Cited by 17 (5 self)
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. We introduce a domaintheoretic foundation for disjunctive logic programming. This foundation is built on clausal logic, a representation of the Smyth powerdomain of any coherent algebraic dcpo. We establish the completeness of a resolution rule for inference in such a clausal logic; we introduce a natural declarative semantics and a fixedpoint semantics for disjunctive logic programs, and prove their equivalence; finally, we apply our results to give both a syntax and semantics for default logic in any coherent algebraic dcpo. 1. Introduction Domain theory, as introduced by Scott in the 1970's, has many connections with logic. Such connections are usually made by extracting an appropriate language /syntax from a category of domains. To name a few examples, we have Abramsky's "domain theory in logical form" [Abr91], Scott's own representation of Scott domains as information systems [Sco82], extended to other domains by Zhang [Zha91], and Smyth's treatment of observable prope...
A Semantic Theory for ValuePassing Processes Late Approach  Part I: A Denotational Model and Its Complete Axiomatization
, 1995
"... A general class of languages and denotational models for valuepassing calculi based on the late semantic approach is defined. A concrete instantiation of the general syntax is given. This is a modification of the standard CCS according to the late approach. A denotational model for the concrete ..."
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Cited by 11 (4 self)
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A general class of languages and denotational models for valuepassing calculi based on the late semantic approach is defined. A concrete instantiation of the general syntax is given. This is a modification of the standard CCS according to the late approach. A denotational model for the concrete language is given, an instantiation of the general class. An equationally based proof system is defined and shown to be sound and complete with respect to the model.
Topology, Domain Theory and Theoretical Computer Science
, 1997
"... In this paper, we survey the use of ordertheoretic topology in theoretical computer science, with an emphasis on applications of domain theory. Our focus is on the uses of ordertheoretic topology in programming language semantics, and on problems of potential interest to topologists that stem from ..."
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Cited by 10 (2 self)
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In this paper, we survey the use of ordertheoretic topology in theoretical computer science, with an emphasis on applications of domain theory. Our focus is on the uses of ordertheoretic topology in programming language semantics, and on problems of potential interest to topologists that stem from concerns that semantics generates. Keywords: Domain theory, Scott topology, power domains, untyped lambda calculus Subject Classification: 06B35,06F30,18B30,68N15,68Q55 1 Introduction Topology has proved to be an essential tool for certain aspects of theoretical computer science. Conversely, the problems that arise in the computational setting have provided new and interesting stimuli for topology. These problems also have increased the interaction between topology and related areas of mathematics such as order theory and topological algebra. In this paper, we outline some of these interactions between topology and theoretical computer science, focusing on those aspects that have been mo...
Probability, Nondeterminism and Concurrency: Two Denotational Models for Probabilistic Computation
 PHD THESIS, UNIV. AARHUS, 2003. BRICS DISSERTATION SERIES
, 2003
"... Nondeterminism is modelled in domain theory by the notion of a powerdomain, while probability is modelled by that of the probabilistic powerdomain. Some problems arise when we want to combine them in order to model computation in which both nondeterminism and probability are present. In particular t ..."
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Cited by 5 (1 self)
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Nondeterminism is modelled in domain theory by the notion of a powerdomain, while probability is modelled by that of the probabilistic powerdomain. Some problems arise when we want to combine them in order to model computation in which both nondeterminism and probability are present. In particular there is no categorical distributive law between them. We introduce the powerdomain of indexed valuations which modifies the usual probabilistic powerdomain to take more detailed account of where probabilistic choices are made. We show the existence of a distributive law between the powerdomain of indexed valuations and the nondeterministic powerdomain. By means of an equational theory we give an alternative characterisation of indexed valuations and the distributive law. We study the relation between valuations and indexed valuations. Finally we use indexed valuations to give a semantics to a programming language. This semantics reveals the computational intuition lying behind the mathematics. In the second part of the thesis we provide an operational reading of continuous valuations on certain domains (the distributive concrete domains of Kahn and Plotkin) through the model of probabilistic event structures. Event structures are a model for concurrent computation that account for causal relations between events. We propose a way of adding probabilities to confusion free event structures, defining the notion of probabilistic event structure. This leads to various ideas of a run for probabilistic event structures. We show a confluence theorem for such runs. Configurations of a confusion free event structure form a distributive concrete domain. We give a representation theorem which characterises completely the powerdomain of valuations of such concrete domains in terms of prob...
Powerdomains and Zero Finding
, 2002
"... Traditionally, powerdomains have been used to provide models for various forms of nondeterminism in semantics. We establish a similar analogy between zero nding methods in numerical analysis and powerdomains: Different powerdomain constructions correspond to dierent types of behavior exhibited by n ..."
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Cited by 2 (1 self)
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Traditionally, powerdomains have been used to provide models for various forms of nondeterminism in semantics. We establish a similar analogy between zero nding methods in numerical analysis and powerdomains: Different powerdomain constructions correspond to dierent types of behavior exhibited by numerical methods for zero finding. By combining this observation with the basic quantitative paradigm provided by measurement, a simple and uniform method for analyzing zero finding algorithms is obtained.
A Note on Processes for PlanExecution and Powerdomains for PlanComparison
"... This paper proposes a representation for plans and actions based on the algebraic theory of processes. It is argued that the requirements of planexecution are better met by representing actions through the processes by which changes occur than by the more widely used statechange representation. A ..."
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This paper proposes a representation for plans and actions based on the algebraic theory of processes. It is argued that the requirements of planexecution are better met by representing actions through the processes by which changes occur than by the more widely used statechange representation. A simple algebra of plans, based on processcombinators, is described and shown to be adequate for a wide variety of plans. The implications of this type of planrepresentation are discussed and its advantages for metareasoning (including plancomparison) outlined. This paper presents the theory of processes from the point of view of planning and describes a novel method of plancomparison which draws upon ideas in domain theory. Keywords: Planrepresentation; planexecution; plancomparison; philosophical foundations A note on processes for planexecution and powerdomains for plancomparison David Pym Louise Pryor David Murphy Queen Mary & Westfield College Department of Artificial Intell...
Presenting Functors by Operations and Equations
"... Abstract. We take the point of view that, if transition systems are coalgebras for a functor T, then an adequate logic for these transition systems should arise from the ‘Stone dual ’ L of T. We show that such a functor always gives rise to an ‘abstract’ adequate logic for Tcoalgebras and investiga ..."
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Abstract. We take the point of view that, if transition systems are coalgebras for a functor T, then an adequate logic for these transition systems should arise from the ‘Stone dual ’ L of T. We show that such a functor always gives rise to an ‘abstract’ adequate logic for Tcoalgebras and investigate under which circumstances it gives rise to a ‘concrete ’ such logic, that is, a logic with an inductively defined syntax and proof system. We obtain a result that allows us to prove adequateness of logics uniformly for a large number of different types of transition systems and give some examples of its usefulness. 1