Results 1  10
of
10
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 respectively), allowing the maximal val ..."
Abstract

Cited by 26 (0 self)
 Add to MetaCart
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. ..."
Abstract

Cited by 23 (6 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 17 (5 self)
 Add to MetaCart
. 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 ..."
Abstract

Cited by 11 (4 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
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...
Analyse Statique De Programmes : Fondements Et Applications
, 1999
"... domains . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.2 Lattices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.3 Specification of analyses . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.4 Semantic correctness . . . . . . . . . . . . . . . . . . . . . . . . ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
domains . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.2 Lattices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.3 Specification of analyses . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.4 Semantic correctness . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2.5 Solving systems of equations . . . . . . . . . . . . . . . . . . . . . 13 1.3 This document . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2 Program analysis with conjunctive types 17 2.1 Strictness types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.1.1 Lindenbaum algebras . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 The strictness logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3 Relationship to abstract interpretation . . . . . . . . . . . . . . . . . . . . 22 2.4 A variation: bindingtime analysis . . . . . . . . . . . . . . . . . . . . . . 22 3 Disjunctions and data structures: Properties 25 3.1 Axiomatisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.1.1 Normal Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2 Abstract domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2.1 Base Types, Products, Sums and Functions . . . . . . . . . . . . . 31 3.2.2 Recursive Data Structures . . . . . . . . . . . . . . . . . . . . . . 32 3.2.3 Strictness Properties of Lists . . . . . . . . . . . . . . . . . . . . . 35 4 Disjunctions and data structures: Logic 37 4.1 Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.1.1 Strictness Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.1.2 Proving properties for lists . . . . . . . . . . . . . . . . . . . . . . 42 4.2 Bibliographical not...
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 ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
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...
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 ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
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.
General Terms: Theory
"... Abstract. A simple model, AT, for nondeterministic machines is presented which is based on certain types of trees. A set of operations, 2, is defined over AT and it is shown to be completely characterized by a set of inequations over 2. AT is used to define the denotational semantics of a language f ..."
Abstract
 Add to MetaCart
Abstract. A simple model, AT, for nondeterministic machines is presented which is based on certain types of trees. A set of operations, 2, is defined over AT and it is shown to be completely characterized by a set of inequations over 2. AT is used to define the denotational semantics of a language for defining nondeterministic machines. The significance ofthe model is demonstrated by showing that this semantics reflects an intuitive operational semantics of machines based on the idea that machines should only be differentiated if there is some experiment that differentiates between them.