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	Domain theory - Wikipedia, the free encyclopedia
		Domain theory is a branch of mathematics that studies special kinds of partially ordered sets commonly called domains.
		Domain theory formalizes the intuitive ideas of approximation and convergence in a very general way and has close relations to topology.
		Indeed, in the theory of metric spaces, sequences play a role that is in many aspects analogue to the role of directed sets in domain theory.
	en.wikipedia.org /wiki/domain_theory (2657 words)

	Encyclopedia: Domain theory (Site not responding. Last check: 2007-11-07)
		Order theory is a branch of mathematics that studies various kinds of binary relations that capture the intuitive notion of a mathematical ordering.
		In mathematics, especially in order theory, the greatest element of a subset S of a partially ordered set is an element of S which is greater than or equal to any other element of S. The term least element is defined dually.
		In mathematics, especially in order theory, an upper bound of a subset S of some partially ordered set is an element which is greater than or equal to every element of S. The term lower bound is defined dually.
	www.nationmaster.com /encyclopedia/Domain-theory (3992 words)

	Category theory - Wikipedia, the free encyclopedia
		The subsequent development of the theory was powered first by the computational needs of homological algebra; and then by the axiomatic needs of algebraic geometry, the field most resistant to the Russell-Whitehead view of united foundations.
		These broadly-based foundational applications of category theory are contentious; but they have been worked out in quite some detail, as a commentary on or basis for constructive mathematics.
		Categorical logic is now a well-defined field based on type theory for intuitionistic logics, with application to the theory of functional programming and domain theory, all in a setting of a cartesian closed category as non-syntactic description of a lambda calculus.
	en.wikipedia.org /wiki/Category_theory (2348 words)

	Domain (ring theory) - Wikipedia, the free encyclopedia
		In abstract algebra, a domain is a ring with 0 ≠ 1 such that ab = 0 implies that either a = 0 or b = 0.
		That is, it is a nontrivial ring without left or right zero divisors.
		A commutative domain is called an integral domain.
	en.wikipedia.org /wiki/Domain_(ring_theory) (82 words)

	Domain theory (Site not responding. Last check: 2007-11-07)
		{(iv)} bifinite, for a domain expressible as a bilimit of finite posets and
		Although the case for sequences of projections is sufficient for solving domain equations, this general form arises naturally from ``indexed retracts''.
		One of the objectives of category theory is to provide a foundation for itself in particular and mathematics in general which is independent of the traditional use of set theory.
	www.cs.man.ac.uk /~pt/domains (1062 words)

	Type Theory, Set Theory and Domain Theory
		The logic of Nuprl is a constructive type theory, but its types include those of partial objects, so it is also a domain theory.
		Zermelo set theory, Z. The constructive version of second order type theory allows a fully impredicative notion of proposition, which at first sight seems to violate the notion of construction in that the propositions cannot be built up systematically from simpler ones.
		His approach is now known as Domain Theory and is a flourishing branch of mathematics and computer science.
	www.cs.cornell.edu /Info/Projects/NuPrl/Intro/TypeSetDomain/typesetd.html (1988 words)

	domain theory from FOLDOC (Site not responding. Last check: 2007-11-07)
		A branch of mathematics introduced by Dana Scott in 1970 as a mathematical theory of programming languages, and for nearly a quarter of a century developed almost exclusively in connection with denotational semantics in computer science.
		Domain theory is the study of such structures.
		In a language containing functions, we might have a domain X -> Y which is the set of functions from domain X to domain Y with the ordering f <= g iff for all x in X, f x <= g x.
	wombat.doc.ic.ac.uk /foldoc/foldoc.cgi?domain+theory (297 words)

	Domain theory - Open Encyclopedia (Site not responding. Last check: 2007-11-07)
		Since this often is not ambiguous one also may speak of continuous functions.
		Starting from these definitions, one obtains a number of other interesting special classes of ordered structures that could be suitable as "domains".
		A standard ressource on domain theory, which is freely available online:
	open-encyclopedia.com /Domain_theory (2500 words)

	Quantitative Domain Theory
		Domain Theory, a formal basis for the semantics of programming languages, originated in work by Dana Scott in the mid-1960s.
		Domain Theory originated in the revolutionary work by Strachey and Scott on the development of models (semantics) for programming languages.
		In this framework, the least fixed point of a functional, defined on a domain of Scott continuous functions and with range in the same set, is obtained as a topological limit.
	www.ercim.org /publication/Ercim_News/enw50/schellekens.html (702 words)

	Domain Theory
		In particular, we will learn how to solve domain equations such as D = A + (D --> D) (which means that D is the sum of some given domain A and the domain of all functions from D to itself).
		Domains satisfying such equations are needed for assigning mathematical meanings to programs in some programming languages.
		We study domains both as a pure mathematical structure and as an important foundation for computer science.
	web.comlab.ox.ac.uk /oucl/courses/topics03-04/dt (152 words)

	Domain Theory
		The Domain Theory consists of a schema to represent requirements and design-related knowledge; a library of generic models that can be reused in software design and problem solving more generally; and supporting methods and tools for reuse.
		The Domain Theory has been developed from several investigations into problems of abstraction and granularity to create schemata and laws that define how reuse components should be structured and how generic models can be composed to create solutions to new problems.
		More recently the Domain Theory was unified with the task-artefact theory and claims analysis from Professor Jack Carroll to provide representations of design knowledge that linked to requirements knowledge and generic problem models in the Domain Theory.
	www.co.umist.ac.uk /centre_hci/domain3.htm (347 words)

	MATHS: Domains
		Domains have been used to explain why recursive definitions can be approximated by iterative computations.
		Another way of looking at domain theory is to say that it is a way of modelling the fact that certain computations don't have a defined result and using the model to prove that certain computations will ultimately provide as close to a complete definition as we could demand.
		A solution to a recursive set of definitions is the often defined as the least object in the domain that is not changed by applying the definition to it - the least fixed_point(_).
	www.csci.csusb.edu /dick/maths/math_24_Domains.html (945 words)

	ortega95a Abstract (Site not responding. Last check: 2007-11-07)
		This note reports a simple change and reinterpretation of the domain theory in terms of M-of-N concepts, involving no learning, that results in an accuracy of 93.4% on the 106 items of the database.
		Moreover, an exhaustive search of the space of M-of-N domain theory interpretations indicates that the expected accuracy of a randomly chosen interpretation is 76.5%, and that a maximum accuracy of 97.2% is achieved in 12 cases.
		This demonstrates the informativeness of the domain theory, without the complications of understanding the interactions between various learning algorithms and the theory.
	www.jair.org /abstracts/ortega95a.html (155 words)

	Computable Banach Spaces via Domain Theory - Edalat, Sunderhauf (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		We employ the domain of formal balls to define a computability theory for complete metric spaces.
		is similar to the corresponding theory induced from representing the metric space by an # algebraic domain as in the work of Blanck [19] In, it is shown that the vector space structure of a separable Banach space can also be extended to the domain of formal balls and be...
		Domain Representations of Partial Functions, With Applications to..
	citeseer.ist.psu.edu /edalat98computable.html (704 words)

	Domain Theory (Site not responding. Last check: 2007-11-07)
		The existence of domains is hinted at by the observation that some magnetic properties, and in particular, coercivity and remanence vary greatly with grain size.
		Experimentally, it is observed that for a homogeneous specimen at constant temperature, the magnitude of Ms is uniform but the direction of Ms is in general not uniform from one region to another (on a scale of microns to millimeters).
		Domain walls have a finite width that is determined principally by exchange and magnetocrystalline energy.
	www.geo.umn.edu /orgs/irm/hg2m/hg2m_d/hg2m_d.html (1955 words)

	Theory and Semantics Group (Site not responding. Last check: 2007-11-07)
		The work of the Theory and Semantics Group is centred around mathematical models of a variety of languages and logics.
		Work is in progress on the underlying mathematical structures of these, and on their application to the study of higher order typed programming languages such as Standard ML, to object-based languages, to foundational languages for concurrent, distributed and mobile computation, to hardware description languages, and to security problems.
		The syntax and semantics of the lambda calculus, general recursion theory, sheaf models for intuitionistic theories, general categorical logic and topos theory, the effective topos, other realizability toposes and constructive mathematics as developed in such frameworks, topos theoretic models for polymorphism, linear logic and game theoretic semantics.
	www.cl.cam.ac.uk /Research/TSG (1102 words)

	Introduction to Domain Theory (Site not responding. Last check: 2007-11-07)
		Domain theory has its roots in the seminal work of Scott and Strachey in the 1970s on denotational semantics, in particular on solving the technical problems that arise in giving semantics to recursively defined programs and types.
		As well as being one of the most fascinating topics in the foundations of computing science, domain-theoretic ideas are used in many branches of modern research on programming languages and their semantics.
		The aim of this course is to teach the basic concepts of domain theory.
	www.cs.nott.ac.uk /~gmh/domains.html (181 words)

	PLT Online (Site not responding. Last check: 2007-11-07)
		This is a collection of programming language theory texts and resources, all of which are freely available over the Internet.
		Many valuable reference texts on programming language theory, previously only available in paper form, have in recent years become publicly accessible from the net.
		Part of the reason PL theory and advanced programming languages seem impenetrable to other communities is that learning materials are hard to obtain, or demand a sizeable investment of resources (time, money,...) even if the potential reader is only exploring the subject.
	www.cs.uu.nl /~franka/ref (985 words)

	Domain Theory - Abramsky, Jung (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		81 A domain equation for bisimulation (context) - Abramsky - 1991 ACM DBLP
		17 Domain Theory in Realizability Toposes (context) - Phoa - 1991
		4 Universal domains in the theory of denotational semantics of..
	citeseer.ist.psu.edu /abramsky94domain.html (2189 words)

	General Synthetic Domain Theory - A Logical Approach - Reus, Streicher (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		Axioms and (Counter)examples in Synthetic - Domain Theory Jaap
		8: An extension of models of axiomatic domain theory to models of synthetic domain..
		17 Domain theory in realizability toposes (context) - Phoa - 1990
	citeseer.ist.psu.edu /72546.html (742 words)

	CS 15-859 Domain Theory (Site not responding. Last check: 2007-11-07)
		The theory of domains has many applications in programming-language semantics and type theory, computability theory, and recently also in measure theory and chaos.
		The course will offer a basic foundational discussion of the idea building up to the solution of domain equations in suitable categories and constructions of special domains such as powerdomains and continuous algebras.
		A general theory of "propositions as types" will also be discussed to give an appropriate logic of domains.
	www.cs.cmu.edu /Groups/LTC/dt (229 words)

	Category Theory
		Category theory reveals that many of these constructions are in fact special cases of objects in a category with what is called a "universal property".
		For it is in his thesis that Lawvere proposed the idea of developing the category of categories as a foundation for category theory, set theory and, thus, the whole of mathematics, as well as using categories for the study of theories, that is the logical aspects of mathematics.
		Given these simple facts, it remains to be seen whether category theory should be "on the same plane", so to speak, with set theory, whether it should be considered seriously as providing a foundational alternative to set theory or whether it is foundational in a different sense altogether.
	plato.stanford.edu /entries/category-theory (7029 words)

	Domain at opensource encyclopedia (Site not responding. Last check: 2007-11-07)
		in biochemistry and protein science, a domain is an autonomously folding functional module of a protein
		in physics a domain is a region of a solid inside which a property is uniform (for example in ferromagnetism)
		application domain, the kind of uses a computer program or something else is used for
	wiki.tatet.ru /en/Domain.html (245 words)

	Australia Affordable Domain Registration (Site not responding. Last check: 2007-11-07)
		Domaine fourrier - HISTORY OF DOMAINE The Domaine Fourrier (previously known as Pernot-Fourrier) has a long history in his ascension, the wines of Domaine Fourrier have garnered critical acclaim.
		Eminant domain - A Coalition of Activists and Homeowners to brought together to fight state and local abuse of Eminent Domain.
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	www.affordablewebsitesaustralia.com /ContentST47.asp (5502 words)

	Domain theory Details, Meaning Domain theory Article and Explanation Guide
		Domain theory Details, Meaning Domain theory Article and Explanation Guide
		Domain theory Guide, Meaning, Facts, Information and Description
		Computation then is modeled by applying monotone functionss repeatedly on elements of the domain in order to refine a result.
	www.e-paranoids.com /d/do/domain_theory.html (2307 words)

	Education in the Moral Domain - Cambridge University Press
		This book brings together the results of 25 years of research on the domain theory of social cognitive development.
		On the basis of that research - which shows that morality is a domain distinct from other social values - the author provides concrete suggestions for creating a moral classroom climate, dealing with student discipline, and integrating moral values within the curriculum.
		Integrated answers to these questions result in a comprehensive approach that does not reduce moral education to a process of induction or inculcation, but rather harnesses children’s intrinsic motivation to comprehend and master their social worlds.
	www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521652324 (357 words)

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