BibTeX
@MISC{Abramsky_domaintheory,
author = {Samson Abramsky},
title = {Domain Theory in Logical Form},
year = {}
}
Years of Citing Articles
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
... Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for denotational semantics. The theory of concurrency and systems behaviour developed by Milner, Hennessy based on operational semantics. Logics of programs. Stone duality provides a junction between semantics (spaces of points = denotations of computational processes) and logics (lattices of of processes). Moreover, the underlying logic is, which can be computationally interpreted as the logic of properties--i.e. properties which can be determined to hold of a process on the basis of a finite amount of information about its execution. These ideas lead to the following programme: 1. A metalanguage is introduced, comprising types = universes of discourse for various computational situations. terms = programs = syntactic intensions for models or points. 2. A standard denotational interpretation of the metalanguage is given, assigning do-mains to types and domain elements to terms. 3. The metalanguage is also given a interpretation, in which types are interpreted as propositional theories and terms are interpreted a program logic, which ax- iomatizes the properties they satisfy. 4. The two interpretations are related by showing that they are Stone duals of each other. Hence, semantics and logic are guaranteed to be in harmony with each other, and in fact each determines the other up to isomorphism. 5. This opens the way to a whole range of applications. Given a denotational description of a computational situation in our meta-language, we can turn the handle to obtain a logic for that situation.
