Domain Theory in Logical Form

  title={Domain Theory in Logical Form},
  author={Samson Abramsky},
  journal={Ann. Pure Appl. Log.},
  • S. Abramsky
  • Published 14 March 1991
  • Computer Science, Philosophy
  • Ann. Pure Appl. Log.
Domain Theory and the Logic of Observable Properties
The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: - Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for denotational semantics, which opens the way to a whole range of applications.
Continuous Domains in Logical Form
Finitary Logical Semantics (Abstract)
Stone dualitiesallow to describe special classes of topological spaces by means of (possibly finitary) partial orders. Typically, these partial orders are given by the topology, a basis for it, or a
A Unified Theory of Program Logics: An Approach based on the π-Calculus
Embedding of Hoare logic for sequential programs and a rely-guarantee logic for shared variable concurrency are shown, suggesting that the proposed framework can offer a unifying basis to capture fundamental notions in program logics such as partial/total correctness, sequentiality and different kinds of concurrent computing.
Mathematics of Domains
Two groups of naturally arising questions in the mathematical theory of domains for denotational semantics are addressed and a novel approach is presented, and the answers are supplied with much more compelling and clear justifications, than were known before.
A logic for Lawson compact algebraic L-domains
Logical Semantics for Stability
A Categorical View on Algebraic Lattices in Formal Concept Analysis
The paper provides a relatively comprehensive account of the representation theory of algebraic lattices in the framework of Stone duality, relating well-known structures such as Scott information systems with further formalisms from logic, topology, domains and lattice theory.
Morphisms in Logic, Topology, and Formal Concept Analysis
The general topic of this thesis is the investigation of various notions of morphisms between logical deductive systems, motivated by the intuition that additional (categorical) structure is needed
Full abstraction for nominal Scott domains
A full abstraction result is proved for nominal Scott domains analogous to Plotkin's classic result about PCF and conventional Scott domains: two program phrases have the same observable operational behaviour in all contexts if and only if they denote equal elements of the nominal Scott domain model.


Processes and the Denotational Semantics of Concurrency
The category-theoretic solution of recursive domain equations
  • M. Smyth, G. Plotkin
  • Mathematics
    18th Annual Symposium on Foundations of Computer Science (sfcs 1977)
  • 1977
The purpose of the present paper is to set up a categorical framework in which the known techniques for solving equations find a natural place, generalizing from least fixed-points of continuous functions over cpos to initial ones of continuous functors over $\omega $-categories.
Computability concepts for programming language semantics
A notion of computability on continuous higher types (for all types) is defined and its equivalence to effective operators is shown and shows that the authors' computable operators can model mathematically everything that can be done in an operational semantics.
The Largest First-Order-Axiomatizable Cartesian Closed Category of Domains
The purpose of this paper is to state and prove an analog to Smyth's theorem which says that the bounded complete domains form the largest cartesian closed category of domains.
LCF Considered as a Programming Language
A Filter Lambda Model and the Completeness of Type Assignment
In [6, p. 317] Curry described a formal system assigning types to terms of the type-free λ-calculus. In [11] Scott gave a natural semantics for this type assignment and asked whether a completeness
The theory of representations for Boolean algebras
Boolean algebras are those mathematical systems first developed by George Boole in the treatment of logic by symbolic methodsf and since extensively investigated by other students of logic, including
Algebraic laws for nondeterminism and concurrency
The paper demonstrates, for a sequence of simple languages expressing finite behaviors, that in each case observation congruence can be axiomatized algebraically and the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties.
Full Abstraction for a Simple Parallel Programming Language
A denotational semantics for a simple language with parallelism was given, treating parallelism in terms of non-deterministic mergeing of uninterruptible actions, and expected identities such as the associativity and commutativity of the parallel combinator were true in this semantics.
Domains for Denotational Semantics
This paper discusses many examples in an informal way that should serve as an introduction to the theory of domains and proves many things that were done previously axiomatically can now be proved in a straightfoward way as theorems.