# Domain Theory in Logical Form

@article{Abramsky1987DomainTI,
title={Domain Theory in Logical Form},
author={Samson Abramsky},
journal={Ann. Pure Appl. Log.},
year={1987},
volume={51},
pages={1-77}
}
• S. Abramsky
• Published 14 March 1991
• Computer Science, Philosophy
• Ann. Pure Appl. Log.
543 Citations
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
• Computer Science
Comput. J.
• 2011
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
• Computer Science
Theor. Comput. Sci.
• 2020
Logical Semantics for Stability
• Computer Science, Mathematics
MFPS
• 2009
A Categorical View on Algebraic Lattices in Formal Concept Analysis
• Computer Science, Mathematics
Fundam. Informaticae
• 2006
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
• Computer Science
POPL
• 2013
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.

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