 
Summary: DOMAIN THEORY IN LOGICAL FORM
(To appear in Proceedings of LICS `87)
Samson Abramsky
Department of Computing
Imperial College of Science and Technology
November 10, 2006
Abstract
A metalanguage for denotational semantics is given a logical inter
pretation: types are interpreted as propositional theories; terms (in an
extended typed calculus, denoting elements of types) are embedded
in an endogenous program logic, which characterises their behaviour
in terms of which properties they satisfy; terms (in an extension of
the algebraic metalanguage of cartesian closed categories, denoting
morphisms between types) are embedded in an exogenous logic, which
characterises their behaviour as predicate transformers or modal oper
ators. This interpretation is related to the standard domaintheoretic
one via the machinery of Stone duality, and an exact correspondence
is obtained. Some applications to logics for specific computational
situations (e.g. concurrency) are mentioned.
1 Introduction
