Typed Logics With States
Jan van Eijck
The paper presents a simple format for typed logics with states by adding a
function for register update to standard typed lambda calculus. It is shown
that universal validity of equality for this extended language is decidable
(extending a wellknown result of Friedman for typed lambda calculus). This
system is next extended to a full fledged typed dynamic logic, and it is
illustrated how the resulting format allows for very simple and intuitive
representations of dynamic semantics for natural language and denotational
semantics for imperative programming. The proposal is compared with some
alternative approaches to formulating typed versions of dynamic logics.
1991 Mathematics Subject Classification: 03B15, 03B65, 03B70, 68Q55, 68Q65
1991 Computing Reviews Classification System: D.3.3, F.3.2, I.2.4, I.2.7
Keywords and Phrases: Type theory, compositionality, denotational semantics,
dynamic semantics