Typed Logics With States

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 well-known 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.