Possible world semantics underlies many of the applications of modal logic in computer
science and philosophy. The standard theory arises from interpreting the semantic …

We show that a type system based on the intuitionistic modal logic S4 provides an
expressive framework for specifying and analyzing computation stages in the context of …

In 1933 Gödel introduced a calculus of provability (also known as modal logic S4) and left
open the question of its exact intended semantics. In this paper we give a solution to this …

We reconsider the foundations of modal logic, following Martin-Löf's methodology of
distinguishing judgments from propositions. We give constructive meaning explanations for …

In this paper we consider an intuitionistic variant of the modal logic S4 (which we call IS4).
The novelty of this paper is that we place particular importance on the natural deduction …

We consider two systems of constructive modal logic which are computationally motivated.
Their modalities admit several computational interpretations and are used to capture …

Moggi's computational lambda calculus is a metalanguage for denotational semantics which
arose from the observation that many different notions of computation have the categorical …

Models of intuitionistic linear logic also provide models of Moggi's computational
metalanguage. We use the adjoint presentation of these models and the associated adjoint …

In this thesis we carry out a detailed study of the (propositional) intuitionistic fragment of
Girard's linear logic (ILL). Firstly we give sequent calculus, natural deduction and axiomatic …

We present natural deduction systems and associated modal lambda calculi for the
necessity fragments of the normal modal logics K, T, K4, GL and S4. These systems are in …