Fitch-style modal deduction, in which modalities are eliminated by opening a subordinate
proof, and introduced by shutting one, were investigated in the 1990s as a basis for lambda …

In recent years, we have seen several new models of dependent type theory extended with
some form of modal necessity operator, including nominal type theory, guarded and clocked …

A variety of intuitionistic versions of modal logic have been proposed in the literature. An
apparent misconception is that all these logics coincide on their-only (or-free) fragment …

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 …

This paper presents a uniform and modular method to prove uniform interpolation for several
intermediate and intuitionistic modal logics. The proof-theoretic method uses sequent calculi …

We define a family of intuitionistic non-normal modal logics; they can be seen as intuitionistic
counterparts of classical ones. We first consider monomodal logics, which contain only …

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The logics CS4 and IS4 are intuitionistic variants of the modal logic S4. Whether the finite
model property holds for each of these logics has been a long-standing open problem. In …

We derive an intuitionistic version of G\" odel-L\" ob modal logic ($\sf {GL} $) in the style of
Simpson, via proof theoretic techniques. We recover a labelled system, $\sf {\ell IGL} $, by …

We provide a new sequent calculus that enjoys syntactic cut-elimination and strongly
terminating backward proof search for the intuitionistic Strong Löb logic, an intuitionistic …