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 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 …

We introduce FIK, a natural intuitionistic modal logic specified by Kripke models satisfying
the condition of forward confluence. We give a complete Hilbert-style axiomatization of this …

We investigate a simply typed modal λ-calculus, λ^→\square, due to Pfenning, Wong and
Davies, where we define a well-typed term with respect to a context stack that captures the …

We present a family of minimal modal logics (namely, modal logics based on minimal
propositional logic) corresponding each to a different classical modal logic. The minimal …

In this paper we investigate the Curry-Howard correspondence for constructive modal logic
in light of the gap between the proof equivalences enforced by the lambda calculi from the …

In this paper we investigate the Curry-Howard-Lambek correspondence for constructive
modal logic in light of the gap between the proof equivalences enforced by the lambda …

The field of intuitionistic modal logics studies intuitionistic counterparts of classical modal
logics. Classically, 2 and 3 are dual operators, but this is not necessarily true …

Proof theory is the branch of mathematical logic whose aim is studying the properties of
proofs, as well as their structure and invariants. For this purpose, the most used …