The axiomatic presentation of modal systems and the standard formulations of natural
deduction and sequent calculus for modal logic are reviewed, together with the difficulties …

The book is about Gentzen calculi for (the main systems of) modal logic. It is divided into
three parts. In the first part we introduce and discuss the main philosophical ideas related to …

Although sequent calculi constitute an important category of proof systems, they are not as
well known as axiomatic and natural deduction systems. Addressing this deficiency, this …

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 …

Sequent calculus for the provability logic GL is considered, in which provability is based on
the notion of a circular proof. Unlike ordinary derivations, circular proofs are represented by …

This paper provides a study of sequent calculi for intuitionistic Gödel–Löb logic (iGL), which
is the intuitionistic version of the classical modal logic GL, known as Gödel–Löb logic. We …

Recently, Brighton gave another cut-admissibility proof for the standard set-based sequent
calculus GLS for modal provability logic GL. One of the two induction measures that Brighton …

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 …

The key strength of preference-based logics for conditional obligation is their ability to
handle contrary-to-duty paradoxes and account for exceptions. Here we investigate Åqvist's …