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 …

The book presents a thoroughly elaborated logical theory of generalized truth-values
understood as subsets of some established set of (basic) truth values. After elucidating the …

We introduce translations between display calculus proofs and labeled calculus proofs in
the context of tense logics. First, we show that every derivation in the display calculus for the …

A comparison is given between two conditions used to define logical constants: B elnap's
uniqueness and H acking's deducibility of identicals. It is shown that, in spite of some surface …

This paper is dedicated to extending and adapting to modal logic the approach of fractional
semantics to classical logic. This is a multi-valued semantics governed by pure proof …

The difficulty in finding analytic Gentzen sequent calculi for non-classical logics has lead to
the development of many new proof frameworks (proof systems) that have been used to give …

We define a bi-directional embedding between hypersequent calculi and a subclass of
systems of rules (2-systems). In addition to showing that the two proof frameworks have the …

We study two logics of knowledge and belief stemming from the work of Stalnaker (2006),
omitting positive introspection for knowledge. The two systems are equivalent with positive …

This paper deals with the question of the logicality of modal logics from a proof-theoretic
perspective. It is argued that if Dos̆en's analysis of logical constants as punctuation marks …

The aim of this paper is to introduce and explain display calculi for a variety of logics. We
provide a survey of key results concerning such calculi, though we focus mainly on the …