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 …

In this paper we present a sequent calculus for the modal propositional logic GL (the logic of
provability) obtained by means of the tree-hypersequent method, a method in which the …

Modal logic is traditionally the logic obtained by adding to basic propositional logic, like
classical logic, the concepts of necessity (□) and possibility (♦). There is a wide consensus …

This chapter explores in a detailed yet accessible way the different logics of grounding that
have been proposed in recent years. Logically, the notion of grounding can be formalized in …

In this paper we present a sequent calculus for propositional dynamic logic built using an
enriched version of the tree-hypersequent method and including an infinitary rule for the …

A syntactic proof of cut-elimination yields a procedure to eliminate every instance of the cut-
rule from a derivation in the sequent calculus thus leading to a cutfree derivation. This is a …

Many more examples could easily be given. These in-virtue-of questions are also among
philosophy's oldest. Attempts to answer them stretch back to antiquity. And in-virtue-of …

In the first part of the book we defined what it means for a sequent calculus to be good and
we explained the reasons why it is important for a logic to have a good Gentzen calculus. In …