Gentzen Calculi for Modal Propositional Logic

  • Francesca Poggiolesi

Part of the Trends in Logic book series (TREN, volume 32)

Table of contents

  1. Front Matter
    Pages i-xi
  2. An Overview of the Sequent Calculus

    1. Front Matter
      Pages 1-1
    2. Francesca Poggiolesi
      Pages 3-35
  3. Sequent Calculi for Modal Logic

    1. Front Matter
      Pages 37-37
    2. Francesca Poggiolesi
      Pages 39-53
    3. Francesca Poggiolesi
      Pages 55-74
    4. Francesca Poggiolesi
      Pages 75-100
  4. Tree-Hypersequent Calculi

    1. Front Matter
      Pages 117-117
    2. Francesca Poggiolesi
      Pages 119-141
    3. Francesca Poggiolesi
      Pages 143-163
    4. Francesca Poggiolesi
      Pages 165-174
    5. Francesca Poggiolesi
      Pages 175-186
    6. Francesca Poggiolesi
      Pages 203-207
  5. Back Matter
    Pages 209-222

About this book


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 proof theory, and we try to identify criteria for distinguishing good sequent calculi. In the second part we present  the several attempts made from the 50’s until today to provide modal logic with Gentzen calculi. In the third and and final part we analyse new calculi for modal logics, called tree-hypersequent calculi, which were recently introduced by the author. We show in a precise and clear way the main results that can be proved with and about them.



Gentzen calculus cut-elimination modal logic tree-hypersequent

Authors and affiliations

  • Francesca Poggiolesi
    • 1
  1. 1., Department of PhilosophyVRIJE UNIVERSITEIT BRUSSELSBrusselsBelgium

Bibliographic information