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Abstract:
It is a delight to review this book. Heinrich Wansing has done more than anyone to study and apply Nuel Belnap's Display Logic, a generalisation or refinement of traditional Gentzen-style sequent calculi. Wansing has written over 10 papers on Display logic, and this volume collects together a almost all of his work in the area up until 1998. The volume is very much a collection of papers. It is a revised version of Wansing's Habilitationschrift, and it is a repository of all of Wansing's recent work on proof theory for intensional logic. Often, these kinds of volumes are disjointed and lack coherence: chapters are brought together because they share authorship, not because of any shared content. Wansing 's book shares just a little of this quality (despite being entitled Displaying Modal Logic, some chapters feature neither Display proof theory nor modal logic) but the over-arching coherence provided by Wansing's sensibilities and insights, manifest in each chapter, more than makes up for any discontinuity. The book is unified by its study of proof theories of intensional logics. The highlight is its treatment of Belnap's Display Logic [1]. Display logic generalises traditional Gentzen proof theories at the level of punctuation. Traditional Gentzen systems for classical logic work with sequents of the form
Citations
| 77 | Display Logic – Belnap - 1982 |
| 23 | The Logic of Information Structures – Wansing - 1993 |
| 19 | and weakness of the modal display calculus – Power - 1996 |
| 13 | Displaying and deciding substructural logics 1: Logics with contraposition – Restall - 1998 |
| 4 | A `Gentzen' System for Positive Relevant Implication – DUNN - 1974 |
| 2 | Cut-elimination theorem in relevant logics – Minc - 1976 |
