Conceived by Johan van Benthem and Yde Venema, arrow logic started as an attempt to give a general account of the logic of transitions. THe generality of the approach provided a wide application area ranging from philosophy to computer science. The book gives a comprehensive survey of logical research within and around arrow logic.

Since the natural operations on transitions include composition and taking inverses, and a special transition is the ‘do-nothing’ or the identity transition, the logic of transitions–arrow logic–can be studied from two different perspectives, and by two (complementary) methodologies: modal logic and the algebra of relations. Some of the results in this volume can be interpreted as price tages. They show what the prices of desirable properties, such as decidability, (finite) axiomatizability, Craig interpolation property, Beth definability, are in terms of semantic logic.

The research program of arrow logic has considereably broadened in the last couple of years and recently also covers the enterprise to explore the border between decidability, are in terms of semantic properites of logic.

The esearch program of arrow logic has considerably broadened in the last couple of years and recently also covers the enterprise to explore the border between decidable and undecidable versions of other applied logics. THe content of this volume reflects this broadening. The editors included a number of papers which are in the spirit of this generalized research program.

Maarten Marx is a research associate at the Department of Computing, Imperial College, London. László Pólos is a senior researcher at the Applied Logic Laboratory, Certer for Computer Science in Organization and Management (CCSOM) at the University of Amsterdam. Michael Masuch is the scientific director of the Center for Computer Science in Organization and Management (CCSOM) at the University of Amsterdam.

- Contributors
- Preface
- Part I Arrow Logic
- 1 A Crash Course in Arrow Logic
Yde Venema
- 2 Investigations in Arrow Logic
Maarten Marx, Szabolcs Mikulás, István Németi, and Ildikó Sain
- 3 Causes and Remedies for Undecidability in Arrow Logics and in Multi-Modal Logics
Hajnal Andréka, Ágnes Kurucz, István Németi, Ildikó Sain and András Simon
- 4 Associativity Does Not Imply Undecidability without the Axiom of Modal Logic
Viktor Gyuris
- 5 Dynamic Arrow Logic
Maarten Marx
- 6 Complete Calculus for Conjugated Arrow Logic
Szabolcs Mikulás
- 7 Many-Dimensional Arrow Structures: Arrow Logics II
Dimiter Vakarelov
- Part II Multi-Modal Logic
- 8 What is Modal Logic?
Maarten de Rijke
- 9 Content versus Wrapping: an Essay in Semantic Complexity
Johan van Benthem
- 10 A Fine-Structure Analysis of First-Order Logic
István Németi

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