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 transitionsarrow logiccan 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.
is a research associate at the Department of Computing, Imperial College, London. is a senior researcher at the Applied Logic Laboratory, Certer for Computer Science in Organization and Management (CCSOM) at the University of Amsterdam. is the scientific director of the Center for Computer Science in Organization and Management (CCSOM) at the University of Amsterdam.
- Part I Arrow Logic
- 1 A Crash Course in Arrow Logic
- 2 Investigations in Arrow Logic
- 3 Causes and Remedies for Undecidability in Arrow Logics and in Multi-Modal Logics
- 4 Associativity Does Not Imply Undecidability without the Axiom of Modal Logic
- 5 Dynamic Arrow Logic
- 6 Complete Calculus for Conjugated Arrow Logic
- 7 Many-Dimensional Arrow Structures: Arrow Logics II
- Part II Multi-Modal Logic
- 8 What is Modal Logic?
- 9 Content versus Wrapping: an Essay in Semantic Complexity
- 10 A Fine-Structure Analysis of First-Order Logic