Modal Logic (Cambridge Tracts in Theoretical Computer Science)

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Summary: The Amsterdam Text: All Tomorrow's Standards
Review: *The* definitive treatment of propositional modal logic; the vastly more expensive Oxford Logic Guide adds nothing essential to what is also a *thoroughly* up-to-date introduction to the methods of formal logic, concerned less with stylistic beauty than the nitty-gritty of fine structures. How long will it take you to read this? Don't worry about it, because the pedagogical approach of the book makes transitions to more specialized texts on particular topics easy. What's missing? A wide-scope view of computation such as functional programming languages employ, and an adequate explanation for why the practically limited and theoretically thorny modal predicate calculi are excluded (such as one imagines could be whipped up rather quickly using correspondence-theoretic techniques). But for a very reasonable price, you need not feel obligated to join the ranks of contemporary computer scientists.

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Summary: Finally, an approach to Modal Logic for the new century...
Review: If you're wondering why modal language is so useful but are dismayed about possible worlds, then this is your book. (Side note: when does Blackburn sleep? how can you be at the forefront of modal logic and natural language processing at the same time?)

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Summary: A great gateway into the world of Modal Logics
Review: This book is excellent in content. It is definitely not a book that one should expect to read in one sitting, nor two or three. This is a book one needs to grow into. There is a basic track and an advanced track and these are clearly marked throughout the book. It is presumed that the reader should have at least some familiarity with both basic set theory and first order logic. The first four chapters would be the best introduction as a first read. If you are interested in modern algebra, chapter 5 will present interesting connections between Modal Logic and Algebra. The book has several Appendixes: A Logical Toolkit, An Algebraic Toolkit and A Computational Toolkit. These can be very handy if you can't remember what an ultrafilter is or what the difference is between NP and PSPACE. Another very nice feature of this book is that every chapter ends with a historical overview of the people and concepts involved in the material just covered. This really makes the subject more "alive" and makes the study of Modal Logic more purposeful and motivated.

At the time of writing this, I do not know how this book compares to other introductions to the field of Modal Logic. Moreover, as a student of Yde Venema and of Maarten de Rijke (two of the authors), I am perhaps slightly biased. Nevertheless, I would recommend this book to anyone who wants to seriously delve into the world of Modal Logic.

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Summary: A modern perspective on modal logic
Review: This book outstands for how the authors present the wide field of modal logics. In a unified framework where classic unimodal logic, dynamic logic and arrow logic are treated as case studies, the authors put forth their view on modal logics as instruments to speak about local properties of relation algebras. This view mandates a novel way to present the subject (this is one of the few books of my knowledge on modal logic which introduces bisimulation from the first chapter), a task that the authors perform wonderfully with a deep and rigorous yet truly understandable presentation of the main issues in modal logics. This is a book whose importance cannot be underestimated. Note however that the book does not treat topics as model checking, mu calculus or properties of a specific logic, be it a K-anything, C/LTL(*), a dynamic logic or whatever. Citing: "The reader looking for a catalogue of facts about his or her favorite modal system probably won't find it here. But such a reader may well find the technique needed to algebraize it, to analyze its expressive power, to prove a completeness result, or to establish its decidability or undecidability - and may even discover that the relevant results are a special case of something known".