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Modal Logic for Open Minds cover

Modal Logic for Open Minds

Johan van Benthem

In Modal Logic for Open Minds, Johan van Benthem provides an introduction to the field of modal logic, outlining its major ideas and exploring the numerous ways in which various academic fields have adopted it. Van Benthem begins with the basic theories of modal logic, examining its relationship to language, semantics, bisimulation, and axiomatics, and then covers more advanced topics, such as expressive power, computational complexity, and intelligent agency. Many of the chapters are followed by exercises, making this volume ideal for undergraduate and graduate students in philosophy, computer science, symbolic systems, cognitive science, and linguistics.

Johan van Benthem is University Professor of pure and applied logic at the University of Amsterdam, the Henry Waldgrave Stuart Professor of Philosophy at Stanford University, and the Weilun Visiting Professor of Humanities at Tsinghua University in Beijing.

Contents

    • Preface
    1. A whirlwind history, and changes in perspective 1
  • I Core Concepts 7
    1. Basic language and semantics 11
    2. Expressive power and invariance 25
    3. Validity and decidability 37
    4. Axioms, proofs, and completeness 49
    5. Computation and complexity 61
  • II Basic Theory 71
    1. Translation and varieties of expressive power 75
    2. Increasing deductive power: the landscape of modal logics 91
    3. What axioms say: frame correspondence 101
    4. Descriptive power: extended modal languages 109
    5. Modal predicate logic 119
  • III Selected Applications 127
    1. Epistemic logic 133
    2. Doxastic and conditional logic 147
    3. Dynamic logic of actions and events 155
    4. Logic and information dynamics 171
    5. Preference and deontic logic 189
    6. Modal logic and games 197
    7. The structure and flow of time 207
    8. Modal patterns in space 219
    9. Intuitionistic logic 233
    10. Provability logic 243
  • IV Recent Theoretical Themes 251
    1. Fixed-points, computation, and equilibrium 255
    2. Issues in information dynamics 265
    3. System combination and undecidability 281
    4. Abstract model theory 293
    5. Deductive incompleteness 303
  • V Coda 311
    1. Modal foundations for classical logic 315
    1. First-order predicate logic 323
    2. Modal algebra 333
    • Answers and hints to selected exercises 341
    • Guide to further literature 371
    • References 373
    • Index 379

April 2010

ISBN (Paperback): 9781575865980
ISBN (electronic): 9781575866581

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