Proof Theory of Modal Logic

1. Front Matter

   Pages i-x

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2. Standard Proof Systems

   1. Front Matter

      Pages 1-1

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   2. A Contraction-Free Sequent Calculus for S4

      • Jörg Hudelmaier

      Pages 3-15

   3. Transfer of Sequent Calculus Strategies to Resolution for S4

      • Grigori Mints, Vladimir Orevkov, Tanel Tammet

      Pages 17-31

   4. A Linear Approach to Modal Proof Theory

      • Harold Schellinx

      Pages 33-43

   5. Refutations and Proofs in S4

      • Tomasz Skura

      Pages 45-51

3. Extended Formalisms

   1. Front Matter

      Pages 53-53

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   2. Relational Proof Systems for Modal Logics

      • Ewa Orlowska

      Pages 55-78

   3. The Display Problem

      • Nuel Belnap

      Pages 79-92

   4. Power and Weakness of the Modal Display Calculus

      • Marcus Kracht

      Pages 93-121

   5. A Proof-Theoretic Proof of Functional Completeness for Many Modal and Tense Logics

      • Heinrich Wansing

      Pages 123-136

   6. On the Completeness of Classical Modal Display Logic

      • Rajeev Goré

      Pages 137-140

   7. Modal Sequents

      • Claudio Cerrato

      Pages 141-166

   8. Modal Functional Completeness

      • Kosta Došen, Zoran Petrić

      Pages 167-211

   9. A Computational Interpretation of Modal Proofs

      • Simone Martini, Andrea Masini

      Pages 213-241

   10. Gabbay-Style Calculi

       • Szabolcs Mikulás

       Pages 243-252

4. Translation-Based Proof Systems

   1. Front Matter

      Pages N3-N3

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   2. Translating Graded Modalities into Predicate Logics

      • H. J. Ohlbach, R. Schmidt, U. Hustadt

      Pages 253-291

   3. From Classical to Normal Modal Logics

      • Olivier Gasquet, Andreas Herzig

      Pages 293-311

5. Back Matter

   Pages 313-317

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Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.

• automated deduction
• knowledge
• knowledge representation
• logic
• modal logic
• predicate logic
• proof
• proof theory
• sequent calculus

• Institute of Logic and Philosophy of Science, University of Leipzig, Germany

  Heinrich Wansing

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