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Proof Theory of Modal Logic

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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.

Author(s): Heinrich Wansing (eds.)
Series: Applied Logic Series 2
Publisher: Springer Netherlands
Year: 1996

Language: English
Pages: 318
Tags: Logic; Artificial Intelligence (incl. Robotics); Mathematical Logic and Foundations

Front Matter....Pages i-x
Front Matter....Pages 1-1
A Contraction-Free Sequent Calculus for S 4....Pages 3-15
Transfer of Sequent Calculus Strategies to Resolution for S4....Pages 17-31
A Linear Approach to Modal Proof Theory....Pages 33-43
Refutations and Proofs in S4....Pages 45-51
Front Matter....Pages 53-53
Relational Proof Systems for Modal Logics....Pages 55-78
The Display Problem....Pages 79-92
Power and Weakness of the Modal Display Calculus....Pages 93-121
A Proof-Theoretic Proof of Functional Completeness for Many Modal and Tense Logics....Pages 123-136
On the Completeness of Classical Modal Display Logic....Pages 137-140
Modal Sequents....Pages 141-166
Modal Functional Completeness....Pages 167-211
A Computational Interpretation of Modal Proofs....Pages 213-241
Gabbay-Style Calculi....Pages 243-252
Front Matter....Pages N3-N3
Translating Graded Modalities into Predicate Logics....Pages 253-291
From Classical to Normal Modal Logics....Pages 293-311
Back Matter....Pages 313-317