Proof Theory of Modal Logic

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.

I Standard Proof Systems.- A Contraction-free Sequent Calculus for S4.- Transfer of Sequent Calculus Strategies to Resolution for S4.- A Linear Approach to Modal Proof Theory.- Refutations and Proofs in S4.- II Extended Formalisms.- Relational Proof Systems for Modal Logics.- The Display Problem.- Power and Weakness of the Modal Display Calculus.- A Proof-theoretic Proof of Functional Completeness for Many Modal and Tense Logics.- On the Completeness of Classical Modal Display Logic.- Modal Sequents.- Modal Functional Completeness.- A Computational Interpretation of Modal Proofs.- Gabbay-style Calculi.- III Translation-based Proof Systems.- Translating Graded Modalities into Predicate Logics.- From Classical to Normal Modal Logics.