Abstract
Modal logic is traditionally the logic obtained by adding to basic propositional logic, like classical logic, the concepts of necessity (□) and possibility (◊). There is a wide consensus on which are the main systems of modal logic—systems such as K, KT, KB, S4, S5 and the provability logic GL—and their canonical interpretation, Kripke models. Beyond that, there is little consensus. In particular, there is little consensus on the way to understand what it is to prove a statement like □A. While we have a systematic and rigorous formal account of truth conditions of modal statements (in Kripke models with points and accessibility relations with different properties, underwriting different principles governing □ and ◊ and their interaction), we have no such consensus on what the basic items of deduction in modal vocabulary are.
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© 2012 Francesca Poggiolesi and Greg Restall
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Poggiolesi, F., Restall, G. (2012). Interpreting and Applying Proof Theories for Modal Logic. In: Restall, G., Russell, G. (eds) New Waves in Philosophical Logic. New Waves in Philosophy. Palgrave Macmillan, London. https://doi.org/10.1057/9781137003720_4
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DOI: https://doi.org/10.1057/9781137003720_4
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