Interpreting and Applying Proof Theories for Modal Logic
Francesca Poggiolesi, Greg Restall · Palgrave Macmillan UK eBooks · 2012
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. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.