Modal Logic as Dialogical Logic

Patrick Blackburn 1
1 LANGUE ET DIALOGUE - Human-machine dialogue with a significant language component
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The title reflects my conviction that, viewed semantically, modal logic is fundamentally dialogical; this conviction is based on the key role played by the notion of bisimulation in modal model theory. But this dialogical conception of modal logic does not seem to apply to modal proof theory, which is notoriously messy. Nonetheless, by making use of ideas which trace back to Arthur Prior (notably the use of nominals, special proposition symbols which `name' worlds) I will show how to lift the dialogical conception to modal proof theory. I argue that this shift to hybrid logic has consequences for both modal and dialogical logic, and I discuss these in detail.
Type de document :
Article dans une revue
Synthese, Springer Verlag (Germany), 2001, 127 (1/2), pp.57-93
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Soumis le : mardi 26 septembre 2006 - 14:46:20
Dernière modification le : jeudi 11 janvier 2018 - 06:19:48


  • HAL Id : inria-00100503, version 1



Patrick Blackburn. Modal Logic as Dialogical Logic. Synthese, Springer Verlag (Germany), 2001, 127 (1/2), pp.57-93. 〈inria-00100503〉



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