| Sumario: | In the literature there are at least two main formal structures to deal with situations of interactive epistemology: Kripke models and type spaces. As shown in many papers (see Aumann and Brandenburger in Econometrica 36:1161-1180, ; Baltag et al. in Synthese 169:301-333, ; Battigalli and Bonanno in Res Econ 53(2):149-225, ; Battigalli and Siniscalchi in J Econ Theory 106:356-391, ; Klein and Pacuit in Stud Log 102:297-319, ; Lorini in J Philos Log 42(6):863-904, ), both these frameworks can be used to express epistemic conditions for solution concepts in game theory. The main result of this paper is a formal comparison between the two and a statement of semantic equivalence with respect to two different logical systems: a doxastic logic for belief and an epistemic-doxastic logic for belief and knowledge. Moreover, a sound and complete axiomatization of these logics with respect to the two equivalent Kripke semantics and type spaces semantics is provided. Finally, a probabilistic extension of the result is also presented. A further result of the paper is a study of the relationship between the epistemic-doxastic logic for belief and knowledge and the logic STIT (the logic of 'seeing to it that') by Belnap and colleagues (Facing the future: agents and choices in our indeterminist world, ).
|
|---|