From Type Spaces to Probability Frames and Back, via Language

Adam Bjorndahl
(Carnegie Mellon University)
Joseph Y. Halpern
(Cornell University)

We investigate the connection between the two major mathematical frameworks for modeling interactive beliefs: Harsanyi type spaces and possible-worlds style probability frames. While translating the former into the latter is straightforward, we demonstrate that the reverse translation relies implicitly on a background logical language. Once this "language parameter" is made explicit, it reveals a close relationship between universal type spaces and canonical models: namely, that they are essentially the same construct. As the nature of a canonical model depends heavily on the background logic used to generate it, this work suggests a new view into a corresponding landscape of universal type spaces.

In Jérôme Lang: Proceedings Sixteenth Conference on Theoretical Aspects of Rationality and Knowledge (TARK 2017), Liverpool, UK, 24-26 July 2017, Electronic Proceedings in Theoretical Computer Science 251, pp. 75–87.
Published: 25th July 2017.

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