Zhou, Chunlai - Probability Logic for Harsanyi Type Spaces

lmcs:898 - Logical Methods in Computer Science, June 24, 2014, Volume 10, Issue 2
Probability Logic for Harsanyi Type Spaces

Authors: Zhou, Chunlai

Probability logic has contributed to significant developments in belief types for game-theoretical economics. We present a new probability logic for Harsanyi Type spaces, show its completeness, and prove both a de-nesting property and a unique extension theorem. We then prove that multi-agent interactive epistemology has greater complexity than its single-agent counterpart by showing that if the probability indices of the belief language are restricted to a finite set of rationals and there are finitely many propositional letters, then the canonical space for probabilistic beliefs with one agent is finite while the canonical one with at least two agents has the cardinality of the continuum. Finally, we generalize the three notions of definability in multimodal logics to logics of probabilistic belief and knowledge, namely implicit definability, reducibility, and explicit definability. We find that S5-knowledge can be implicitly defined by probabilistic belief but not reduced to it and hence is not explicitly definable by probabilistic belief.

Source : oai:arXiv.org:1405.6355
DOI : 10.2168/LMCS-10(2:13)2014
Volume: Volume 10, Issue 2
Published on: June 24, 2014
Submitted on: September 4, 2012
Keywords: Mathematics - Logic


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