Abstract
We present here a novel approach to the analysis of common knowledge based on category theory. In particular, we model the global epistemic state for a given set of agents through a hierarchy of beliefs represented by a presheaf construction. Then, by employing the properties of a categorical monad, we prove the existence of a state, obtained in an iterative fashion, in which all agents acquire common knowledge of some underlying statement. In order to guarantee the existence of a fixed point under certain suitable conditions, we make use of the properties entailed by Sergeyev's numeral system called grossone, which allows a finer control on the relevant structure of the infinitely nested epistemic states.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
