Open AccessCommon Knowledge in an Epistemic Logic with Hypotheses
Author(s) -
Levan Uridia,
Dirk Walther
Publication year - 2020
Publication title -
epic series in computing
Language(s) - English
Resource type - Conference proceedings
ISSN - 2398-7340
DOI - 10.29007/43wj
Subject(s) - distributive property , epistemic modal logic , extension (predicate logic) , decidability , computer science , completeness (order theory) , epistemology , knowledge based systems , artificial intelligence , multimodal logic , mathematics , theoretical computer science , description logic , philosophy , pure mathematics , programming language , mathematical analysis
We extend epistemic logic S5r for reasoning about knowledge under hypotheses with distributive knowledge operator. This extension gives possibility to express distributive knowledge of agents with different background assumptions. The logic is important in com- puter science since it models agents behavior which already have some equipped knowledge. Extension with distributive knowledge shows to be extremely interesting since knowledge of an arbitrary agent whose epistemic capacity corresponds to any system between S4 and S5 under some restrictions can be modeled as distributive knowledge of agents with cer- tain background knowledge. We present an axiomatization of the logic and prove Kripke completeness and decidability results.