Common Knowledge in an Epistemic Logic with Hypotheses

9 pages•Published: April 27, 2020

Abstract

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.

Keyphrases: distributive knowledge, kripke completeness, modal logic

In: Gregoire Danoy, Jun Pang and Geoff Sutcliffe (editors). GCAI 2020. 6th Global Conference on Artificial Intelligence (GCAI 2020), vol 72, pages 83-91.

Links:	https://easychair.org/publications/paper/K6hP
	https://doi.org/10.29007/43wj

BibTeX entry

@inproceedings{GCAI2020:Common_Knowledge_Epistemic_Logic,
  author    = {Levan Uridia and Dirk Walther},
  title     = {Common Knowledge in an Epistemic Logic with Hypotheses},
  booktitle = {GCAI 2020. 6th Global Conference on Artificial Intelligence (GCAI 2020)},
  editor    = {Gregoire Danoy and Jun Pang and Geoff Sutcliffe},
  series    = {EPiC Series in Computing},
  volume    = {72},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/K6hP},
  doi       = {10.29007/43wj},
  pages     = {83-91},
  year      = {2020}}

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