Common Knowledge in Epistemic Logic With Hypotheses

13 pages•Published: December 10, 2019

Abstract

We recall the epistemic logic S5r for reasoning about knowledge under hypotheses and we investigate the extension of the logic with an operator for common knowledge. The logic S5r is equipped with a modal operator of necessity that can be parameterized with hypotheses representing background assumptions while the extension with the common knowledge operator enables us to describe and reason about common knowledge among agents with possibly different background assumptions. We present an axiomatization of the logic and prove Kripke completeness and decidability results.

Keyphrases: kripke completeness, logic of hypotheses, modal logic

In: Diego Calvanese and Luca Iocchi (editors). GCAI 2019. Proceedings of the 5th Global Conference on Artificial Intelligence, vol 65, pages 139-151.

Links:	https://easychair.org/publications/paper/gq75
	https://doi.org/10.29007/glrl

BibTeX entry

@inproceedings{GCAI2019:Common_Knowledge_Epistemic_Logic,
  author    = {Levan Uridia and Dirk Walther},
  title     = {Common Knowledge in Epistemic Logic With Hypotheses},
  booktitle = {GCAI 2019. Proceedings of the 5th Global Conference on Artificial Intelligence},
  editor    = {Diego Calvanese and Luca Iocchi},
  series    = {EPiC Series in Computing},
  volume    = {65},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/gq75},
  doi       = {10.29007/glrl},
  pages     = {139-151},
  year      = {2019}}

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