Skip to main content
SpringerLink
Log in

Awareness as Potential for Knowledge

  • Published:
Journal of Philosophical Logic Aims and scope Submit manuscript

Abstract

With the idea of analyzing awareness as potential for knowledge, we propose a novel semantics for awareness logic. Expressivities of languages with different combinations of modalities for this semantics are investigated. We explore the properties of our semantics and compare our model with Fagin & Halpern model and the model by Heifetz et al. in partitional settings. A series of equivalence results are established from the comparison. Finally, we provide two axiomatizations for implicit knowledge and explicit knowledge, respectively, and prove soundness and completeness for them.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ågotnes, T., & Alechina, N. (2007). Full and relative awareness: A decidable logic for reasoning about knowledge of unawareness. In Proceedings of the 11th Conference on theoretical aspects of rationality and knowledge. TARK ’07, pp. 6–14. Association for Computing Machinery, New York, NY, USA. https://doi.org/10.1145/1324249.1324255.

  2. Blackburn, P., Rijke, M.d., & Venema, Y. (2001). Modal Logic. Cambridge tracts in theoretical computer science. Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9781107050884.

    Google Scholar 

  3. Fagin, R., & Halpern, J.Y. (1987). Belief, awareness, and limited reasoning. Artificial Intelligence, 34 (1), 39–76. https://doi.org/10.1016/0004-3702(87)90003-8.

    Article  Google Scholar 

  4. Fagin, R., Halpern, J.Y., Moses, Y., & Vardi, M. (1995). Reasoning about knowledge. Cambridge: MIT Press.

    Google Scholar 

  5. Grossi, D., & Velázquez-Quesada, F.R. (2009). Twelve angry men: a study on the fine-grain of announcements. In He, X., Horty, J., Pacuit, E. (eds.) Logic, rationality, and interaction, pp. 147–160. Springer, Berlin, Heidelberg.

  6. Halpern, J.Y. (2001). Alternative semantics for unawareness. Games Econ Behav, 37(2), 321–339. https://doi.org/10.1006/game.2000.0832.

    Article  Google Scholar 

  7. Halpern, J.Y., & Rêgo, L.C. (2008). Interactive unawareness revisited. Games Econ Behav, 62(1), 232–262. https://doi.org/10.1016/j.geb.2007.01.012.

    Article  Google Scholar 

  8. Heifetz, A., Meier, M., & Schipper, B.C. (2006). Interactive unawareness. J Econ Theory, 130(1), 78–94. https://doi.org/10.1016/j.jet.2005.02.007.

    Article  Google Scholar 

  9. Heifetz, A., Meier, M., & Schipper, B.C. (2008). A canonical model for interactive unawareness. Games Econ Behav, 62(1), 304–324. https://doi.org/10.1016/j.geb.2007.07.003.

    Article  Google Scholar 

  10. Hintikka, J. (1962). Knowledge and belief cornell university press.

  11. Levesque, H.J. (1984). A logic of implicit and explicit belief. In Proceedings of the Fourth AAAI Conference on Artificial Intelligence. AAAI’84, pp. 198–202. AAAI Press.

  12. Lorini, E. (2020). Rethinking epistemic logic with belief bases. Artificial Intelligence, 282, 103233. https://doi.org/10.1016/j.artint.2020.103233.

    Article  Google Scholar 

  13. Meyer, J.-J.C., & Hoek, W.v.d. (1995). Epistemic logic for AI and computer science. Cambridge tracts in theoretical computer science. Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9780511569852https://doi.org/10.1017/CBO9780511569852.

    Google Scholar 

  14. Modica, S., & Rustichini, A. (1999). Unawareness and partitional information structures. Games Econ Behav, 27(2), 265–298. https://doi.org/10.1006/game.1998.0666.

    Article  Google Scholar 

  15. Schipper, B.C. (2015). 3. In van Ditmarsch, H., Halpern, J. Y., van der Hoek, W., Kooi, B. (eds.) Awareness. Handbook of epistemic logic, pp. 77–146. College publications, Lightning Source, Milton Keynes.

  16. Song, P., & Xiong, W. (2019). A two-layer partition awareness structure. In Blackburn, P.,Lorini, E., Guo, M. (eds.) Logic, rationality, and interaction, pp. 313–325. Springer, Berlin, Heidelberg.

  17. van Ditmarsch, H., van der Hoak, W, & Kooi, B. (2007). Dynamic epistemic logic synthese library Vol. 337. Dordrecht, The Netherlands: Springer.

    Google Scholar 

  18. van Ditmarsch, H., & French, T. (2009). Awareness and forgetting of facts and agents. In 2009 IEEE/WIC/ACM International joint conference on Web intelligence and intelligent agent technology, vol. 3, pp. 478–483. https://doi.org/10.1109/WI-IAT.2009.330.

  19. van Ditmarsch, H., & French, T. (2011). Becoming aware of propositional variables. In Banerjee, M., Seth, A. (eds.) Logic and its applications, pp. 204–218. Springer, Berlin, Heidelberg.

  20. van Ditmarsch, H., & French, T. (2014). Semantics for knowledge and change of awareness. Journal of Logic, Language and Information, 23(2), 169–195. https://doi.org/10.1007/s10849-014-9194-z.

    Google Scholar 

  21. van Ditmarsch, H., French, T., Velázquez-Quesada, F.R., & Wáng, Y.N. (2018). Implicit, explicit and speculative knowledge. Artificial Intelligence, 256, 35–67. https://doi.org/10.1016/j.artint.2017.11.004https://doi.org/10.1016/j.artint.2017.11.004.

    Article  Google Scholar 

  22. Velázquez-Quesada, F.R. (2009). Inference and update. Synthese, 169(2), 283–300. https://doi.org/10.1007/s11229-009-9556-2https://doi.org/10.1007/s11229-009-9556-2.

    Article  Google Scholar 

  23. Wheeler, G. (2020). Bounded rationality. In Zalta, E.N. The stanford encyclopedia of philosophy, fall 2020 edn. Metaphysics Research Lab, Stanford University.

Download references

Acknowledgements

This research was supported by the Key Project of National Social Science Foundation of China (No. 16AZX017). This paper rebuilds and extends the previous work “A Two-Layer Partition Awareness Structure”, in the proceedings of the 7th LORI. The authors would like to thank Professor Joseph Y. Halpern for his valuable comments on earlier versions of this paper during his visit to Sun Yat-sen University. Thank the editors for giving us more time to revise the paper. Great gratitude is paid to the anonymous reviewer for the exceptionally detailed comments and suggestions. The latter is crucial and indispensable for all the substantial improvements of this paper.

Author information

Authors and Affiliations

  1. College of Philosophy, Law & Political Science, Shanghai Normal University, Shanghai, 200234, China

    Pengfei Song

  2. Institute of Logic and Cognition, Department of Philosophy, Sun Yat-sen University, Guangzhou, 510275, China

    Wei Xiong

Authors
  1. Pengfei Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei Xiong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wei Xiong.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Song, P., Xiong, W. Awareness as Potential for Knowledge. J Philos Logic 52, 669–703 (2023). https://doi.org/10.1007/s10992-022-09684-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10992-022-09684-2

Keywords

Search

Navigation