Skip to main content
SpringerLink
Log in
Book cover

International Workshop on Logic, Rationality and Interaction

LORI 2019: Logic, Rationality, and Interaction pp 413–424Cite as

A Logic of Knowing How with Skippable Plans

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11813))

Abstract

The paper expands upon the work by Wang [16], who proposes a single-agent modal logic framework for reasoning about “knowing how”. This paper proposes a more flexible semantics to the knowing-how operator. According to this semantics, an agent knows how to achieve \(\varphi \) given \(\psi \) if there exists a finite linear plan such that it will end up with some \(\varphi \)-state from any \(\psi \)-state by executing the plan, either fully or skipping some non-executable steps. We give a sound and complete axiomatization of this logic. Finally we introduce a suitable notion of bisimulation for this logic.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    It is a variant of the example in [16].

  2. 2.

    \({\mathbb {SKHS}}\) is exactly the same proof system as in [16].

  3. 3.

    Please refer to the proof of Proposition 2 in [16].

  4. 4.

    It is exactly the Proposition 5.

  5. 5.

    Please refer to the proof of Proposition 6 in [16].

  6. 6.

    We can prove it via the filtration method. Consider the filtrations of canonical models through the subformula closed set generated by \(\varphi \). The filtration model is indeed a bounded small model for \(\varphi \). Here we do not show the details of the proof, since the proposition is a corollary of Proposition 8 in [16], for \(\mathbb {SKHS}\) is same as the proof system in [16] and both systems are sound and complete.

  7. 7.

    This section borrows ideas from [4].

References

  1. Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. J. ACM 49(5), 672–713 (2002). https://doi.org/10.1145/585265.585270

    Article  MathSciNet  MATH  Google Scholar 

  2. Ågotnes, T., Goranko, V., Jamroga, W., Wooldrige, M.: Knowledge and ability. In: van Ditmarsch, H., Halperen, J., van der Hoek, H., Kooi, B. (eds.) Handbook of Epistemic Logic, pp. 543–589. College Publications, London (2015)

    Google Scholar 

  3. Fervari, R., Herzig, A., Li, Y., Wang, Y.: Strategically knowing how. In: Proceedings of IJCAI, pp. 1031–1038 (2017). https://doi.org/10.24963/ijcai.2017/143

  4. Fervari, R., Velázquez-Quesada, F.R., Wang, Y.: Bisimulation for knowing how logics. Manuscript, Presented at SR 2017 (2017)

    Google Scholar 

  5. Gochet, P.: An open question in the logic of knowing how. In: Open Problems in Epistemlogy. The Philosophical Society of Finland (2013)

    Google Scholar 

  6. Li, Y.: Stopping means achieving: a wearker logic of knowing how. Stud. Log. 9(4), 34–54 (2016)

    Google Scholar 

  7. Li, Y.: Knowing what to do: a logical approach to planning and knowing how. Ph.D. thesis, University of Groningen (2017)

    Google Scholar 

  8. Li, Y., Wang, Y.: Achieving while maintaining: a logic of knowing how with intermediate constraints. In: Ghosh, S., Prasad, S. (eds.) ICLA 2017. LNCS, vol. 10119, pp. 154–167. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54069-5_12

    Chapter  Google Scholar 

  9. McCarthy, J., Hayes, J.P.: Some philosophical problems from the standpoint of artificial intelligence. In: Meltzer, B., Michie, D. (eds.) Machine Intelligence, pp. 463–502. Edinburgh University Press, Edinburgh (1969)

    MATH  Google Scholar 

  10. McCarthy, J.: First-order theories of individual concepts and propositions. Mach. Intell. 9, 129–147 (1979)

    MathSciNet  Google Scholar 

  11. Moore, R.C.: A formal theory of knowledge and action. In: Hobbs, J.R., Moore, R.C. (eds.) Formal Theories of the Commonsense World. Ablex Publishing Corporation, Norwood (1985)

    Google Scholar 

  12. Naumov, P., Tao, J.: Together we know how to achieve: an epistemic logic of know-how. Artif. Intell. 262, 279–300 (2018). https://doi.org/10.1016/j.artint.2018.06.007

    Article  MathSciNet  MATH  Google Scholar 

  13. Pauly, M.: A modal logic for coalitional power in games. J. Log. Comput. 12(1), 149–166 (2002). https://doi.org/10.1093/logcom/12.1.149

    Article  MathSciNet  MATH  Google Scholar 

  14. Raymond, R.: Knowledge in Action. The MIT Press, Cambridge (2001)

    MATH  Google Scholar 

  15. Wang, Y.: A logic of knowing how. In: van der Hoek, W., Holliday, W.H., Wang, W. (eds.) LORI 2015. LNCS, vol. 9394, pp. 392–405. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48561-3_32

    Chapter  Google Scholar 

  16. Wang, Y.: A logic of goal-directed knowing how. Synthese 195(10), 4419–4439 (2018). https://doi.org/10.1007/s11229-016-1272-0

    Article  MathSciNet  Google Scholar 

  17. Wang, Y.: Beyond knowing that: a new generation of epistemic logics. In: van Ditmarsch, H., Sandu, G. (eds.) Jaakko Hintikka on Knowledge and Game-Theoretical Semantics. OCL, vol. 12, pp. 499–533. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-62864-6_21

    Chapter  Google Scholar 

Download references

Acknowledgments

The author thanks Yanjing Wang for giving the author the ideas of the skippable plan and the bisimulation, and his helpful comments to make the paper more readable. The author thanks the three anonymous reviewers for their insightful comments on the early version of the paper.

Author information

Authors and Affiliations

  1. Department of Philosophy, Peking University, Beijing, China

    Xun Wang

Authors
  1. Xun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xun Wang .

Editor information

Editors and Affiliations

  1. Roskilde University, Roskilde, Denmark

    Patrick Blackburn

  2. Université Paul Sabatier, IRIT-CNRS, Toulouse, France

    Emiliano Lorini

  3. Southwest University, Chongqing, China

    Meiyun Guo

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer-Verlag GmbH Germany, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Wang, X. (2019). A Logic of Knowing How with Skippable Plans. In: Blackburn, P., Lorini, E., Guo, M. (eds) Logic, Rationality, and Interaction. LORI 2019. Lecture Notes in Computer Science(), vol 11813. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-60292-8_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-60292-8_30

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-60291-1

  • Online ISBN: 978-3-662-60292-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation