Skip to main content Accessibility help
×
Home
Hostname: page-component-55597f9d44-54jdg Total loading time: 0.445 Render date: 2022-08-13T11:02:53.648Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

BISIMULATIONS FOR KNOWING HOW LOGICS

Published online by Cambridge University Press:  22 March 2021

RAUL FERVARI
Affiliation:
FACULTAD DE MATEMÁTICA, ASTRONOMÍA, FÍSICA Y COMPUTACIÓN UNIVERSIDAD NACIONAL DE CÓRDOBA MEDINA ALLENDE S/N, CÓRDOBA, ARGENTINAE-mail: rfervari@unc.edu.arURL: http://cs.famaf.unc.edu.ar/~rfervari
FERNANDO R. VELÁZQUEZ-QUESADA
Affiliation:
INSTITUTE FOR LOGIC, LANGUAGE AND COMPUTATION UNIVERSITEIT VAN AMSTERDAM P.O. BOX 94242, 1090, GE AMSTERDAM, THE NETHERLANDSE-mail: F.R.VelazquezQuesada@uva.nlURL: http://staff.fnwi.uva.nl/f.r.velazquezquesada
YANJING WANG
Affiliation:
FACULTAD DE MATEMÁTICA, ASTRONOMÍA, FÍSICA Y COMPUTACIÓN UNIVERSIDAD NACIONAL DE CÓRDOBA MEDINA ALLENDE S/N, CÓRDOBA, ARGENTINAE-mail: rfervari@unc.edu.arURL: http://cs.famaf.unc.edu.ar/~rfervari DEPARTMENT OF PHILOSOPHY PEKING UNIVERSITY 100871 BEIJING, CHINAE-mail: y.wang@pku.edu.cnURL: http://wangyanjing.com/

Abstract

As a new type of epistemic logics, the logics of knowing how capture the high-level epistemic reasoning about the knowledge of various plans to achieve certain goals. Existing work on these logics focuses on axiomatizations; this paper makes the first study of their model theoretical properties. It does so by introducing suitable notions of bisimulation for a family of five knowing how logics based on different notions of plans. As an application, we study and compare the expressive power of these logics.

Type
Research Article
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ågotnes, T. & Alechina, N. (2019). Coalition logic with individual, distributed and common knowledge. Journal of Logic and Computation, 29(7), 10411069.CrossRefGoogle Scholar
Ågotnes, T., Goranko, V., & Jamroga, W. (2007). Alternating-time temporal logics with irrevocable strategies. In Proceedings of Conference on Theoretical Aspects of Rationality and Knowledge. New York: ACM, pp. 1524.Google Scholar
Ågotnes, T., Goranko, V., Jamroga, W., & Wooldridge, M. (2015). Knowledge and ability (see van Ditmarsch et al. (2015), Ch. 11). In Handbook of Epistemic Logic. London: College Publications, pp. 543589.Google Scholar
Alur, R., Henzinger, T., & Kupferman, O. (2002). Alternating-time temporal logic. Journal of the ACM, 49(5), 672713.CrossRefGoogle Scholar
Areces, C. & Figueira, D. (2009). Which semantics for neighbourhood semantics? In Proceedings of IJCAI 2009. San Francisco, CA: AAAI Press. pp. 671676.Google Scholar
Artemov, S. & Fitting, M. (2019). Justification Logic: Reasoning with Reasons. Cambridge Tracts in Mathematics, Vol. 216. Cambridge: Cambridge University Press.Google Scholar
Bakhtiari, Z., van Ditmarsch, H., & Hansen, H. H. (2017). Neighbourhood contingency bisimulation. In Proceedings of ICLA. Berlin: Springer, pp. 4863.Google Scholar
Baltag, A. (2016). To know is to know the value of a variable. In Proceedings of Advances in Modal Logic, Vol. 11. London: College Publications, pp. 135155.Google Scholar
Baltag, A. & Ciná, G. (2018). Bisimulation for conditional modalities. Studia Logica, 106(1), 133.CrossRefGoogle Scholar
Belardinelli, F., Condurache, R., Dima, C., Jamroga, W., & Jones, A. V. (2017). Bisimulations for verifying strategic abilities with an application to threeballot. In Proceedings of AAMAS. New York: ACM, pp. 12861295.Google Scholar
Belardinelli, F., Dima, C., & Murano, A. (2018). Bisimulations for logics of strategies: a study in expressiveness and verification. In Thielscher, M., Toni, F., and Wolter, F., editors. Proceedings of KR. San Francisco, CA: AAAI Press. pp. 425434.Google Scholar
Blackburn, P., de Rijke, M., & Venema, Y. (2002). Modal Logic. Cambridge: Cambridge University Press.Google Scholar
Blackburn, P. & van Benthem, J. (2006). Modal logic: a semantic perspective. In Handbook of Modal Logic. North Holland: Elsevier. pp. 184.Google Scholar
Bolander, T. & Andersen, M. B. (2011). Epistemic planning for single and multi-agent systems. Journal of Applied Non-Classical Logics, 21(1), 934.CrossRefGoogle Scholar
Bulling, N. & Jamroga, W. (2014). Comparing variants of strategic ability: how uncertainty and memory influence general properties of games. Autonomous Agents and Multi-Agent Systems, 28(3), 474518.CrossRefGoogle Scholar
Dovier, A., Piazza, C. & Policriti, A. (2004). An efficient algorithm for computing bisimulation equivalence. Theoretical Computer Science, 311(1–3), 221256.CrossRefGoogle Scholar
Duijf, H. (2018). Let’s Do It!: Collective Responsibility, Joint Action, and Participation. PhD Thesis, Utrecht University, Utrecht, The Netherlands.Google Scholar
Fagin, R., Halpern, J. Y., Moses, Y., & Vardi, M. Y. (1995). Reasoning About Knowledge. Cambridge, MA: The MIT Press.Google Scholar
Fan, J., Wang, Y., & van Ditmarsch, H. (2015). Contingency and knowing whether. The Review of Symbolic Logic, 8, 75107.CrossRefGoogle Scholar
Fantl, J. (2017). Knowledge how. In Zalta, E. N., editor. The Stanford Encyclopedia of Philosophy (Fall 2017 edition). Stanford, CA: Metaphysics Research Lab.Google Scholar
Fervari, R., Herzig, A., Li, Y., & Wang, Y. (2017). Strategically knowing how. In Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence. IJCAI, USA: IJCAI, pp. 10311038.CrossRefGoogle Scholar
Fervari, R., Velázquez-Quesada, F. R., & Wang, Y. (2017). Bisimulations for knowing how logics. Presented at 5th International Workshop on Strategic Reasoning. Liverpool, UK.Google Scholar
Gochet, P. (2013). An open problem in the logic of knowing how. In Hintikka, J., editor. Open Problems in Epistemology. Helsinki: The Philosophical Society of Finland.Google Scholar
Goranko, V. & Otto, M. (2006). Model theory of modal logic. In Handbook of Modal Logic, Vol. 3. New York: Elsevier Science, Inc., pp. 249329.CrossRefGoogle Scholar
Goranko, V. & Passy, S. (1992). Using the universal modality: gains and questions. Journal of Logic and Computation, 2(1), 530.CrossRefGoogle Scholar
Gu, T. & Wang, Y. (2016). “knowing value” logic as a normal modal logic. In Proceedings of Advances in Modal Logic, Vol. 11. London: College Publications, pp. 362381.Google Scholar
Hansen, H. H. (2003). Monotonic modal logics. Master’s Thesis, Universiteit van Amsterdam.Google Scholar
Hansen, H. H., Kupke, C., & Pacuit, E. (2007). Bisimulation for neighbourhood structures. In Mossakowski T., Montanari U., and Haveraaen M., editors. Algebra and Coalgebra in Computer Science. Lecture Notes in Computer Science, Vol. 4624. Berlin: Springer, pp. 279293.CrossRefGoogle Scholar
Hansen, H. H., Kupke, C., & Pacuit, E.. (2009). Neighbourhood structures: bisimilarity and basic model theory. Logical Methods in Computer Science, 5(2), 138.CrossRefGoogle Scholar
Hart, S., Heifetz, A., & Samet, D. (1996). Knowing whether, knowing that, and the cardinality of state spaces. Journal of Economic Theory, 70(1), 249256.CrossRefGoogle Scholar
Herzig, A. (2015). Logics of knowledge and action: critical analysis and challenges. Autonomous Agents and Multi-Agent Systems, 29(5), 719753.CrossRefGoogle Scholar
Herzig, A. & Troquard, N. (2006). Knowing how to play: uniform choices in logics of agency. In Proceedings of AAMAS. New York: ACM, pp. 209216.CrossRefGoogle Scholar
Hintikka, J. (1962). Knowledge and Belief: An Introduction to the Logic of the Two Notions. Ithaca, NY: Cornell University Press.Google Scholar
Hodges, W. (1993). Model Theory. Encyclopedia of Mathematics and Its Applications, Vol. 42. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Horty, J. F. & Pacuit, E. (2017). Action types in STIT semantics. Review of Symbolic Logic, 10(4), 617637.CrossRefGoogle Scholar
Jamroga, W. & Ågotnes, T. (2007). Constructive knowledge: what agents can achieve under imperfect information. Journal of Applied Non-Classical Logics, 17(4), 423475.CrossRefGoogle Scholar
Li, Y. (2017). Stopping means achieving: a weaker logic of knowing how. Studies in Logic, 9(4), 3454.Google Scholar
Li, Y. & Wang, Y. (2017). Achieving while maintaining: a logic of knowing how with intermediate constraints. In Proceedings of ICLA. Heidelberg: Springer, pp. 154167.Google Scholar
Li, Y. & Wang, Y.. (2019). Multi-agent knowing how via multi-step plans: a dynamic epistemic planning based approach. In Proceedings of LORI 2019. Berlin: Springer Nature, pp. 126139.Google Scholar
Li, Y., Yu, Q., & Wang, Y. (2017). More for free: a dynamic epistemic framework for conformant planning over transition systems. Journal of Logic and Computation, 27(8), 23832410.CrossRefGoogle Scholar
Meyer, J.-J. C. & van Der Hoek, W. (1995). Epistemic Logic for AI and Computer Science. New York: Cambridge University Press.CrossRefGoogle Scholar
Naumov, P. & Tao, J. (2017a). Coalition power in epistemic transition systems. In Proceedings of AAMAS. New York: ACM, pp. 723731.Google Scholar
Naumov, P. & Tao, J.. (2017b). Together we know how to achieve: an epistemic logic of know-how (extended abstract). In Proceedings of Conference on Theoretical Aspects of Rationality and Knowledge. Australia: Open Publishing Association, pp. 441453.Google Scholar
Naumov, P. & Tao, J.. (2018a). Second-order know-how strategies. In Proceedings of AAMAS, Richland, SC: IFAAMAS, pp. 390398.Google Scholar
Naumov, P. & Tao, J.. (2018b). Strategic coalitions with perfect recall. In Proceedings of AAAI. San Francisco, CA: AAAI Press, pp. 47024709.Google Scholar
Naumov, P. & Tao, J.. (2018c). Together we know how to achieve: an epistemic logic of know-how. Artificial Intelligence, 262, 279300.CrossRefGoogle Scholar
Naumov, P. & Tao, J.. (2019). Knowing-how under uncertainty. Artificial Intelligence, 276, 4156.CrossRefGoogle Scholar
Nissim, R., Hoffmann, J., & Helmert, M. (2011). Computing perfect heuristics in polynomial time: on bisimulation and merge-and-shrink abstraction in optimal planning. In Proceedings of IJCAI 2011. Menlo Park, CA: AAAI, pp. 19831990.Google Scholar
Pacuit, E. (2017). Neighborhood Semantics for Modal Logic. Berlin: Springer.CrossRefGoogle Scholar
Parikh, R. & Ramanujam, R. (2003). A knowledge based semantics of messages. Journal of Logic, Language and Information, 12(4), 453467.CrossRefGoogle Scholar
Pauly, M. (1999). Bisimulation for general non-normal modal logic. Unpublished manuscript.Google Scholar
Sangiorgi, D. (2011). Introduction to Bisimulation and Coinduction. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Stanley, J. & Williamson, T. (2001). Knowing how. The Journal of Philosophy, 98(8), 411444.CrossRefGoogle Scholar
van Benthem, J., Bezhanishvili, N., Enqvist, S., & Yu, J. (2017). Instantial neighbourhood logic. The Review of Symbolic Logic, 10(1), 116144.CrossRefGoogle Scholar
van der Hoek, W. & Wooldridge, M. (2003). Cooperation, knowledge, and time: alternating-time temporal epistemic logic and its applications. Studia Logica, 75(1), 125157.CrossRefGoogle Scholar
van Ditmarsch, H., Halpern, J. Y., van der Hoek, W., & Kooi, B., editors. (2015). Handbook of Epistemic Logic. London: College Publications.Google Scholar
van Eijck, J., Gattinger, M., & Wang, Y. (2017). Knowing values and public inspection. In Proceedings of ICLA. Berlin, pp. 7790.Google Scholar
Wang, X. (2019). A logic of knowing how with skippable plans. In Proceedings of LORI. Berlin: Springer Nature, pp. 413424.Google Scholar
Wang, Y. (2015). A logic of knowing how. Proceedings of LORI. Lecture Notes in Computer Science, Vol. 9394. Berlin: Springer, pp. 392405.Google Scholar
Wang, Y.. (2017). A new modal framework for epistemic logic. In Proceedings of Conference on Theoretical Aspects of Rationality and Knowledge. Australia: Open Publishing Association, pp. 515534.Google Scholar
Wang, Y.. (2018a). Beyond knowing that: a new generation of epistemic logics. In van Ditmarsch, H. & Sandu, G., editors. Jaakko Hintikka on Knowledge and Game Theoretical Semantics. Berlin: Springer, pp. 499533.CrossRefGoogle Scholar
Wang, Y.. (2018b). A logic of goal-directed knowing how. Synthese, 195(10), 44194439.CrossRefGoogle Scholar
Wang, Y. & Li, Y. (2012). Not all those who wander are lost: dynamic epistemic reasoning in navigation. In Advances in Modal Logic, Vol. 10. pp. 559580.Google Scholar
Xu, C., Wang, Y., & Studer, T. (2021). A logic of knowing why. Synthese, 198, 12591285.CrossRefGoogle Scholar
1
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

BISIMULATIONS FOR KNOWING HOW LOGICS
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

BISIMULATIONS FOR KNOWING HOW LOGICS
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

BISIMULATIONS FOR KNOWING HOW LOGICS
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *