Abstract
In this paper, we propose a single-agent modal logic framework for reasoning about goal-direct “knowing how” based on ideas from linguistics, philosophy, modal logic and automated planning. We first define a modal language to express “I know how to guarantee ϕ given ψ” with a semantics not based on standard epistemic models but labelled transition systems that represent the agent’s knowledge of his own abilities. A sound and complete proof system is given to capture the valid reasoning patterns about “knowing how” where the most important axiom suggests its compositional nature.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Von Wright, G.H.: An Essay in Modal Logic. North-Holland, Amsterdam (1951)
Hintikka, J.: Knowledge and Belief: An Introduction to the Logic of the Two Notions. Cornell University Press, Ithaca (1962)
Wang, R.J.: Timed Modal Epistemic Logic. PhD thesis, City University of New York (2011)
van Ditmarsch, H., Halpern, J.Y., van der Hoek, W., Kooi, B. (eds.): Handbook of Epistemic Logic. College Publications (2015)
Egré, P.: Question-embedding and factivity. Grazer Philosophische Studien 77(1), 85–125 (2008)
Harrah, D.: The logic of questions. In: Gabbay, D. (ed.) Handbook of Philosophical Logic, vol. 8, Springer (2002)
Hintikka, J.: Socratic Epistemology: Explorations of Knowledge-Seeking by Questioning. Cambridge University Press (2007)
Hintikka, J., Hintikka, M.: Reasoning about knowledge in philosophy: The paradigm of epistemic logic. In: The Logic of Epistemology and the Epistemology of Logic. Synthese Library, vol. 200, pp. 17–35. Springer, Netherlands (1989)
Fitting, M., Mendelsohn, R.L.: First-order modal logic. Synthese Library. Springer (1998)
Fagin, R., Halpern, J., Moses, Y., Vardi, M.: Reasoning about knowledge. MIT Press (1995)
Ciardelli, I., Groenendijk, J., Roelofsen, F.: Inquisitive semantics: A new notion of meaning. Language and Linguistics Compass 7(9), 459–476 (2013)
Ciardelli, I., Roelofsen, F.: Inquisitive dynamic epistemic logic. Synthese 192(6), 1643–1687 (2015)
Plaza, J.A.: Logics of public communications. In: Emrich, M.L., Pfeifer, M.S., Hadzikadic, M., Ras, Z.W. (eds.) Proceedings of the 4th International Symposium on Methodologies for Intelligent Systems, pp. 201–216 (1989)
Hart, S., Heifetz, A., Samet, D.: Knowing whether, knowing that, and the cardinality of state spaces. Journal of Economic Theory 70(1), 249–256 (1996)
van der Hoek, W., Lomuscio, A.: Ignore at your peril - towards a logic for ignorance. In: Proceedings of AAMAS 2003, pp. 1148–1149. ACM (2003)
Wang, Y., Fan, J.: Knowing that, knowing what, and public communication: Public announcement logic with kv operators. In: Proceedings of IJCAI, 2013 (2013)
Wang, Y., Fan, J.: Conditionally knowing what. In: Advances in Modal Logic, vol. 10, pp. 569–587 (2014)
Fan, J., Wang, Y., van Ditmarsch, H.: Almost necessary. In: Advances in Modal Logic, vol. 10, pp. 178–196 (2014)
Fan, J., Wang, Y., van Ditmarsch, H.: Contingency and knowing whether. The Review of Symbolic Logic 8, 75–107 (2015)
Xiong, S.: Decidability of ELKv r. Bachelaor thesis (2014)
Stanley, J., Williamson, T.: Knowing how. The Journal of Philosophy, 411–444 (2001)
Ryle, G.: Knowing how and knowing that: The presidential address. In: Proceedings of the Aristotelian Society, vol. 46, pp. 1–16 (1946)
Fantl, J.: Knowing-how and knowing-that. Philosophy Compass 3(3), 451–470 (2008)
McCarthy, J., Hayes, P.J.: Some philosophical problems from the standpoint of artificial intelligence. In: Machine Intelligence, pp. 463–502. Edinburgh University Press (1969)
McCarthy, J.: First-Order theories of individual concepts and propositions. Machine Intelligence 9, 129–147 (1979)
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 (1985)
Gochet, P.: An open problem in the logic of knowing how. In: Hintikka, J. (ed.) Open Problems in Epistemology. The Philosophical Society of Finland (2013)
Ågotnes, T., Goranko, V., Jamroga, W., Wooldridge, M.: Knowledge and ability. In: van Ditmarsch, H., Halpern, J., van der Hoek, W., Kooi, B. (eds.) Handbook of Epistemic Logic, pp. 543–589. College Publications (2015)
Vendler, Z.: Linguistics in Philosophy. Cornell University Press (1967)
Lau, T., Wang, Y.: Formalizing “knowing how”. (unpublished manuscript) (2015)
Lau, T.: Formalizing “knowing how”. Master’s thesis, Peking University (2015) (in Chinese)
Morgenstern, L.: A first order theory of planning, knowledge, and action. In: Proceedings of the 1986 Conference on Theoretical Aspects of Reasoning About Knowledge, pp. 99–114. Morgan Kaufmann Publishers Inc., San Francisco (1986)
Herzig, A., Troquard, N.: Knowing how to play: uniform choices in logics of agency. In: Proceedings of AAMAS 2006, pp. 209–216 (2006)
Broersen, J.: A logical analysis of the interaction between ‘obligation-to-do’ and ‘knowingly doing’. In: van der Meyden, R., van der Torre, L. (eds.) DEON 2008. LNCS (LNAI), vol. 5076, pp. 140–154. Springer, Heidelberg (2008)
Jamroga, W., van der Hoek, W.: Agents that know how to play. Fundamenta Informaticae 63(2-3), 185–219 (2004)
Carr, D.: The logic of knowing how and ability. Mind 88(351), 394–409 (1979)
Noë, A.: Against intellectualism. Analysis, 278–290 (2005)
Tillio, A.D., Halpern, J.Y., Samet, D.: Conditional belief types. Games and Economic Behavior 87, 253–268 (2014)
Smith, D.E., Weld, D.S.: Conformant graphplan. In: AAAI 1998, pp. 889–896 (1998)
Wang, Y., Li, Y.: Not all those who wander are lost: Dynamic epistemic reasoning in navigation. In: Advances in Modal Logic, vol. 9, pp. 559–580 (2012)
Yu, Q., Li, Y., Wang, Y.: A dynamic epistemic framework for conformant planning. In: Proceedings of TARK 2015, pp. 249–259. ACM (2015)
Brown, M.A.: On the logic of ability. Journal of Philosophical Logic 17(1), 1–26 (1988)
Stanley, J.: Know how. Oxford University Press (2011)
Wang, Y.: Representing imperfect information of procedures with hyper models. In: Banerjee, M., Krishna, S.N. (eds.) ICLA. LNCS, vol. 8923, pp. 218–231. Springer, Heidelberg (2015)
Kracht, M., Wolter, F.: Simulation and transfer results in modal logic - A survey. Studia Logica 59(1), 149–177 (1997)
Goranko, V., Passy, S.: Using the universal modality: Gains and questions. Journal of Logic and Computation 2(1), 5–30 (1992)
van Benthem, J., van Eijck, J., Kooi, B.: Logics of communication and change. Information and Computation 204(11), 1620–1662 (2006)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, Y. (2015). A Logic of Knowing How. In: van der Hoek, W., Holliday, W., Wang, Wf. (eds) Logic, Rationality, and Interaction. LORI 2015. Lecture Notes in Computer Science(), vol 9394. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48561-3_32
Download citation
DOI: https://doi.org/10.1007/978-3-662-48561-3_32
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-48560-6
Online ISBN: 978-3-662-48561-3
eBook Packages: Computer ScienceComputer Science (R0)