Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-17T11:03:26.427Z Has data issue: false hasContentIssue false
  • English
  • Français

CONTINGENCY AND KNOWING WHETHER

Published online by Cambridge University Press:  09 January 2015

JIE FAN ,
YANJING WANG  and
HANS VAN DITMARSCH
JIE FAN*
Affiliation:
Department of Philosophy, Peking University
YANJING WANG*
Affiliation:
Department of Philosophy, Peking University
HANS VAN DITMARSCH*
Affiliation:
LORIA-CNRS/Univeristy of Lorraine
*
*DEPARTMENT OF PHILOSOPHY, PEKING UNIVERSITY, BEIJING 100871, CHINA E-mail: fanjie@pku.edu.cn
†DEPARTMENT OF PHILOSOPHY, PEKING UNIVERSITY, BEIJING 100871, CHINA E-mail: y.wang@pku.edu.cn
‡LORIA-CNRS/UNIVERSITY OF LORRAINE, 54506 VANDUVRE-LÈS-NANCY, FRANCE E-mail: hans.van-ditmarsch@loria.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

A proposition is noncontingent, if it is necessarily true or it is necessarily false. In an epistemic context, ‘a proposition is noncontingent’ means that you know whether the proposition is true. In this paper, we study contingency logic with the noncontingency operator Δ but without the necessity operator □. This logic is not a normal modal logic, because Δ(φ → ψ) → (Δφ → Δψ) is not valid. Contingency logic cannot define many usual frame properties, and its expressive power is weaker than that of basic modal logic over classes of models without reflexivity. These features make axiomatizing contingency logics nontrivial, especially for the axiomatization over symmetric frames. In this paper, we axiomatize contingency logics over various frame classes using a novel method other than the methods provided in the literature, based on the ‘almost-definability’ schema AD proposed in our previous work. We also present extensions of contingency logic with dynamic operators. Finally, we compare our work to the related work in the fields of contingency logic and ignorance logic, where the two research communities have similar results but are apparently unaware of each other’s work. One goal of our paper is to bridge this gap.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 8 , Issue 1 , March 2015 , pp. 75 - 107
Copyright
Copyright © Association for Symbolic Logic 2014 

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

BIBLIOGRAPHY

Aloni, M., Égré, P., & Jager, T. (2013). Knowing whether A or B. Synthese, 190(14), 2595–2621.CrossRefGoogle Scholar
Attamah, M., van Ditmarsch, H., Grossi, D., & van der Hoek, W. (2014). Knowledge and gossip. In Proceedings of 21st ECAI. Amsterdam: IOS Press, pp. 21–26.Google Scholar
Balbiani, P., Baltag, A., van Ditmarsch, H., Herzig, A., Hoshi, T., & De Lima, T. (2008). ‘Knowable’ as ‘known after an announcement’. Review of Symbolic Logic, 1(3), 305–334.CrossRefGoogle Scholar
Baltag, A., Moss, L. S., & Solecki, S. (1998). The logic of public announcements, common knowledge, and private suspicions. In Proceedings of the 7th TARK, San Francisco, CA: Morgan Kaufmann, pp. 43–56.Google Scholar
Brogan, A. (1967). Aristotle’s logic of statements about contingency. Mind, 76(301), 49–61.CrossRefGoogle Scholar
Ciardelli, I., & Roelofsen, F. (2014). Inquisitive dynamic epistemic logic. Synthese, doi:10.1007/s11229-014-0404-7. To appear.Google Scholar
Demri, S. (1997). A completeness proof for a logic with an alternative necessity operator. Studia Logica, 58(1), 99–112.CrossRefGoogle Scholar
Égré, P. (2008). Question-embedding and factivity. Grazer Philosophische Studien, 77, 85–125.CrossRefGoogle Scholar
Fan, J., Wang, Y., & van Ditmarsch, H. (2014). Almost necessary. Advances in Modal Logic, Vol. 10. pp. 178–196.Google Scholar
Hansen, J. (2011). A logic toolbox for modeling knowledge and information in multi-agent systems and social epistemology. PhD Thesis, Roskilde University.Google Scholar
Hart, S., Heifetz, A., & Samet, D. (1996). Knowing whether, knowing that, and the cardinality of state spaces. Journal of Economic Theory, 70(1), 249–256.CrossRefGoogle Scholar
Hedetniemi, S., Hedetniemi, S., & Liestman, A. (1988). A survey of gossiping and broadcasting in communication networks. Networks, 18, 319–349.CrossRefGoogle Scholar
Heifetz, A., & Samet, D. (1993). Universal Partition Structures. Working paper (Israel Institute of business research). Tel Aviv: Tel Aviv University.Google Scholar
Hendricks, V. (2010). Knowledge transmissibility and pluralistic ignorance: A first stab. Metaphilosophy, 41, 279–291.CrossRefGoogle Scholar
Humberstone, L. (1995). The logic of noncontingency. Notre Dame Journal of Formal Logic, 36(2), 214–229.CrossRefGoogle Scholar
Humberstone, L. (2002). The modal logic of agreement and noncontingency. Notre Dame Journal of Formal Logic, 43(2), 95–127.CrossRefGoogle Scholar
Kuhn, S. (1995). Minimal non-contingency logic. Notre Dame Journal of Formal Logic, 36(2), 230–234.CrossRefGoogle Scholar
McCarthy, J. (1979). First-order theories of individual concepts and propositions. Machine Intelligence, 9, 129–147.Google Scholar
Montgomery, H., & Routley, R. (1966). Contingency and non-contingency bases for normal modal logics. Logique et Analyse, 9, 318–328.Google Scholar
Moses, Y., Dolev, D., & Halpern, J. (1986). Cheating husbands and other stories: a case study in knowledge, action, and communication. Distributed Computing, 1(3), 167–176.CrossRefGoogle Scholar
Petrick, R., & Bacchus, F. (2004). Extending the knowledge-based approach to planning with incomplete information and sensing. In Proceedings of the 9th KR, Palo Alto: AAAI Press, pp. 613–622.Google Scholar
Plaza, J. (1989). Logics of public communications. In Proceedings of the 4th ISMIS. Oak Ridge, TN: Oak Ridge National Laboratory, pp. 201–216.Google Scholar
Reiter, R. (2001). Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems. Cambridge: The MIT Press.CrossRefGoogle Scholar
Steinsvold, C. (2008). A note on logics of ignorance and borders. Notre Dame Journal of Formal Logic, 49(4), 385–392.CrossRefGoogle Scholar
van der Hoek, W., & Lomuscio, A. (2003). Ignore at your peril - towards a logic for ignorance. In Proceedings of 2nd AAMAS. New York: ACM, pp. 1148–1149.CrossRefGoogle Scholar
van der Hoek, W., & Lomuscio, A. (2004). A logic for ignorance. Electronic Notes in Theoretical Computer Science, 85(2), 117–133.CrossRefGoogle Scholar
van Ditmarsch, H. (2007). Comments to ‘Logics of public communications’. Synthese, 158(2), 181–187.CrossRefGoogle Scholar
van Ditmarsch, H., Fan, J., van der Hoek, W., & Iliev, P. (2014). Some exponential lower bounds on formula-size in modal logic. Advances in Modal Logic, Vol. 10. pp. 139–157.Google Scholar
van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2007). Dynamic Epistemic Logic, Vol. 337 of Synthese Library. Dordrecht: Springer.Google Scholar
Wang, Y., & Cao, Q. (2013). On axiomatizations of public announcement logic. Synthese, 190(1S), 103–134.CrossRefGoogle Scholar
Wang, Y., & Fan, J. (2013). Knowing that, knowing what, and public communication: Public announcement logic with Kv operators. In Proceedings of 23rd IJCAI, Palo Alto: AAAI Press, pp. 1147–1154.Google Scholar
Wang, Y., & Fan, J. (2014). Conditionally knowing what. Advances in Modal Logic, Vol. 10. pp. 569–587.Google Scholar
Wang, Y., Sietsma, F., & van Eijck, J. (2011). Logic of information flow on communication channels. In Omicini, A., Sardina, S., and Vasconcelos, W., editors. Declarative Agent Languages and Technologies VIII, Vol. 6619 of Lecture Notes in Computer Science. Berlin, Heidelberg: Springer, pp. 130–147.CrossRefGoogle Scholar
Zolin, E. (1999). Completeness and definability in the logic of noncontingency. Notre Dame Journal of Formal Logic, 40(4), 533–547.CrossRefGoogle Scholar
Zolin, E. (2001). Infinitary expressibility of necessity in terms of contingency. In Striegnitz, K., editor. Proceedings of the Sixth ESSLLI Student Session. pp. 325–334.Google Scholar
Zuber, R. (1982). Semantics restrictions on certains complementizers. In Proceedings of the 13th International Congress of Linguists, Tokyo, pp. 434–436.Google Scholar