Learning Conditional Information by Jeffrey Imaging on Stalnaker Conditionals
- 153 Downloads
We propose a method of learning indicative conditional information. An agent learns conditional information by Jeffrey imaging on the minimally informative proposition expressed by a Stalnaker conditional. We show that the predictions of the proposed method align with the intuitions in Douven (Mind & Language, 27(3), 239–263 2012)’s benchmark examples. Jeffrey imaging on Stalnaker conditionals can also capture the learning of uncertain conditional information, which we illustrate by generating predictions for the Judy Benjamin Problem.
KeywordsLearning conditional information Stalnaker conditional Imaging Douven’s examples Judy Benjamin problem
Thanks to Hannes Leitgeb, Stephan Hartmann, Igor Douven, and Hans Rott for helpful discussions. Special thanks go to an anonymous referee for very constructive comments. I am grateful that I had the opportunity to present parts of this paper and obtain feedback at the Munich Centre for Mathematical Philosophy (LMU Munich), at the Inaugural Conference of the East European Network for Philosophy of Science (New Bulgarian University), at the International Rationality Summer Institute 2016 (Justus Liebig University), at the Centre for Advanced Studies Workshop on “Learning Conditionals” (LMU Munich), at the University of Bayreuth and the University of British Columbia. This research is supported by the Graduate School of Systemic Neurosciences.
- 1.Crestani, F. (1998). Logical imaging and probabilistic information retrieval. In Crestani, F., Lalmas, M., van Rijsbergen, C.J. (Eds.) Information Retrieval: Uncertainty and Logics: Advanced Models for the Representation and Retrieval of Information (pp. 247–279). Boston: Springer.Google Scholar
- 6.Gärdenfors, P. (1988). Knowledge in flux. Cambridge: MIT Press.Google Scholar
- 7.Günther, M. (2017). Learning conditional and causal information by jeffrey imaging on stalnaker conditionals. Organon F, 24(4), 456–486.Google Scholar
- 8.Hartmann, S., & Rad, S.R. (2017). Learning indicative conditionals. Unpublished manuscript, 1–28.Google Scholar
- 9.Jeffrey, R.C. (1965). The logic of decision. New York: Mc Graw-Hill.Google Scholar
- 13.Sebastiani, F. (1998). Information retrieval, imaging and probabilistic logic. Computers and Artificial Intelligence, 17(1), 1–16.Google Scholar
- 14.Stalnaker, R.C. (1975). A theory of conditionals. In Sosa, E. (Ed.) Causation and Conditionals (pp. 165–179). OUP.Google Scholar
- 16.Van Benthem, J., & Smets, S. (2015). Dynamic logics of belief change. In Van Ditmarsch, H., Halpern, J. Y., Van der Hoek, W., Kooi, B. (Eds.) Handbook of Logics for Knowledge and Belief, chapter 7 (pp. 299–368): College Publications.Google Scholar