Interfacing Probabilistic and Epistemic Update Amsterdam, September 7, 2005

This workshop aims at exploring shared topics between the communities in dynamic epistemic logic and in Bayesian update. The speakers are open-minded spokespersons for both traditions.

Date: The workshop will be held on September 7, 2005.

Location: P.3.27, Plantage Muidergracht 24, Universiteit van Amsterdam. For directions please click here.

The workshop is open to all interested. There is no entrance fee.

For more information, please contact Fenrong Liu.

Branden Fitelson, Old Evidence, Logical Omniscience, and Bayesian Learning. Slides

In this talk, I will explain what the problem of old evidence is, and how Garber and Jeffrey try to resolve it by offering (different) ways of relaxing the standard assumption of logical omniscience implicit in (naive) Bayesian theories of learning. I will critically evaluate the approaches of Garber and Jeffrey. Then, I will discuss Stalnaker's approach to logical omniscience and how it might be useful for proponents of Garber/Jeffrey-style approaches to the old evidence problem. This should raise interesting questions about both probabilistic updating and epistemic updating in logico-mathematical contexts. Time permitting, I will try to say something about how thinking about Garber, Jeffrey, and Stalnaker might help us think about the general problem of modeling logico-mathematical evidence in a Bayesian framework.

I recommend five readings as background for this talk. Items (1)-(4) are essential, and item (5) is the "time permitting" stuff (with some neat concrete problems for would-be Bayesian modelers of logico-mathematical evidence).

(1) Garber, D., 1983, Old Evidence and Logical Omniscience in Bayesian Confirmation Theory, Minnesota Studies in Philosophy of Science 10.

(2) Jeffrey, R., 1992, Probability and the Art of Judgment, Cambridge Press, pages 90-98; 103-107 (The Problem of New Explanation; Postscript: New Explanation Revisited).

(3) Jeffrey, R., 2004, Subjective Probability: The Real Thing, Cambridge Press, section 2.5 (Old News Explained). Available at http://www.princeton.edu/~bayesway/Book*.pdf

(4) Stalnaker, R., 2004, The Problem of Logical Omniscience (I and II), reprinted in Context and Content (Chapters 13 and 14), Oxford Press. These are available online (with Oxford Scholarship Online subscription), at http://www.oxfordscholarship.com/oso/private/ content/philosophy/0198237073/p059.html#acprof-0198237073-chapter-14, and http://www.oxfordscholarship.com/oso/private/content/philosophy/ 0198237073/p061.html#acprof-0198237073-chapter-15

(5) Martin, D. A., 1998, Mathematical Evidence, in Truth in mathematics, Edited by HG Dales and G. Oliveri, Oxford University Press, 1998, pages 215-231.

Wouter Meijs, Coherentism, Reliability and the Truth Conduciveness of Coherence. Slides

Recently, both Olsson (Against coherence, OUP, 2005) and Shogenji ('Justification by coherence from scratch', forthcoming in Philosophical Studies, see http://www.ric.edu/tshogenji/publications.htm) have argued that coherence cannot be a truth conducive property. The basic model that has dominated this discussion is one in which independent witnesses report on the same proposition. With respect to this model, coherence would be a truth conducive property if multiple reports by independent witnesses would make us more confidence that the proposition is true. Both Shogenji and Olsson have argued that this can only be the case if the witnesses are at least believed to be partially reliable. This would pose a serious problem for the coherentist account of the justification of our beliefs, since we do not generally know whether or not our sources are reliable. In my talk I will present an alternative model in which coherence can be truth-conducive, even if we do not know at all whether the witnesses are reliable. The model is very similar to the model that Bovens and Hartmann present in chapter 3 of their Bayesian Epistemology (OUP, 2003), but differs from it in explicitly taking into account the possibility that the witnesses are deliberate liars.

Johan van Benthem & Jelle Gerbrandy, Probability and Epistemic Actions. Slides

The theory of epistemic actions of Baltag, Moss and Solecki (1) seems to be a natural framework to study probabilistic actions as well. Such probabilistic epistemic actions may be observations about a probabilistic processes, communication acts that are about probabilities or happen with a certain probability, etc. To extend the theory of epistemic actions with probabilities, there are several choices to be made. Along one dimension is the question of where to add probabilistic information to an epistemic action model. The choice is between the chance that a certain action is happening (1) given certain preconditions, or (2) given that another action is happening. Another question is what these probabilities represent -- how to update prior probabilities to obtain posterior ones. There are two obvious options: (A) the probabilities express 'Bayes factors', 'rates of change' that say to what extend we should change the prior probabilities, or (B) they are Jeffrey-style probabilities that tell us what the posterior probabilities must look like. These choices carve out four classes of probabilistic updates. Van Benthem (2) has studied the class 1A, but we will discuss examples of the other classes as well. At the moment of writing this abstract, this work is still in a very preliminary stage, but we hope to make some material available on the web before the date of the workshop.

(1) Baltag, A. and Moss, L. S., 2004, Logics for Epistemic Programs. Synthese 139(2), 165-224.

(2) van Benthem, J., 2003, Conditional Probability Meets Update Logic, Journal of Logic, Language and Information 12 (4), 409-421.

Barteld Kooi, The Problems of Probability in Update Logics. Slides

Update logics are extensions of epistemic logic with additional operators that express information change. In probability theory information change is modeled with Bayesian updating. It seems natural for probability theory and update logics to join forces. Although progress has been made in combining the two, there are some problems that seem hard to overcome. One of the problems is that in update logics strategic information of protocol information is not taken into account. Another problem is that update logics model situations with more than one agent, and probability theory does not. This leads to problems regarding the information the agents have about each other, and problems with 'group rationality'. In my talk I will address these problems, and suggest ways to resolve them.

Jan Willem Romeijn, Dutch Books and Epistemic Events. Slides

This paper investigates the viability of the Bayesian model of belief change. Following van Benthem (Journal of Logic, Language and Information 12: 409-421, 2003), it shows that certain epistemic actions invalidate the diachronic Dutch book argument for the Bayesian model. It is then suggested how the problem can be solved by employing a semantics that incorporates epistemic events. The paper closes with a general claim on choosing appropriate semantics for the Bayesian model.

Sep 21, 2005, Amsterdam.