Logic--Connecting Stanford and ILLC
General InformationTime: 9:00-13:00
Place: P3.27, Plantage Muidergracht 24, Universiteit van Amsterdam.
This informal seminar on current research is open to everyone.
If you have any questions, please contact Fenrong Liu.
Speakers and Abstracts
In general, an epistemic model M may attribute more information to an agent A than can be captured by the object language L. M may contain two worlds, for example, which can be distinguished by A, even though they satisfy exactly the same formulas in L. So, given L, we can ask: which (L-dependent) properties of M assure that L is able to capture all the information modelled by M.
I will give intuitive motivations and formal definitions of two such properties: tightness and saturation. Also, I will outline some applications of this idea. But I will leave its general relevance open to discussion.
Standard epistemic logics assume that the agents can reason about all contingencies of the world, as expressed by the set of atomic sentences. Consequently, all the agents are equal in what they can reason about: when we model an interaction, an epistemic situation including a NY stockbroker and a Guinea tribesman, the latter also either knows that NASDAQ will go up, or considers the opposite possible. To our best knowledge, all the existing articles dealing with unawareness problem considered only the relation of unawareness to knowledge. However, if we want to include awareness issues in standard rational choice modelling, establishing relation between awareness and probabilistic reasoning seems unavoidable. In this paper we purport to build a logic for knowledge, awareness and probabilistic reasoning. We do so in both a nonstartegic and strategic setting, which includes actions and utilities. This allows us to extend such notions as Bayesian Equilibrium to situation with awareness differences.
You can download the paper 'Onions to Broccoli: Generalizing Lewis's Counterfactual Logic' from here.
Dynamic-epistemic logic and Bayesian update seem close in spirit. So, what is the proper merge of the two paradigms? Barteld Kooi's 2003 dissertation shows how such a merge works well for public announcement. Van Benthem 2003 does the same for more general action-update in the BMS-style, be it at the price of a complex form of probabilized action preconditions. Van Benthem & Gerbrandy 2005 propose a 'lighter' version in terms of 'protocols' defining probabilistic processes which suffices for many standard cases.
In my talk, I will state and review the relevant formal definitions, and then discuss the following issues:
Moreover, I will analyze a recurrent challenge to BMS-style update analyses, stated by Halpern & Friedman, Parikh, and most recently Kooi 2005. The framework is claimed to be unable to deal with 'protocols' defining special types of process or agent, corresponding to subsets of possible runs. This issue is not specifically probabilistic, but we will discuss it in the present setting. While the criticism makes sense for very general topological protocols, we will show how most normal protocols can be handled just fine with an appropriate choice of relevant 'events' plus their pre- conditions. Our method yields a uniform transformation.
J. van Benthem, 2003, 'Conditional Probability Meets Update Logic', Journal of Logic, Language and Information 12:4, 409-421.
J. van Benthem & J. Gerbrandy, 2005, 'Interfacing Probabilistic and Epistemic Update', talk at Update Workshop, ILLC, 7 september 2005.
B. Kooi, 2003, 'Knowledge, Chance, and Change', Dissertation DS-2003-01, ILLC Amsterdam & Department of Informatics, University Groningen.
B. Kooi, 2005, talk on 'Strategy Models' and problems with DEL-style probabilistic update, at the same Update Workshop, ILLC, 7 september 2005.