Dear all,

We will have our next LIRa session tomorrow, on Thursday, 3 March 16:30.

Please use our recurring zoom link: https://uva-live.zoom.us/j/88142993494?pwd=d1BsQWR4T2UyK0Job29YNThjaGRkUT09 (Meeting ID: 881 4299 3494, Passcode: 352984)

You can find the details of the talk below.

Speaker: Louwe Kuijer (University of Liverpool)

Date and Time: Thursday, March 3rd 2022, 16:30-18:00, Amsterdam time.

Venue: online.

Title: Doing the best I can.

Abstract.

A preference structure is a graph that indicates preferences between alternatives. These alternatives could be possible worlds, outcomes of an action, strategies in a game or something else entirely. The preferences, similarly, can mean many different things: a world might be preferred over another if it is more plausible, an outcome if it improves social welfare, and a strategy might be preferred over another strategy that it defeats.

From these preferences we can determine the set of "best" worlds,

outcomes and strategies. Generally, one should believe the best worlds, strive to obtain the best outcomes and play the best strategies. As usual in deontic logic, we can then define a notion of obligation (to believe, bring about or play), where ϕ is obligatory, denoted B(ϕ) if all of the best alternatives satisfy ϕ (and thus it is impossible to satisfy the obligation to be "best'' without making ϕ true).

This notion of obligation can be extended to a conditional one, B(ϕ|ψ), where ϕ is obligatory given ψ, by relativization. In other words, we restrict the preference structure to those alternatives that satisfy ψ, and check whether ϕ is true in all of the best alternatives in that structure.

The properties of this conditional obligation operator depend on (1) exactly how we define what the "best" states in a preference structure are and (2) what properties the preference relation satisfies (e.g., transitive, total, anti-symmetric).

In this talk, I will discuss characterizations of the conditional belief operator under various such assumptions. We will also consider one case where, despite searching for a long time, I did not manage to find a characterization: this turned out to be because such a characterization does not exist.

Hope to see you there!

The LIRa team