### The Research Project

It is the eve of the 2006 World Cup Final at Berlin's Olympic Stadium: Italy is going to play France. Consider the sentence X ="*Italy will score in the match against France*". You do not know for sure whether X will turn out to be true or false after the match. That is why bookmakers take bets on (the event described by) the sentence X - because the information conveyed by X is uncertain. Uncertainty is the realm of the theory of probability. Certainty, by contrast, is the realm of logic. Logic and probability are intimately related. Betting on the compound sentence X ∨ ¬X ="

*Either Italy will score or Italy will not score in the match against France*" is hardly exciting precisely because the logic of the original sentence X is classical - and so, in particular, X satisfies the

*tertium non datur*law that X ∨ ¬X is always true. We can reprhase this by saying X describes a classical, yes/no event: one that either obtains, or it does not. Consider next a slight variant of X, the sentence Y ="

*Italy will score early in the match against France*". The information conveyed by Y now suffers from two types of imperfection: first, you do not know for sure which instants of time in the course of the match should count as ‘early’; second, even if you knew that, you would still not know whether Y will turn out to be true or false after the match. In other words, not only is the information conveyed by Y uncertain, as before; it is also vague. The vague, non-classical proposition Y denotes a vague, non-classical event. This research project tackles the question, can one develop a substantive, mathematically significant probability theory of non-classical events. The research we plan to conduct can be categorised into five major areas.

The project is structured into five work packages.

- Foundational issues for the subjective probability theory of non-classical events.
- Duality theory (Stone duality and generalisations).
- Measure theory over dual spaces.
- Modalities over many-valued logics for reasoning about assignments of probabilities.
- Implementation of a software platform to handle bets on non-classical events.

## News

**[03/22/2012]**
Call for a Postdoctoral Position in Mathematics and Mathematical Logic - Deadline: **April 22, 2012**.
[link] [download pdf]

**[03/22/2012]**
Preliminary website online. Further content with details on the research project will be coming soon.