Logical Theories for Uncertainty and Learning

• Describe a number of the most prevalent techniques in modelling uncertainty and learning.
• Describe the role of logic in the modelling of knowledge, uncertainty, and knowledge change.
• Describe the respective limitations of logic and probability in modelling learning.
• Compare and assess the appropriateness of various techniques for solving a given knowledge modelling problem.
• Assess difficulties specific to single-agent modelling of knowledge.
• Assess difficulties specific to multi-agent modelling of knowledge.
• Independently explore the literature relevant for the project.
• Write a paper in the style of a conference article.

1. From Propositional Logic to Epistemic Logic: Language and Models,
2. Logical Properties of (Group) Knowledge,
3. Axiomatic Systems and Proofs, Soundness and Completeness of Epistemic Logic
4. Knowledge Change: Public Announcement Logic, Belief Revision
5. Probability Based Modelling of Uncertainty: Bayes Theorem, Bayesian Update
6. Modelling Uncertainty about Probability Distribution: Belief Functions, Possibility Measures, Ranking Functions, Relative Likelihood, Plausibility Measures
7. Game Theory: Cooperation and Conflict, Nash Equilibrium, Mixed strategies, Pareto Efficiency
8. Extensive Form Games: Harsanyi Transformation, Bayesian Update in Games, Backward Induction, Infinite Payoffs

01017/02156/02180, Discrete mathematics, in particular propositional logic and first order logic; elementary probability theory.

Lectures, exercises, written assignments (theoretical and/or programming).