Single-Course Engelsk 5 ECTS

# Logical Theories for Uncertainty and Learning

## Overall Course Objectives

Reasoning with and managing uncertainty is important in many areas of artificial intelligence, for example, in expert systems and robotics, but also in various approaches to automated learning. The course will overview a representative selection of different mathematical models for dealing with uncertain knowledge and learning in an interactive context, such as (Multi-agent Epistemic) Modal Logic, Belief Revision Theory, Bayesian Probability Theory, and Game Theory. The aim of the course is to provide the student with theory and tools necessary to apply the models in research and in programming practice.

See course description in Danish

Learning Objectives

• 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.

Course Content

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

Recommended prerequisites

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

Teaching Method

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

Faculty

See course in the course database.

## Registration

Language Engelsk 13 weeks Compute DTU Lyngby Campus 02287 Candidate Week 36 Week 49 Thurs 8-12
Price 9.250,00 DKK