Logic and Computation advanced course:
Reasoning with Probabilities.

• Eric Pacuit ()
• Joshua Sack ()

Course material: epprob-outline.pdf

Both logic and probability provide powerful tools for reasoning about uncertainty in a dynamic environment. Our goal in this course is to examine logical frameworks that incorporate probabilistic modeling of multiagent uncertainty. We will then see how merging these two perspectives on uncertainty can help clarify various conceptual issues and puzzles (such as the Monty Hall puzzle or the sleeping beauty problem). The primary objective is to explore the formal tools used by logicians, computer scientists, philosophers and game theorists for modeling uncertainty. We will focus on both the important conceptual issues (eg., Dutch book arguments, updating with probability zero events and higher-order probabilities) and the main technical results (eg., completeness and decidability of probabilistic modal logics).

Course Outline: The course will cover all of the following topics:

0. Background in dynamic epistemic logic and probabilistic models of uncertainty (including issues of measurability and Dutch book arguments)

1. Various puzzles about probability, beliefs and time (including the Monty Hall puzzle, the Sleeping Beauty problem and the Absent-Minded Driver problem)

2. Higher-order probability measures (including a definition of "common p-belief'' and uses of the concept in game theory)

3. Modal probabilistic logic (including proofs of completeness, decidability, and other standard results)

4. Uncertainty in a dynamic environment (including Bayesian/Jeffrey updates)

5. Updating with probability zero events (including lexicographic probability distributions, conditional probability distributions and relations with belief revision models) 6. Dynamic Epistemic Probabilistic Logic (including discussion of reduction axioms and temporal extensions)

Prerequisites: This is an advanced but self-contained course. Students will be expected to have had some exposure to (dynamic) epistemic logic and probabilistic logic. In particular, it will be assumed that students have already been introduced to epistemic logic and some of its dynamic extensions (i.e., public announcement logic); and although we will introduce many basic concepts of probabilistic theory (e.g., measure spaces), it will be expected that students have had previous exposure to probabilistic models of uncertainty.

http://ai.stanford.edu/~epacuit/classes/esslli/epprob.html