## Logic and Computation advanced course:

Reasoning with Probabilities.

Teachers
- Eric Pacuit ()
- Joshua Sack ()

Course material: epprob-outline.pdf

Abstract:
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