ESSLLI 2013 Advanced Course
Reasoning with Probabilities

[General Information]   [Overview]   [Motivation and Description]   [Lectures]  

General Information

Meeting Dates:ESSLLI 2013 Week 1: August 5-9
Meeting Times:Slot 1
Instructor:Joshua Sack
Email:J.H.Sack AT uva DOT nl

Here is a detailed description of the course and recommended materials.

  • Course description: [here]

This general information (as well as the rest of the website) will be updated as more information becomes available.


Both logic and probability provide a powerful tool for reasoning about uncertainty in diverse and dynamic environments. The goal of this course is to explore tools used by logicians, computer scientists, philosophers, and game theorists for modeling systems that employ logic and incorporate probability. Such tools will address logical frameworks of multi-agent uncertainty, clarify various conceptual issues (Aumann's agree to disagree result) and puzzles (such as Monty Hall puzzle). This course will focus on both important conceptual issues (e.g., Dutch book arguments, higher-order probabilities, and interactions between qualitative and quantitative uncertainty) and main technical results (e.g., completeness and decidability of probabilistic modal logics).

Motivation and Description

Probability logic has been developed in philosophy, computer science, and game theory, often toward different goals, but using similar frameworks. This course aims to strengthen the understanding a student from one of these disciplines may have of reasoning about probabilities in general, while also gaining an appreciation for the utility of probabilistic reasoning in other disciplines. This course discusses a number of issues that are involved in philosophy, such as Dutch book arguments that motivate the general properties of probability, as well as a number of puzzles and conceptual issues, such as Aumann's agree to disagree result and the Monty Hall puzzle. Issues in game theory will be discussed such as higher-order probabilities, common p-belief, mixed strategies, and type spaces. Also stochastic interpretations of modal probability logics often used in computer science will be discussed, such as logics for deterministic and non-deterministic probabilistic transition systems. This course will also discuss different ways the interaction between qualitative and quantitative uncertainty are addressed; logics for non-deterministic probabilistic transition systems and probabilistic automata help us reason about non-determinism over probabilities while probabilistic epistemic logics help us reason about uncertainty of probabilities. This course will also cover dynamics by presenting logics for reasoning about how new information may result in changes to both subjective probabilities that individual agents in a group have about the state of the world and qualitative uncertainties the agents have. Variations of this dynamic probabilistic epistemic logic will be discussed as well as some technical goals, such as completeness and decidability theorems.


Day 1 (August 5):Background and basic concepts[pdf]
Day 2 (August 6):Probabilistic modal logic[pdf]
Day 3 (August 7):Mixing qualitative and quantitative uncertainty[pdf]
Day 4 (August 8):Probabilistic epistemic dynamics[pdf]
Day 5 (August 9):Mixed strategies and general remarks[pdf]