# A logical analysis of Monty Hall and Sleeping Beauty

## TL;DR

This paper models variants of the Monty Hall problem and the Sleeping Beauty problem using an extended form of IF logic called stochastic IF logic, providing new insights into these classic probability puzzles.

## Contribution

It introduces stochastic IF logic to incorporate chance moves in semantic games and applies it to analyze and resolve debates in the Sleeping Beauty problem.

## Key findings

- Thirders' view on Sleeping Beauty is correct
- Identifies main error in halfers' argument
- Extends IF logic to include chance moves

## Abstract

Hintikka and Sandu's independence-friendly (IF) logic is a conservative extension of first-order logic that allows one to consider semantic games with imperfect information. In the present article, we first show how several variants of the Monty Hall problem can be modeled as semantic games for IF sentences. In the process, we extend IF logic to include semantic games with chance moves and dub this extension stochastic IF logic. Finally, we use stochastic IF logic to analyze the Sleeping Beauty problem, leading to the conclusion that the thirders are correct while identifying the main error in the halfers' argument.