# Modal logic, the logic of provability

**Lecturer**: Jaime Sevilla

**Date**: 26/04/2017

**Time**: 17:00

**Place**: Room 103

**Abstract**:
Through this talk we will introduce the basic notions used in the different systems of modal logic,
after a review of the concepts of the first order provability predicate and Löb’s theorem.

After that we will focus on the Gödel-Löb modal system (GL), also known as the logic of provability. We will discuss Solovay’s arithmetical adecuacy theorems, modal fixed points and the Kripke models of GL.

Lastly if time permits we will discuss the applications of modal logic in artifical intelligence and decision theory with a toy model, modal combat.

## Video & slides

## Bibliography

- G. Boolos, J. Burgess & R. Jeffrey,
*Computability and Logic* - G. Boolos,
*The Logic of Provability* - R. J. Buehlen,
*The Logic of Provability: Notes* - P. LaVictoire,
*An Introduction to Löb’s Theorem in MIRI Research* - J. Sevilla,
*Fixed point theorem of provability logic* - J. Sevilla,
*Modal Logic in the Wolfram Language* - R. Verbrugge,
*Provability Logic. The Stanford Encyclopedia of Philosophy*