Modal Logics of Provability and Interpretability

 

 

Logic and Computation Courses

Advanced Course

Modal Logics of Provability and Interpretability,
Tin Perkov (University of Zagreb, Croatia)

Week 2, 9:00 – 10:30, Room 224, Floor 1

This course presents modal treatment of provability and interpretability in arithmetical theories. The focus is on Kripke semantics for provability logic GL and Veltman semantics for interpretability logic IL and its extensions. The proofs of modal completeness for these logics will be presented and arithmetical ramifications will be discussed. The course is concluded with an overview of some of the latest developments in model theory of interpretability logic.

Slides

Course outline

Day 1: Introduction.

Day 2: Provability predicate of Peano arithmetic. Hilbert-Bernays-Löb conditions.
Modal logic GL. Kripke semantics and modal completeness.

Day 3: Arithmetical interpretation and Solovay’s Theorem. Extensions of GL.

Day 4: Topological semantics for GLP. Interpretability predicate. Modal logic IL. Veltman semantics.

Day 5: Modal completeness of IL. Extensions of IL. Montagna’s principle and the system ILM. Arithmetical completeness of ILM.