Projects in Previous Years

1st Semester 2005/06: Intuitionistic Logic

Nick Bezhanishvili

If you are interested in this project, please contact the instructor by e-mail.
Goal. Become familiar with Kripke and algebraic semantics of intuitionistic logic and the connections between intuitionistic logic and modal logic. Learn the construction of universal models and the technique of frame-based formulas.
This project is intended to give an overview of the intuitionistic propositional calculus IPC. The following topics will be covered in the course:
  • The BHK (Brouwer-Heyting-Kolmogorov) interpretation
  • Proof systems (Hilbert type systems, natural deduction, sequent systems)
  • Kripke semantics, completeness and the finite model property
  • Translations of the classical propositional calculus CPC into IPC and of IPC into S4 and other modal logics (i.e., Glivenko's theorem)
  • algebraic semantics: Heyting algebras
  • Henkin models and universal models of IPC
  • Jankov-de Jongh formulas and intermediate logics
Grades are based on weekly homework (25%) and a final paper (75%).
Nick Bezhanishvili and Dick de Jongh, Intuitionistic Logic, ESSLLI'05 course notes.
A. Chagrov and M. Zakharyaschev, Modal Logic, Oxford University Press, 1997.