Intuitionistic logic

Time and location

Wednesdays, 15-17, room B0.203
Thursdays, 15-17, room G0.18A


Basic course material

Lecture notes by Nick Bezhanishvili and Dick de Jongh
Slides by Dick de Jongh


Teaching assistant

Gianluca Grilletti


Assessment

Weekly assignments and a final exam. Exercises are assigned on Thursdays, and solutions should be handed in before the following class on Wednesday, either in person or by email to Gianluca. Deadlines are strict.


Program, assignments, and additional material
(this will be updated as the course proceeds)


8 Feb. Course introduction. BHK Interpretation.
Teacher: Ivano and Dick
Material: pp. 1-7 of the lecture notes + note on constructive proofs.


9 Feb. Intuitionistic propositional logic IPC: proof system and Kripke semantics.
Teacher: Ivano
Material – Homework


15 Feb. Completeness of IPC for Kripke semantics. Finite model property, decidability. Unraveling models into trees.
Teacher: Ivano
Material: pp. 27-33 of the slides.
Supplementary material: some useful intuitionistic equivalences


16 Feb. Relations between IPC and classical propositional and modal logic.
Teacher: Dick
Material: pp. 41-52 of the slides – Homework


22 Feb. Topological and algebraic semantics.
Teacher: Ivano
Material: pp. 30-34 + 38-39 (up to Cor. 74) of the lecture notes.


23 Feb. Diego’s theorem. Rieger-Nishimura lattice and ladder.
Teacher: Dick
Material: note on Diego’s theorem + pp. 24-25 and 42-43 of the lecture notes
Homework


1 Mar. Intermediate logics.
Teacher: Ivano


2 Mar. n-universal models, Jankov formulas.
Teacher: Dick


8 Mar. Intuitionistic predicate logic IQC.
Teacher: Ivano


9 Mar. Heyting arithmetic
Teacher: Dick


15 Mar. Completeness of HA for IPC
Teacher: Dick


16 Mar. Curry-Howard correspondence
Teacher: Ivano


22 Mar. Inquisitive logic, part 1
Teacher: Ivano


23 Mar. Inquisitive logic, part 2
Teacher: Ivano