**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**

**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

Material: class notes.

2 Mar. n-universal models, Jankov formulas.

Teacher: Dick

Material: pp. 92-117 of the slides, pp. 1-7 of paper by deJongh-Yang on n-universal models.

Homework

8 Mar. Intuitionistic predicate logic IQC.

Teacher: Ivano

Material: Troelstra-vanDalen, pp. 35-49, 56-59, 75-84 and 87-89

9 Mar. more on n-universal models, Heyting arithmetic

Teacher: Dick

Material: pp. 7-9 + 16-17 of the deJongh-Yang paper, pp. 115-126 of the slides.

P. 10 of the lecture notes.

Homework

15 Mar. Completeness of HA for IPC

Teacher: Dick

Material: pp 339-354 of Troelstra, Metamathematical investigations of Intuitionistic Arithmetic and Analysis

16 Mar. Curry-Howard correspondence

Teacher: Ivano

Material: Ch. 3 and 4 of the book by Sorensen and Urzyczyn (excerpt; notice that some of the relevant notions are defined in Chapter 1).

Extra material (optional): Wadler-propositions-as-types

Homework

22 Mar. Inquisitive logic, part 1

Teacher: Ivano

Material: sections 1-4 of Questions as Information Types.

23 Mar. Inquisitive logic, part 2

Teacher: Ivano

Material: sections 2-6 of Inquisitive Logic.

Homework 7

29 Mar. Practice and Q&A session.

Teacher: Gianluca

Usual time and room.

30 Mar. Final exam.

Usual time, room SP B0.203

(the room where we usually are on Wednesdays)