| Date | Room | Material covered | Syllabus | Homework |
| Tuesday 05 February | G-S.08 |
-History and philosophy of intuitionism -Informal "proofs" versus formal "derivations" -Intuitionistic propositional calculus |
pp 1-8 Slides 1-19 (page number on bottom of slides) |
Homework 1 (due Friday 08 February) |
| Tuesday 12 February | G-S.08 |
-Hilbert-type systems -Gödel's negative translation -Kripke models |
p 8; pp 15-16; pp 22-23 Slides 19-24; 49-50 |
Homework 2 (due Friday 15 February) |
| Tuesday 19 February | G-S.08 |
-Completeness of IPC w.r.t. Kripke semantics -Extensions of IPC (KC, LC) -Frame characterizations -Completeness of extending logics w.r.t. sub-classes of frames -Finite model property -Predicate logic (syntax) |
pp 18-19 Slides 27-33 |
Homework 3 (due Friday 29 February) |
| Tuesday 26 February |
LECTURE CANCELLED due to the PhD defenses of Olivier Roy and Fenrong Liu |
|||
| Tuesday 4 March | G-S.08 |
-Kripke models for predicate logic -Some valid and invalid principles of intuitionistic predicate logic -Generated submodels -p-morphisms |
pp 16-17; slides 22; 24; 36-39 |
Homework 4 (due Tuesday 11 March) |
| Tuesday 11 March | P-0.18 |
-p-morphisms -Splitting p-morphisms of finite frames into α- and β-reductions -Completeness of predicate logic -Disjuction property -Admissible rules. |
pp 17; 48-49; 20-21 slides 37; 39; 40-41 |
Homework 5 (due Tuesday 18 March) |
| Tuesday 18 March | P-0.18 |
-Homework 4, exercise 4 -Heyting Arithmetic (HA) -Proofs in HA -Kripke models for HA -Disjunction property for HA -Formulation of De Jongh's Theorem |
pp 20; 22 |
Homework 6 (due Tuesday 1 April) |
| Tuesday 25 March | NO LECTURE | |||
| Tuesday 1 April | P-0.18 |
-Proof of De Jongh's Theorem -Translation to S4 |
pp 22; 23-24 slides 51-52 |
No homework this week! |
| Tuesday 8 April | P-0.18 |
-Tranlsations to S4 -Proof of the transaltion -Rieger-Nishimura ladder |
pp 23-25 slides 51-52; 54-56 |
Homework 7 (due Tuesday 15 April) |
| Tuesday 15 April | P-0.18 |
-Lattices -Heyting algebras -More on the Rieger-Nishimura ladder |
pp 30-33; 24-25 slides 54-68; |
Homework 8 (due Tuesday 29 April) Deadline extended with one week! |
| Tuesday 22 April | P-0.18 |
-More about lattices and Heyting algebras -Axiomatization of Heyting algebras -Connection between Kripke frames and Heyting algebras -Upsets, upset algebras, filters, General Kripke Frames -Duality between Krikpe frames and Heyting algebras |
pp 30-35 slides 57-72; 75-78; 81-82 |
No homework this week. |
| Tuesday 29 April | P-0.18 |
-More on algebraic semantics -Algebraic soundness and completeness -Lindenbaum-Tarski algebras -n-Universal models -De Jongh formulas |
pp 38-40; 42-46 slides 86-91; 92-115; |
Homework 9 (due Tuesday 6 May) |
| Tuesday 6 May | P-0.18 |
-More on n-Universal models -More on De Jongh formulas -Kleene/Aczel slash |
pp 42-46; 20-21; slides 111-115; |
Homework 10 (due Tuesday 27 May) submit by email or in mail-box |