Intuitionistic Logic

Spring 2008

IP Location Lecture hours: Tuesday 12-14
Lecturer: Prof. Dr. Dick de Jongh (
Assistant: Yurii Khomskii (
Literature: Credits: 6 ECTS
Remark: Getting credit for this course is only possible on agreement by the lecturer.

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
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)
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