Intuitionistic Logic
Spring 2012
[Announcements] [Lectures]
[Homework] [General Information] [References]
Announcements
Lectures
- Week 6 (6th Feb) : History and philosophy of intuitionism; Informal "proofs" versus formal "derivations";
Intuitionistic propositional calculus (IL pp 1-8, Slides 1-19; A note on Informal proofs.)
- Week 7 (13th Feb) : What is provable in IPC; Hilbert type system; constructive and non-constructive proofs; Kripke models for IPC (IL pp 5-8,15,16; slides 19-21; A note on constructive and non-constructive proofs.)
- Week 8 (20th Feb) : Negative translation; Completeness of IPC w.r.t. Kripke semantics; Extensions of IPC (KC) (IL pp 18-19, 22-23; slides 33,36-41; Additional notes on Completeness, Glivenko's theorem and useful equivalences in IPC).
- Week 9 (27th Feb) : Intermediate logics; Intuitionistic predicate logic (IQC); Kripe models for IQC (IL pp 14-15,19)
- Week 10 (5th March) : Completeness of IQC; p-morphism; Gödel's translation of IPC to S4 (IL pp 18-19,17,23-24)
- Week 11 (12th March) : α, β-reduction; Finite model property using filtration and finite canonical models (IL pp 17-20,48; Additional notes on Filtration)
- Week 12 (19th March) : Disjunction property for IPC; Kleene slash (IL pp 20-21)
- Week 13 (26th March) : No Class (exam week)
- Week 14 (2nd April) : Introduction to Heyting arithmetic; Smorynski's trick; Basic recursion theory (IL pp 10-11,20; Notes on Recursion theory)
- Week 15 (9th April) : No Class (Easter holiday)
- Week 16 (16th April) : Reliazability (IL pp 11-14; Notes on Realizability)
- Week 17 (23rd April) : Completeness of Heyting arithmetic with respect to IPC (IL pp 19-22)
- Week 18 (30th April) : No Class (Queen's day)
- Week 19 (7th May) : Rieger Nishimura lattice and ladder; Universal models (IL pp 24-25,42-44)
Homework
General Information
Contents
This course is based for a large part on the ESSLLI course notes of Dick de Jongh and Nick Bezhanishvili.
The course starts with an introduction to the constructivistic ideas that lead Brouwer and Heyting to intuitionistic logic.
Afterwards the course mainly treats the intuitionistic propositional calculus but treats enough of the predicate calculus to make an excursion to arithmetic. The treatment of the propositional calculus proceeds in depth.
This leads to the fact that the course presupposes the course Introduction to Modal Logic.
Staff
Dates/location
- Monday 17:00-19:00, ScP D1.110
Course Material
- N. Bezhanishvili and D. de Jongh: Intuitionistic Logic (IL),
Lecture Notes presented at the ESSLLI, Edinburgh,
2005. You can find slides here. (errata)
Grading
- This course is worth 6 ECTS.
- The grading is on the basis of weekly homework assignments.
- Deadlines for submission are strict.
- Homework handed in after the deadline will not be taken in consideration.
- Homework should be handed in during the lectures, or sent by email to S.Sourabh[at]uva.nl
- Typed submissions are strongly preferred. Handwritten submissions must be legible. Illegible submissions will not be graded.
- When writing your solutions to exercises, provide motivation (justification in the form of proofs or counterexamples) of all your claims.
- On the other hand, be succinct. In particular:
- Never prove statements that are explicitly mentioned in the book or in the notes (unless specifically asked otherwise); simply refer to the propositions by number if you use them;
- In the case of a routine argument, you do not need to go into all the technical details;
- In case you think there's a mistake in one of the exercises, first check the course web page. If there is no information there, please contact the lecturer immediately.
Previous Editions
Links to the course offered in Spring 2011 and
Spring 2008.
References