Modal logic and intuitionistic logic (Qüestions de lògica II; Official code: 363801, Year 2022--2023)

Organisation

Here is an academic year calendar of the UB.

Lecturer and course coordinator: Joost J. Joosten
The text below shall be updated as we go along in our course.

This is a course of 6 credits which corresponds to 45 contact hours and the students are supposed to dedicate at least 75 more hours of individual dedication. Since we do three hours a week, this will correspond to 15 weeks.
Official information regarding the course is published at the course pages of the UB. From there, one can redirect to the courses. Also, official dates can be consulted here. The lectures will take place in Aula 410 in the Montalegre Building.

The lecture schedule is as follows:
Mondays 11:00 -- 12:00
Tuesdays 11:00 -- 13:00


We strongly advice students to follow the course in the so-called avaluació úinca mode. Here we will have take-home exercises, a mid-term exam and a final exam.

Date and location midterm exam: TBA;

Date and location final exam: TBA.

The distribution of points in the final grade is as follows:

Take-home exercises: 20 %

Midterm exam: 40 %

Final exam: 40 %

Students may also decide --even though we stronly would like to discourage this-- to participate in the so-called avaluació única.

Date and location avaluació única exam: June 9, 2023, 12:00 == 14:00, Aula 410.

Date and location resit exam: July 6, 2023, 12:00 == 14:00, Aula 410.

As mentioned, the lecturer is Joost J. Joosten and the best way to contact is by sending an email. You can also come around to see if I'm in: the Montalegre building in Room 4045 with phone number +34 934031939.

Objectives

Logic can be described as the art of reasoning. In the first part we will see how one can reason in a logical system that allows for modalities of propositions. These modalities can range from `necessary’ to `known’ . We shall have a special interest in the provability interpretation as well giving rise to a frame-work in which, for example, Gödel’s second incompleteness theorem can be formulated.

Further, we shall see how giving a constructive reading to the connectives gives rise to a different logic: constructive or intuitionistic logic. Naturally this requires a ontological stance very different from platonism/realism underlying classical logic. If time allows we shall see how contstructive logic can be related both to classical and to modal logic.


• To get an understanding how modalities add a subtle and complex dimension to reasoning;
• See a couple of standard modal logics and reason in them;
• Understand the ontological presupposition that underly constructive reasoning;
• Understand the ontological presupposition that underly classical reasoning;
• Understand the fundamental difference and tension between the two.
• Learn formal reasoning systems in Natural Deduction style;
• Learn formal reasoning systems in Gentzen Deduction style;
• Learn and understand proofs by induction
• Study modal semantics;
• Learning how to apply the soundness theorem to obtain non-derivability results;
• Learning how to apply the completenss theorem to obtain provability without actually exhibiting a concrete proof

THE REMAINDER OF THIS PAGE NEEDS UPDATING

Week 1 Week 2
Week 3 Week 4
Week 5 Week 6
Week 7 Week 8
Week 9 Week 10
Week 11 Week 12
Week 13 Week 14

Week 1

(Feb 14 -- 18)

Week 2

(Feb 21 -- 25)

Week 3

(Feb 28 -- Mar4)

Week 4

(Mar 7 -- 11)

Week 5

(Mar 14 -- 18)

Week 6

(Mar 21 -- 25)

Week 7

(Mar 28 -- Apr 1)

Week 8

(Apr 4 -- Apr 8)

Week 9

Week 10

(Apr 25 -- 29)

Week 11

(May 2 -- 6) We have introduced the modal logics K, T, S4, K4 and GL and have done various exercis with

Week 12

(May 9 -- 13)

Week 13

(May 16 -- 20)

Week 14

(May 23 -- 27)

Week 15

(May 30 -- June 3)


FINAL EXAM: ???

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Q.: The meaning of the second item is to list all the normal logics that fulfils the statement? Is this also correct?

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A. No, this is not correct. You should either prove that indeed it holds for any normal modal logic or otherwise find a particular normal modal logic for which the implication fails. Even though the answer is easy, the question is sligthly tricky...

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