Modal logic and intuitionistic logic (Qüestions de lògica II; Official code: 363801, Year 2024--2025)

Organisation

Here is an academic year calendar of the UB.

The second semester for the graduate courses runs from February 10, 2025 -- May 30, 2025 as can be checked here.
Lecturer and course coordinator: Joost J. Joosten
Teaching assistant: Vicent Arroyo Navarro.

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 work. 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. The lectures will take place in Aula 406 in the Montalegre Building.

The lecture schedule is as follows:
Mondays 12:00 -- 14:00
Tuesdays 13:00 -- 14:00

We strongly advice students to follow the course in the so-called continua 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: See teaching plan %

Midterm exam: See teaching plan %

Final exam: See teaching plan %

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 2, 2025, 12:00 -- 14:00, Aula 406.

Date and location resit exam: June 30, 2025, 12:00 -- 14:00, Aula 406.

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.

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Objectives

Logic can be described as the art of valid 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 10 -- 14)

Week 2

(Feb 17 -- 21)

Week 3

(Feb 24 -- Feb 28)

Week 4

(Mar 3 -- March 7)

Week 5

(Mar 10 -- 14)

Week 6

(Mar 17 -- 21)

Week 7

(Mar 24 -- 28)

Week 8

(Mar 31 -- Apr 4)

Week 9

(Apr 7 -- Apr 11) No class on Monday! Previous week was Easter holiday.

Week 10

(Apr 21 -- 25)

Week 11

(Apr 28 -- May 2)

Week 12

(May 5 -- 9)

Week 13

(May 12 -- 16)

Week 14

(May 19 -- 23)

Week 15

(May 26 -- 30)

FINAL EXAM: June 6, 12:00 -- 14:00, our usual aula

Question and answer

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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?

Answer

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...