# Modal Logic 2022/2023 (official course code 569070)

## Organisation

Here an academic year calendar of the UB can be found.

For us it is important to know:

Teaching period (including exam): February 13 — June 30, 2023.
Re-sit period: July 3 — 7, 2023.

The lectures will take place

Mondays: 12:30 -- 13:30;

Wednesdays: 11:30 -- 13:30.

See also here.

The classes are in Calle Montalegre 6 in the Maria Zambrano Seminar which is Aula xxx on the fourth floor.
The start date is Monday, February 13.
TO BE UPDATED
Official schedule information can be found here

The page below will be updated as we proceed.

The final grade is determined by

(A) Homework questions (this may include a mid-term exam); (20 %)

(B) Presentation in class (10 %);

(C) Midterm + Final Exam; (35 + 35 %).

All materials and assignments will also be placed on this page.

Joost J. Joosten is the lecturer of this course.
The literature will consist of among others a reader to be distributed among the participants.

The modal logic course constitutes for 5 European credits and as such comprises 42 contact hours, so that makes 14 weeks, 3 hours each.
(Feb 13 -- 19)
On Monday, we spoke on the role of modal logic in modern mathematical and philosophical logic.
We recalled the syntax of basic modal logic with a single modality. On Wednesdays, Joost could not teach do to
a nasty cough so there was no class.
(Feb 20 -- Feb 26)
We have given the formal definition of the logics K, K4, T, S4 and GL. Using translations into propositional
logic we show consistency of various logics. Moreover, we saw that GLT is inconsistent. We saw that GL contains K4.
We spent quite some time also on the provability reading of the Box and how modal logics can be employed as a
calculus to describe (meta)mathematical 'reality'.
(Feb 27 -- March 5)
We dwelled on the inductive definition of the collection of Natural Deduction Proofs. Then, we showed that we
can actually use natural deduction for modal logics as long as we do not have any open assumptions
when applying the necessitation rule. We proved Loebs formula is provable in PA (under any realisation) using
Goedel's fixpoint theorem and the soundness of K4 of the provability interpretation. We also proved that Santaclause exists.
Finally I managed to update the notes a bit and hereby I upload a preliminary version.
The Homework consists of

(+) of one exercise of your choice from 1.6.18 or 1.6.10;

(+) 2.4.3

(+) two exercises of your choice from 2.4.11, 2.4.12, 2.4.13, and 2.4.14.
and is due Friday March 10. The pdf is password protected. You will be sent the password by mail or you can ask me to
send it to you.
(Mar 6 -- 12)
(Mar 13 -- 19)
(Mar 20 -- 26)

(Mar 27 -- Apr 2)
(Apr 10 -- 16)
No class on Monday! Previous week was Easter holiday.
(Apr 17 -- 23)
(April 24 -- 30)
We have introduced the modal logics K, T, S4, K4 and GL and have done various exercis with
(May 1 -- 7) No class on Monday!
(May 8 -- 14)
(May 15 -- 21)
(May 22 -- 28)

**FINAL EXAM: ???**

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