Modal Logic 2014/2015 (official course code 569070)


The lectures will take place
Wednesdays: 18:00 -- 19:30;
Fridays: 12:00 -- 13:30.
Calle Montalegre 6 in Aula 410. The start date is Wednesday, February 18.

The final grade is determined by
(A) Homework questions (this may include a mid-term exam); (60 %)
(B) Final Exam; (40 %).

All materials and assignments will also be placed on this page.
Joost J. Joosten is the lecturer of this course. The best way to contact me is by sending us a mail. You can also come around to see if I am in at the Montalegre building in Room 1095 with phone number +34 934031939.

The teaching assistant for this course is Eduardo Hermo Reyes. He might be grading some of the exercises and is available for helping on theory and exercises outside class-hours. Also, he shall present some worked-out exercise sets. The best way to contact Eduardo is by sending a mail to the address that starts with "ehermo" followed by a dot, that is a symbol ".", then goes "reyes" that an at symbol, and then the reversal of "liamg" and then the dot and then the reversal of "moc".

The literature will consist of among others a reader to be distributed among the participants.

The academic teaching-evaluation period of the the master for the second semester is from February 9 to June 26. Our course comprises 42 contact hours, so that makes 14 weeks, 3 hours each. You can find the complete schedule here. Likewise there is an official page with the course description.
Week 1 | | Week 5 | | Week 9 | | Week 13
Week 2 | | Week 6 | | Week 10| | Week 14
Week 3 | | Week 7 | | Week 11
Week 4 | | Week 8 | | Week 12

Week 1

(Feb 16 -- 20)
We have spoken on the motivation of modal logic, mentioned some high level properties, dealt with the basic syntactical definitions, reflected on inductively defined sets with their corresponding induction principles, defined logic K with a Hilbert-style calculus, and proved consistency of K.

Here is the reader for the first week. The homework consists of Exercises 1.4.1, 1.4.3, and 1.4.4.

Week 2

(Feb 23 -- 27) We introduced the logics K4 and GL and studied the interrelations between them.

Here is the reader for the second week. The homework consists of Exercises 1.6.1, 1.6.11, and 1.6.14, and 1.6.15 and is due for Friday before the start of the next lecture.

Week 3

(Mar 2 -- 6) See Week 4.

Week 4

(Mar 9 -- 13) In weeks 3 and 4 we have introduced a uniform way of obtaining natural deduction systems for a normal modal logic in Hilbert style. We proved the equivalence and started to look at the sequent calculus for classical logic and for the modal logic K.

Here is the reader for the third and fourth week. The homework is slightly more than before since it comprises two weeks of material and consists of Exercises 1.6.1 (note more typos, since some text has not even been proof-read), 1.8.17, and 1.8.18, and 1.8.19 and the rule (L\/) for Exercises 1.8.21 and 1.8.22. (Note that the reference to Lemma 1.10 should be a reference to Lemma 1.7.4 (and this is not allowed as a possible typo anymore :-) )).
The homework is due before our lecture on next Wednesday, March 18.

Week 5

(Mar 16 -- 20) Cut elimination for modal systems.

Week 6

(Mar 23 -- 27) Modal semantics. The exercises consist of spotting 6 typos and 3.2.2, 3.2.4 and 3.2.5 and is due for Friday, April 10. Here is the updated reader.

Week 7

(Apr 6 -- 10 ) We proved a generic completeness theorem for normal modal logics with respect to the local consequence relation.

Week 8

(Apr 13 -- 17) We proved completeness for the global consequence relation and saw some applications like the the admissibility of the rule that allows you to conclude A from Box A. We introduced frame conditions and proved frame correspondences for K, T and K4.

Week 9

(Apr 20 -- 24) We gave two proofs of the frame correspondence for GL: one proof based on the minimal element principle, the other more constructive proof based on transfinite induction along well-founded partial orders. We presented the completeness proof of GL as presented in Chopter 5 of Boolos' book "The Logic of Provability". Here is the updated reader.

Week 10

(Apr 27 -- May 1) We will treat the material of Chapter 10 of Boolos. The presentation will be given by Tuomas. Rather than following Boolos's approach, Tuomas will give the treatment presented in "Tableau Methods for Modal and Temporal Logics" by Rajeev Goré. On citeseer there is a link to the paper. The homework for Weeks 7--10 consists of: providing proofs of Theorems 3.3.10 and 3.3.12 of the reader and Exercises 3.4.6 and 3.4.14. Your answers are due for Wednesday, May 13.

Week 11

(May 4 -- 8) We will treat the material of Chapter 11 of Boolos. The classes will be given by Eduardo Hermo.

Week 12

(May 11 -- 15) We have started reading the paper Circular Proofs Proofs for Gödel-Löb Logic by Danyiar Shamkanov mostly presented by Pilar. The paper can be retrieved here.

Week 13

(May 18 -- 22) We continued reading the paper Circular Proofs Proofs for Gödel-Löb Logic by Danyiar Shamkanov. An important reference for this paper is the PhD thesis of James Brotherston which can be retrieved here.

Week 14

(May 25 -- May 29) Last week. We finished the paper Circular Proofs Proofs for Gödel-Löb Logic by Danyiar Shamkanov mostly via presentations of Richard.

Final Exam

Tuesday, June 16
Aula 410 (Philosophy building).
Here is the final exam.

Question and answer