# Modal Logic 2016/2017 (official course code 569070)

## Organisation

The lectures will take place

Tuesdays: 18:30 -- 20:00;

Wednesdays: 18:30 -- 20:00.

Calle Montalegre 6 in Aula 409. The
start date is Tuesday, February 14.

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 me an e-mail. You can also come around to see if I am in at the Montalegre building in Room 4045 with phone number +34 934037984.

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. You can find the complete schedule here. Likewise there is an official page with the course description.
(Feb 13 -- 17)

In the first week, we started our introduction to Modal Logic.
Here is the reader for the first week.
The homework, to be handed in on Tuesday comprises:
Exercises 1.4.1; 1.4.4; 1.4.5 and 1.4.7
(Feb 20 -- 24)
In the second week, we studied the modal logic K and extensions.
Here is the reader for the second week.
The homework, to be handed in on Tuesday comprises:
Exercises 2.3.1; 2.3.3; 2.3.11.
(Feb 27 -- Mar3)
In the third week, we studied Natural Deduction for Modal Logics.
Here is the reader for the third week.
The homework, to be handed in on Tuesday comprises:
Exercises 3.3.1; 3.3.2; and 3.3.4.
(Mar 6 -- 10)
In the fourth week, we studied Kripke semantics for Modal Logics.
Here is the reader for the fourth week.
The homework, to be handed in on Friday comprises:
Exercises 4.5.1; 4.5.3; and 4.5.7.
(Mar 13 -- 17)
We have done Chapter 5 which you can download in the reader at Week 6. The homework consists of 5.4.1, and 5.4.3 to be handed in Tuesday, March 28.
(Mar 20 -- 24)
We have done Chapter 6 of the reader at Week 6. The homework consists of 6.4.1, and 6.4.3 to be handed in Tuesday, March 28.
(Mar 27 -- 31 ) The classes this week have been taught by Ana Borges. She has covered most of Chapter 11 from The Logic of Provability by George Boolos. (Until the end of the frame incompleteness of the logic KH.)
(Apr 3 -- 7)
We have introduced bisimulations for basic modal logics and proved some basic properties. We have shown how filtration gives us differentiated models, and how it can be used to obtain finite models. The finite model property in turn yields decidability for axiomatizable modal logics. We introduced interpretability logics and some basic principles for interpretability logics. The homework consists of Exercice 8.4.1, 9.6.2, 9.6.1.8, 9.6.1.3 and 9.6.1.2 (that is the recommended order) of the reader at Week 8.
(Apr 18 -- 21)
From April 10 through April 17, the UB will be closed due to Setmana Santa.

We have a guest lecturer: Luka Mikec. He will speak on interpretability logics. We have seen the guest lectures by Mikec and learned on filtration of generalized Veltman models. In particular we have seen why filtration of regular Veltman models is problematic and how these problems were circumvented by resorting to generalized Veltman semantics. As a result we proved the finite model property of the basic interpretability logic IL. There are some preliminary notes here. The homework, due for Tuesday April 25 consists of the following:

On Page 14 of the slides it is mentioned that bisimulations for generalized Veltman semantics are closed under unions. You are asked to perform the following three tasks:

1. Prove that indeed bisimulations for generalized Veltman semantics are closed under unions.

2. From the reader at Week 8, look at Definition 7.1.1. Is this notion of bisimulation closed under unions? If so, prove it, if not, provide a counter-example.

3. From the reader at Week 8, look at Definition 9.5.1. Is this notion of bisimulation closed under unions? If so, prove it, if not, provide a counter-example

(Apr 24 -- 28)
We studied filtrations more in-depth. We proved the finite model property whence the decidability of K, T and K4 via filtration. For GL we used the proof from Boolos' book.
(May 1 -- 5)
We further discussed the arithmetical reading of the Box a provable. Details can be found in Chapter 2 of Boolos.
(May 8 -- 12)
We studied applications of modal logic to arithmetic. Basically, we have done parts of Chapter 7 of Boolos: closed fragment and its relation to reflection principles.
(May 15 -- 19)
We read some papers together and had presentations of the students.
Tuesday: Mireia and Guillermo and Wednesday Juan and Akis.
(May 22 -- May 26)
Last week. We read some papers together and had presentations of the students.
Tuesday: Guim and Martin and Wednesday Jinglun and Jorge.
Some time June probably

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