Modal Logic 2018/2019 (official course code 569070)
Organisation
The lectures will take place (tentative)
Mondays: 12:00 -- 14:00;
Thursdays: 9:00 -- 10:00.
Calle Montalegre 6 in Aula 402. The
start date is Monday, February 11.
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.
Some time between the first and the 28th of June we will have the final exam. An eventual resit could be held between July 8 and 12.
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.
THE INFO BELOW WILL BE UPDATED AND IS CURRENTLY COPIED FROM LAST EDITION
(Feb 11 -- 17)
We spoke about the motivation for modal logics. Particular emphasis was given to employ
Modal logics as calculi that describe parts of (meta)mathematics. We gave the formal definition of our Logic K in terms of a Hilbert-style calculus. As such we have covered the first chapter of my book that shall be given out on this webpage in tasty weekly digests. If you wish to get the password to open it, just send me an email.
Once every two or three weeks I will ask you to hand in a batch of homework exercises.
However, in advance — that is, every week— I will tell you which exercises may be included in the assignment set.
For this week, it could be any collection of exercises from
1.6.1
1.6.2
1.6.3
1.6.4
1.6.5
1.6.11
1.6.12
1.6.14
(Feb 20 -- 24)
This week, we have covered the first two chapters of my book in large parts.
For this week, the homework exercises could be any collection of exercises from
1.6.1
2.4.1
2.4.5
2.4.6
2.4.7
2.4.11
2.4.12
(Feb 27 -- Mar3)
The first homework batch consisted of 1.6.12 and 2.4.11 which is due on Monday the fourth of March.
As to new theory:
We have introduced modal semantics and have seen soundness. We dwelled upon a strategy to come up with a term model leading us to the notion of local consequence. We gave the definition of the canonical model and as such have almost finished the completeness proof.
Thus, this week, we have covered in large part the first three chapters of my book.
For this week, the homework exercises could be any collection of exercises from
3.5.1
3.5.1
3.5.4
3.5.5
3.5.10
3.5.12
3.5.13
3.5.15
(Mar 4 -- 8)
We revisited the completeness proof and introduced the notion of frames.
(Mar 11 -- 15)
We proved frame-correspondence theorems.
(Mar 18 -- 22)
We have shown the logic KH to be frame incomplete and GL to be non canonical.
As such, we have so far covered the first four chapters of the book and Section 5.3.
The homework exercises for the next batch could be any collection of exercises from
4.4.3
4.4.5
4.4.7
4.4.8
4.4.12
The first five chapters of my book.
(Mar 25 -- 29 )
We finished Chapter 5 and started Chapter 6.
(Apr 1 -- 5)
We covered the first three sections of Chapter 6.
The first six chapters of my book.
The homework exercises for the next batch of exercises is
4.4.4
4.4.12
5.4.3
6.5.2
And 6.5.6
(Apr 8 -- 12)
We finished van Benthem's characterisation theorem of the modal logic fragment of first order logic.
(Apr 22 -- 25)
The week after Easter. We started on filtrations.
(Apr 29 -- May 3)
We finished filtrations and proved the finite model property and decidability of the logics K, T, K4 and GL. As such, we have done the first seven chapters of my book.
The homework exercises for the next batch of exercises is
7.5.1,
7.5.3,
7.5.8,
and 7.5.9.
(May 6 -- 10)
We did more results on frame-completeness and also on the finite model property and decidability.
(May 13 -- 17)
We started arithmetization of syntax in Peano Arithmetic. Coding of finite sequences, coding of syntax, substitution as an arithmetical operator. Next we proved the fixpoint lemma and saw some applications of that: undefinability of truth, Goedel's liar sentence, etc. You can read this in Chapter 2 of Boolos.
(May 20 -- May 24)
Now that we finished the arithmetical soundness (Boolos, Chapter 2), we started with the arithmetical completeness of GL (Chapter 9). We outlined the general strategy and showed how to define the Solovay function using finite suquences and the fixpoint theorem.
The final exam will last two hours and will take place on Thursday, June 20 from 9:00 -- 11:00 in Aula 401.
During the exam, you will not be allowed to consult any sources. All material covered in class, lecture notes and Boolos belongs to the curriculum except for the lectures on quantified provability logic.
The final grades have been uploaded to the Campus Virtual.
The resit will be Thursday, June 27 from 9:00 till 11:00 in Maria Zambrano (Room 4029) and will be rather similar in concept to the previous exam.
Question and answer
Question
Q.
In the statement of exercise 7.5.8 point (2) you ask to prove the consistency of a set of formulas. Here by consistent you mean that this set has a model?
Answer
A. It should be clear from the context that local consistency in meant: remember that Diamond top is inconsistent over GL for the global consequence relation. So, consistency means the non-derivability of falsum (using only Modus Ponens). The exercise asks you to use the soundness theorem. Indeed, this then amounts to showing that there is a model where at some world the entire set of sentences holds. I hope that helps.
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