Modal Logic 2024/2025 (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 10 — June 27, 2025.
Re-sit period: June 23 — July 4, 2025.
The lectures will take place
Mondays: 15:30 -- 17:00;
Wednesdays: 15:30 -- 17:00.
See also here.
The classes are in Calle Montalegre 6 in Aula 412 on the fourth floor.
The start date is Monday, February 10.
Official schedule information can be found here
The page below will be updated as we proceed.
The final grade is (as per teaching plan) determined by
(A) Homework questions (this may include a mid-term exam); (40 %)
(B) Presentation in class (10 %);
(C) Midterm + Final Exam; (25 + 25 %).
All materials and assignments will also be placed on this page.
See also here and here.
Joost J. Joosten is the lecturer of this course.
The course counts with a teaching assistant: Vicent Navarro Arroyo.
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.
TO BE UPDATED
(Feb 10 -- 14)
We started the course, gave an introduction to Modal Logic, started by defining the basic modal logics, K, K4, etc.
and did some examples of concrete Hilbert style derivations. We have proven some inclusions and non-inclusions of so-called normal modal logics.
Basically, we have covered the first two chapters of the Book I am writing.
(Feb 17 -- 21)
We have made some exercises in class and then finished Chapter 2 of the reader. Next we started an inductive definition of set
of Natural Deduction proofs in modal logic. As homework you are asked to choose two exercises from
2.4.11; 2.4.12; 2.4.13 and 2.4.14.
(Feb 24 -- Feb 28)
We have given Natural deduction systems for CPC, IPC and normal Hilbert logics. For the modal case we have shown equivalence of the
two formalisms. Upon request there is a new version of the reader.
(Mar 3 -- March 7) We have proven completeness for modal logics through the canonical model.
The new reader is now available.
(Mar 10 -- 14)
We have proven some frame correspondences and frame completeness for various modal logics.
The new reader is now available.
The next batch of homework consists of 4.5.4; 4.5.21, 5.4.3 and 5.4.12.
(Mar 17 -- 21)
We have spoken more on frame conditions and seen the frame incompleteness of the logic KH.
(Mar 24 -- 28)
We have seen three constructions on frames that yield means to show modally undefinable properties.
Next we have spoken on bisimulations and on finite approximations of bisimulations.
The new reader is now available.
(Mar 31 -- Apr 4)
We saw how the first order translation gives us access to all kinds of first-order techniques:
compactness and countable saturated models. Using unraveling we have seen that Löbs rule is admissible for K.
(Apr 7 -- Apr 11)
We had a question hour on Monday and then on Wednesday the Midterm exam.
(Apr 21 -- 25)
No class on Monday nor Wednesday (Sant Jordi)! Previous week was Easter holiday.
(Apr 28 -- May 2)
On Monday there was the great "apagón": no electricity at the entire Iberian peninsula.
Classes in the afternoon were institutionally canceled.
On Wednesday we discussed some matters about the exam and then revisited omega-saturated models of first order logic.
We have seen how omega-saturated models are m-saturated too.
(May 5 -- 9) We have seen the relation between omega-saturation and m-saturation.
We have proven the van Benthem Characterisation Theorem. We have also revisited filters and ultrafilters and have given the definition of
the ultrafilter extension of a modal frame.
The new reader is now available.
(May 12 -- 16)
We studied ultrafilter extensions of frames and models.
(May 19 -- 23)
We finished our chapter on ultrafilter extensions and then moved on to filtration, finite filtrations and decidability.
The new reader is now available.
(May 26 -- 30)
We addressed some questions on the homework set. Then we moved on to Admissible rules.
We have covered Sections 12.1 and 12.2 of the updated reader.
Furthermore, we gave a high-level overview of the paper Best Solving Modal Equations by Silvio Ghilardi.
(June 5 -- 9)
Guest lectures by Mojtaba Mojtahedi.
FINAL EXAM: Tuesday, June 10, 11--13. Seminari de Filosofia (l'aula seminari Núria Folch que està situat entre l'aula 403 i una de les entrades a l'aula Magna).
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