Modal logic and intuitionistic logic (Qüestions de lògica II; Official code: 363801, Year 2019--2020)
Organisation
Lecturer and course coordinator: Joost J. Joosten
The text below and in particular the dates need to be updated.
This is a course of 6 credits which corresponds to 45 contact hours and the students are supposed to dedicate at least 75 more hours of individual dedication. Since we do three hours a week, this will correspond to 15 weeks.
Official information regarding the course is published at the course pages of the UB. From there, one can redirect to the courses.
The lectures will take place in an aula yet to be announced but most close to sure in the Montalegre Building.
The lecture schedule is already known and falls in the so-called L7 time-slot:
Mondays 11:00 -- 12:00
Tuesdays 11:00 -- 13:00
As mentioned, the lecturer is Joost J. Joosten and the best way to contact is by sending an email. You can also come around to see if I'm in: the Montalegre building in Room 4045 with phone number +34 934031939.
Objectives
Logic can be described as the art of reasoning. In the first part we will see how one can reason in a logical system that allows for modalities of propositions. These modalities can range from `necessary’ to `known’ . We shall have a special interest in the provability interpretation as well giving rise to a frame-work in which, for example, Gödel’s second incompleteness theorem can be formulated.
Further, we shall see how giving a constructive reading to the connectives gives rise to a different logic: constructive or intuitionistic logic. Naturally this requires a ontological stance very different from platonism/realism underlying classical logic. If time allows we shall see how contstructive logic can be related both to classical and to modal logic.
• To get an understanding how modalities add a subtle and complex dimension to reasoning;
• See a couple of standard modal logics and reason in them;
• Understand the ontological presupposition that underly constructive reasoning;
• Understand the ontological presupposition that underly classical reasoning;
• Understand the fundamental difference and tension between the two.
• Learn formal reasoning systems in Natural Deduction style;
• Learn formal reasoning systems in Gentzen Deduction style;
• Learn and understand proofs by induction
• Study modal semantics;
• Learning how to apply the soundness theorem to obtain non-derivability results;
• Learning how to apply the completenss theorem to obtain provability without actually exhibiting a concrete proof
THE COURSE WAS TAUGHT THROUGH BBCOLLABORATE DUE TO THE PANDEMIC
FINAL EXAM, TUESDAY, JUNE 12 FROM 11--13 IN AULA 409.
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