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Course by S. L. Kuznetsov and D. S. Shamkanov "Circular proofs"
September 7–December 28, 2020, Steklov Mathematical Institute, Conference hall, 9th floor (8 Gubkina)

From high school we know that an argument which contains a "logical circle" is incorrect. In order to emphasize this, these "logical circles" are called "vicious," and the argument itself is marked ill-formed, since it contains a "vicious circle." In our formal logic course, we shall become acquainted with deductive systems which surprisingly allow absolutely legitimate and, at the same time, formally "circular" (or "cyclic") proofs. Moreover, we shall consider arbitrary proofs in which the way from the conclusion to premises can be infinite, never reaching an axiom. We plan to concentrate on two examples of deductive systems where one can find circular proofs: Gödel–Löb provability logic and action logic (the logic of residuated Kleene algebras). As a prerequisite for this course, the attendees are supposed to be familiar with classical propositional calculus.

Financial support. The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2019-1614).

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Seminar Chairs
Kuznetsov Stepan Lvovich
Shamkanov Daniyar Salkarbekovich

Organizations
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center


Course by S. L. Kuznetsov and D. S. Shamkanov "Circular proofs", September 7–December 28, 2020

September 28, 2020 (Mon)
1. Lecture 4. Circular proofs
S. L. Kuznetsov, D. S. Shamkanov
September 28, 2020 16:30, Steklov Mathematical Institute, Conference hall, 9th floor (8 Gubkina)

September 21, 2020 (Mon)
2. Lecture 3. Circular proofs
S. L. Kuznetsov, D. S. Shamkanov
September 21, 2020 16:30, Steklov Mathematical Institute, Conference hall, 9th floor (8 Gubkina)
  

September 14, 2020 (Mon)
3. Лекция 2. Доказуемостная интерпретация логики Гёделя-Лёба
D. S. Shamkanov
September 14, 2020 16:30, Steklov Mathematical Institute, Conference hall, 9th floor (8 Gubkina)
  

September 7, 2020 (Mon)
4. Лекция 1. Циклические выводы в логике Гёделя-Лёба
D. S. Shamkanov
September 7, 2020 16:00, Steklov Mathematical Institute, Conference hall, 9th floor (8 Gubkina)
D. S. Shamkanov
  
 
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