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 illformed, 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. 0751520191614).
Program
Registration
RSS: Forthcoming seminars
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 ГёделяЛёба 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 ГёделяЛёба D. S. Shamkanov September 7, 2020 16:00, Steklov Mathematical Institute, Conference hall, 9th floor (8 Gubkina)





