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.

Announcement the lecture on November 16th is cancelled.

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).

Lecturers
Kuznetsov Stepan Lvovich
Shamkanov Daniyar Salkarbekovich

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