Traditionally, each logic, except classical, is called "non-classical". There are many non-classical logics. They are used in the foundations of mathematics, computer science, formal philosophy and epistemology, linguistics, etc. There could be various reasons for a logical system to be regarded as non-classical. In particular, a system will be non-classical if it satisfies at least one of the following conditions:

• the behaviour of one of the standard connectives (implication, disjunction, negation, conjunction) in this system differs from the classical one, e.g., implication could be more "relevant", avoiding the "paradoxes of material implication";
• the language of this system includes extra connectives, such as modalities "it is possible that..." or "it is necessary that ...", the concrete interpretation of which depends on the area of applications;
• the language includes quantifiers which cannot be expressed in classical first-order logic, like "there exist infinitely many $x$ such that..."

Financial support. The seminar is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2022-265).

Program

Seminar organizers
Kuznetsov Stepan Lvovich
Speranski Stanislav Olegovich

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