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..."
Non-classical logics could be strongly complete w.r.t. appropriate semantics, which is significantly different from the classical one (these include possible world semantics, topological semantics, algebraic semantic, game-theoretic semantics, etc). At the same time, some non-classical logics do not enjoy complete deductive systems, due to their high algorithmic complexity; such logics can still be studied from the model-theoretic point of view.
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).
RSS: Forthcoming seminars
Seminar organizers
Kuznetsov Stepan Lvovich
Speranski Stanislav Olegovich
Organizations
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow Steklov International Mathematical Center |