Probabilistic logical systems play an important role in applications of logic to computer science, where one often has to deal with knowledge of a probabilistic nature. The study of computational and model-theoretic properties of such systems (either finitary or infinitary) is a relevant task in logic and theoretical computer science. Furthermore, there are interesting related systems, which deal with metric and normed spaces, and also various modal enrichments of probabilistic systems.

Substructural logics are logical systems which lack all or some of the structural rules. Such logics are used for modelling computations with limited resources (unlike a mathematical statement, a resource cannot be used twice), and their non-commutative versions have applications in mathematical linguistics. Infinitary extensions of substructural logics enjoy interesting algorithmic and proof-theoretic properties.

Program
The seminar will be organised in long talks lasting for 2-4 meetings. Each talk will be devoted to a specific system related to probabilities (metrics or norms) or a substructural logical system and will include detailed proofs of the corresponding results. The speakers will be chosen by the heads of the seminar, mostly from students and PhD students.

As the sources for their talks, the speakers may choose articles and chapters from books, as well as their own new texts. Some examples of sources are listed below.

Seminar organizers
Kuznetsov Stepan Lvovich
Speranski Stanislav Olegovich

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