At the next "Mathematical Colloquium" on May 11 at 16:30, Sergey P. Odintsov (Doctor of physical and mathematical sciences, Leading researcher at Laboratory of Logic Systems, Sobolev Institute of Mathematics SB RAS, Chair of Algebra and Mathematical Logic at Department of Mathematics and Mechanics of NSU) will give a lecture "Equations, fixed points, non-classical logics", in memory of Sergey I. Mardaev. The seminar will be held in room 417 of the IM SB RAS.
A fixed point is a solution to an equation of the form p=F(p,q,r,...), where F is some operator, p is a variable, and q,r,... are parameters. The nature of both the operator F and the relation "=" can be different. In the case of modal logics, F is a propositional formula with modal operators, and the relation "=" turns into a logical connective of equivalence "↔". The expression p↔F(p,q,r,...) itself is understood as a theorem of some modal logic or as a formula that is true on a certain class of Kripke models. A fixed point is said to be definable if the solution of the modal equation can be expressed using a formula that does not depend on p. The central direction of research by S. I. Mardaev, a prominent representative of the Novosibirsk school of non-classical logics, is the creation of a theory of definability of fixed points of modal operators.
The talk will provide an accessible introduction to this issue. A general definition of logic as a closure operator on an absolutely free algebra is given, the concept of equivalent algebraic semantics is introduced, as well as Kripke semantics, as a representation of a special kind for algebraic models. In conclusion, examples of the most important results of S. I. Mardaev will be given.
More details can be found on the website of the Mathematical Colloquium http://sobolevmath.tilda.ws.
"Mathematical Colloquium" — a seminar of the Mathematical Center in Akademgorodok and the Sobolev Institute of Mathematics of the Siberian Branch of RAS (IM SB RAS), the purpose of which is to give students a general idea of the areas of research carried out by scientists from the Novosibirsk Scientific Center, as well as Russia and the world. The peculiarity of the seminar is that the emphasis in the talks is on the accessibility of the presentation of the material to a wide circle of the mathematical community, and only then on the detailing of the mathematical content.
Lecture will be read in Russian language.
