### Thursday, December 7, 2017

**Mircea Dumitru (University of Bucharest)
Modal logic as higher-order logic**

**Abstract**: Propositional modal logic is usually viewed as a generalization and extension of propositional classical logic. The main argument of this paper is that a good case can be made that modal logic should be construed as a restricted form of second order classical logic. The paper examines one aspect of this second order connection having to do with an incompleteness phenomenon. The leading concept is that modal incompleteness is to be explained in terms of the incompleteness of standard second order logic, since modal language is basically a second order language.

### Thursday, November 16, 2017

**Ioana Leuștean (University of Bucharest)
Łukasiewicz logic and MV-algebras II **

### Thursday, November 9, 2017

**Ioana Leuștean (University of Bucharest)
Łukasiewicz logic and MV-algebras**

**Abstract**: After a brief introduction to Łukasiewicz logic, we focus on some specific topics connecting logic, algebra and probability theory.

### Thursday, November 2, 2017

**Laurențiu Leuștean (University of Bucharest and IMAR)
Proof mining in convex optimization and nonlinear analysis**

**Abstract**: The research program of proof mining in mathematical logic - first suggested by G. Kreisel in the 1950s as 'unwinding of proofs' and developed by U. Kohlenbach in the 1990s and afterwards - is a field of study that aims to analyze, using proof-theoretic tools, the proofs of existing mathematical theorems in order to obtain their hidden quantitative content. The new information is both of quantitative nature, such as algorithms and effective bounds, as well as of qualitative nature, such as uniformities in the bounds. In this talk we give an introduction to proof mining and present some recent applications in convex optimization and nonlinear analysis.