17.5.2016 13:15 @ Computational Methods
Jacobi matrices, i.e. symmetric tridiagonal matrices with positive subdiagonal entries, represent thoroughly studied objects connected to various mathematical problems. In this presentation, we introduce and study wedge-shaped matrices that can be viewed as a generalization of Jacobi matrices. The definition is motivated by the structure of output matrices in band generalizations of particular Krylov subspace methods.
18.5.2016 10:00 @ Applied Mathematical Logic
Fuzzy logics are systems that aim to formalize approximate reasoning (allowing multiple truth values), while modal logics focus on dealing with qualification of sentences (reasoning with concepts such as ”possible”, ”necessary”,”provable”,etc). Modal expansions of fuzzy logics have received attention in the last years, due to their expressive power and possibly lower complexity than FOL. In this seminar we focus on the study of some modal logics over MTL, using natural generalizations of the classical Kripke relations structures where propositions at possible worlds can be many-valued, but keeping classical accessibility relations. We will first solve the problem on how to (strongly) axiomatize the logic of an arbitrary leftcontinuous t-norm using infinitary axiomatic systems, and later see how this allows us to proceed with the axiomatization of the corresponding expansion with modalities.
