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8.3.2016 13:15 @ Computational Methods
In this talk we consider several algorithms to construct bases for Krylov subspaces. In the first part we show how to build Newton bases to be used in the GMRES or Q-MR methods to solve linear systems. We describe two algorithms to compute the shifts. In the second part we consider algorithms using the distance of a vector to a subspace. We used them within Q-MR methods. We illustrate the performance of all these algorithms with numerical examples.
9.3.2016 10:00 @ Applied Mathematical Logic
Despite of the fact that weighted structures are deeply investigated in computer science, it is surprising that fuzzy logic (a logic of weighted structures) has almost no applications in the abovementioned investigations so far. In the lecture I will present my personal opinion why fuzzy logicians missed the boat to apply their knowledge in computer science. As a case study, I will overview some recent developments on valued constraint satisfaction problems in order to show how these problems are related to fuzzy logic and what kind of questions computer scientists pose about them.
16.3.2016 10:00 @ Applied Mathematical Logic
Fuzzy partial propositional logic, recently proposed by Behounek and Novak, provides a simple framework accommodating propositions with graded as well as undefined truth. A natural next step is to extend the system to predicate logic of the first and higher orders. I will present first steps in this direction (joint work with Martina Dankova, in progress), considering only undefined truth and leaving aside undefined individuals. In particular, I will discuss basic fuzzy partial quantifiers, firstorder and (Russell-style) higher-order fuzzy partial logic, basic properties of first- and higher-order fuzzy partial predicates and functions, and their representation in the usual (non-partial) fuzzy logic.
23.3.2016 10:00 @ Applied Mathematical Logic
We outline two approaches of designing a logical language for coalgebras, parametric in the coalgebra functor, and apply them in a many-valued setting. Our goal is to give sufficient conditions (both on the coalgebra functor and the algebra of truth values) for the resulting language being expressive for bisimilarity. In this respect, we are generalising results of G. Metcalfe and M. Marti on Hennessy-Milner property for language with box and diamond over crisp many-valued imagefinite Kripke frames where the algebra of truth values is a complete MTL-chain; and also results on expressivity of classical coalgebraic logic by D. Pattinson and L. Schroder.