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Algebraické aspekty fuzzy logiky
Víta, Martin ; Hájek, Petr (advisor) ; Kučera, Luděk (referee)
In this thesis we study filters on algebras of fuzzy logics and their possible applications. We are going to generalize the notion of an implicative/ positive implicative/fantastic filter on BL-algebras by introducing a notion of R-S-filter. We state and prove some properties of R-S-filters and then we show the connection between characterization of R-S-filter and alternative axiomatization of a given logic. We are going to describe the way how to characterize given algebra of implicative logic via R-S-filters. We show that the results published in [1] and [3] are simple consequences of our theory. Next topics of this work are uniform spaces and uniform topologies. Filters are there used to set up so-called Leibnitz congruences. A set of this congruences on the algebra is a (sub)base of a uniformity that we are going to study. We are going to show that results published in [2] and [4] can be easily generalized for any implicative logics.
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Vectorization of research projects
Mikuláš, Pavel ; Vidová Hladká, Barbora (advisor) ; Víta, Martin (referee)
The aim of this thesis is to compare different approaches of vectorization of unstructu- red textual data about research projects with government financing. We'll attempt to find some structure in the underlying data with emphasis on meassuring similiarity between projects and their clustering. The thesis is experimental and should serve as an example of processing large number of real world objects using methods of statistics and machine learning. 1
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Algebraické aspekty fuzzy logiky
Víta, Martin ; Kučera, Luděk (referee) ; Hájek, Petr (advisor)
In this thesis we study filters on algebras of fuzzy logics and their possible applications. We are going to generalize the notion of an implicative/ positive implicative/fantastic filter on BL-algebras by introducing a notion of R-S-filter. We state and prove some properties of R-S-filters and then we show the connection between characterization of R-S-filter and alternative axiomatization of a given logic. We are going to describe the way how to characterize given algebra of implicative logic via R-S-filters. We show that the results published in [1] and [3] are simple consequences of our theory. Next topics of this work are uniform spaces and uniform topologies. Filters are there used to set up so-called Leibnitz congruences. A set of this congruences on the algebra is a (sub)base of a uniformity that we are going to study. We are going to show that results published in [2] and [4] can be easily generalized for any implicative logics.
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NCMPL 2011 Abstracts
Cintula, Petr ; Ju, S. ; Víta, Martin
This volume contains (extended) abstracts of all 6 invited and 25 contributed talks presented at the conference Non-Classical Modal and Predicate Logics which took place in Guangzhou, December 5-9, 2011. Modalities and predicates have since ancient time been central notions in logic. In the 20th century, various systems of non-classical logics have emerged, with applications in many disciplines like Computer Science, Linguistics, Mathematics, and Philosophy. This gave rise to the questions of non-classical treatment of quantification and modalities and their accommodation in these non-classical settings. In response, various modal and predicate variants of non-classical logics have been introduced and studied in the past decades. Although there are many good conferences on (mainly propositional) non-classical logics, this conference was solely dedicated to modal and predicate non-classical logics. Its aim was to bring together esearchers from various branches of non-classical logics, not only to present recent advances in their particular fields, but also to identify common problems and methods and foster the exchange of ideas between researchers from separate fields.
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