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Probabilistic semantics for Independence-friendly Logics
Seidl, Julian ; Majer, Ondrej (advisor) ; Švarný, Petr (referee)
(in English): Character of the work is purely theoretical and it pursues game theory in the perspective of mathematical logic and probability. The work is divided into two parts. Introductory part compiles basic concepts and definitions, summarizing the game theory and basics of syntax and semantics of mathematical logic and its extensions suitable for work in the field of game theory. Introductory part also explains following terms: extensive and strategic form of games, Nash equilibrium, pure and mixed strategies, winning strategies or independence-friendly logic. The problems solved in the second part of the work such as question of existence of Nash equilibrium in the games with infinite models or issue which arises when trying to uniformly distribute the probability of strategies in the same class of games are sketched out. The second part continues with analysis of strategic games with imperfect information aiming to the solution of nontrivial problems earlier proposed. Second part also introduces basic concepts and definitions of the probability theory, which helps comprehending the problems mentioned above. The last part of the work before the very presentation of some results induced by the area of infinite games is conversion between strategic and extensive games form. In the end of the...
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Logical problems zebra with pupils in primary school
Laštovková, Tereza ; Slezáková, Jana (advisor) ; Havlíčková, Radka (referee)
This diploma thesis is focusing on analysis of logical zebra problems and finding strategies of pupils solutions and development of these strategies in primary school. For this diploma thesis was created two gradation of those logical problems for pupils from the 1st - 5th class in primary school. Theoretical part is focused on characteristics of logical problems zebra, its definition, history of logical problems zebra and its todays use. In more detail it is based on examples and ways of strategies, how to solve these problems, like with tablets or full charts and so on. It's also focused on parameters of gradation, which serve the possibilities of making gradation for pupils in primary school in the next part, the research part. Research part is based on description and comments of pupils strategies in solving logical problems zebra in two gradation, wich contains ten tasks.. Research part shows how pupils can develop their solving strategies based on their experience with solving logical problems zebra, with described phenomena for pupils solution and for tasks. KEY WORDS graded parameters of problems, context of problems, logic, negation, problems with conditions, relations, solving strategy of pupils in primary school, table as tool for problem solving
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Teaching web application for secondary school mathematical logic
Moravec, Luboš
Teaching web application for secondary school mathematical logic Luboš Moravec Abstract: The head part of thís work is a website intended especially for secondary school students which teaches mathematical logic. The website is divided into two parts - a teaching text and tests. The teaching text, which is divided into seven chapters, explains the idea of propositions and their negations, basic logic connectives (conjunction, disjunction, implication, equivalence), a problem of finding truth value of composite propositions and their negations, work with quantifiers, set operations, Venn's diagrams and proof techniques. Except the teaching chapters there are also tests for verifing new knowledge. The questions in tests are randomly selected from a group of similar questions, so a repeated test has new questions. This text contains an user guide, a programmer documentation and a printed version of teaching chapters.
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Application of SAT Solvers in Circuit Optimization Problem
Minařík, Vojtěch ; Mrázek, Vojtěch (referee) ; Vašíček, Zdeněk (advisor)
This thesis is focused on the task of application of SAT problem and it's modifications in area of evolution logic circuit development. This task is supposed to increase speed of evaluating candidate circuits by fitness function in cases where simulation usage fails. Usage of SAT and #SAT problems make evolution of complex circuits with high input number significantly faster. Implemented solution is based on #SAT problem. Two applications were implemented. They differ by the approach to checking outputs of circuit for wrong values. Time complexity of implemented algorithm depends on logical complexity of circuit, because it uses logical formulas and it's satisfiability to evaluate logic circuits.
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A Logical Characteristic of Read-Once Branching Programs
Žák, Stanislav
We present a mathematical model of the intuitive notions such as the knowledge or the information arising at different stages of computations on branching programs (b.p.). The model has two appropriate properties: i) The ”knowledge” arising at a stage of computation in question is derivable from the ”knowledge” arising at the previous stage according to the rules of the model and according to the local arrangement of the b.p. ii) The model confirms the intuitively well-known fact that the knowledge arising at a node of a computation depends not only on it but in some cases also on a ”mystery” information. (I. e. different computations reaching the same node may have different knowledge(s) arisen at it.) We prove that with respect to our model no such information exists in read-once b.p.‘s but on the other hand in b. p.‘s which are not read-once such information must be present. The read-once property forms a frontier. More concretely, we may see the instances of our models as a systems S = (U,D) where U is a universe of knowledge and D are derivation rules. We say that a b.p. P is compatible with a system S iff along each computation in P S derives F (false) or T (true) at the end correctly according to the label of the reached sink. This key notion modifies the classic paradigm which takes the computational complexity with respect to different classes of restricted b.p.‘s (e.g. read-once b.p.‘s, k-b.p.‘s, b.p.‘s computing in limited time etc.). Now, the restriction is defined by a subset of systems and only these programs are taken into account which are compatible with at least one of the chosen systems. Further we understand the sets U of knowledge(s) as a sets of admissible logical formulae. It is clear that more rich sets U‘s imply the large restrictions on b.p.‘s and consequently the smaller complexities of Boolean functions are detected. More rich logical equipment implies stronger computational effectiveness. Another question arises: given a set of Boolean functions (e.g. codes of some graphs) what logical equipment is optimal from the point of complexity?
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Onto-Logic Conception and Critic of Existence by William F. Vallicella
PRIEHRADNÁ, Markéta
Our concern is to deal with the notion of existence and its status in onto-logical approach among analytic philosophers of the last century. As a draft of this critique we are using works of american philosopher William F. Vallicella, especially his three works: A Critique of the Quantificational Account of Existence (1983), A Paradigm Theory of Existence: Onto-Theology Vindicated (2002) and Existence: Two Dogmas of Analysis (2014). We criticise and analyse the philosophical view which suggests that to exist is what instantiation of existence is. This view is established in the works of Gottlob Frege, Bertrand Russell and Willard V. O. Quine. We also cope with the Vallicella's critique of ontology, which validates the statements about non-existent objects, and with his critique of existence being a first order property.
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Method of Drawing on the right side of the brain from the perspective of art education
DAVIDOVÁ, Eliška
This bachelor thesis presents critical and comparative study devoted to the analytic method called Drawing on the right side of the brain and its comparison to traditional teaching models of drawing. The text is based primarily on an analysis of methodological materials by Betty Edwards (author of the book Learn to draw on the right side of the brain) and confronts them with the latest findings in neuroscience which are dealing with localization of creative acts. This thesis aims to critically point out the differences in the concept of teaching methods of drawing, their professional basis and to update their creative and learning potential for the sphere of art education.
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Using Rough logic for predicting price movements on financial markets
Kutnar, Petr
Financial markets and especially their movements are very difficult to predict. For this reason, it cannot be clearly concluded what market will do. We cannot use basic logical operators such as if A happens, then comes B. Since we cannot use simple decision rules and we work in high uncertainty we cannot easily build classical mathematical model because of uncertainty of each and every result. However to analyze this type of data we can used Rough logic which is design to work with uncertainty. The aim of this thesis is use of Rough logic to create a mathematical model, which will be able to some extent to understand and eventually predict individual market movements. Market uncertainty Purpose of the article: Using Rough logic for predicting price movements. Scientific aim: Rough Set. Conclusions: Methodology for using Rough set in financial markets.
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Thought intersections of philosophy and mathematics
Hlavešová, Ilona ; Hogenová, Anna (advisor) ; Blažková, Miloslava (referee)
The submitted thesis addresses the ideas that are at the intersections of philosophy and mathematics. These intersections have been in the course of the history as follows: Numerical ratios, the concept of infinity, continuum partition, space specification, determinism versus randomness and exploring of the mathematics foundations with an overlap into philosophy. The results herewith presented have been achieved on the basis of the HTF lectures and seminars, available literature, my own knowledge and reasoning. The thesis documents processes of how mathematics stimulated certain philosophical principles and vice versa how mathematics was influenced by philosophical views. Last but not least, there are presented comparisons between philosophic propositions and the current mathematics and physics knowledge in the mentioned intersections.
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