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Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 15 of 15 for “"Universal algebra"”.
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Fractoids
… dissertation will examine the properties of the algebraic structure herein named the fractoid. This structure will be defined and its properties closely examined. In this dissertation we will first provide context for this structure, by looking at both category theory and universal algebra. We …
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Varieties of lattices
An interesting problem in universal algebra is the connection between the internal structure of an algebra and the identities which it satisfies. The study of varieties of algebras provides some insight into this problem. Here we are concerned mainly with lattice varieties, about which a wealth of …
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Algebraic aspects of propositional logic
… seek to examine the connection between abstract algebra and propositional logic. We start by considering the category Bool of Boolean algebras, the algebraic counterpart of classical propositional logic. We provide an algebraic definition of theories and models of classical logic and provide …
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A DOCTRINAL VIEW OF LOGIC
… considers how to describe free constructions in algebra in the context of elementary doctrines. At first, we study the meaning of “adding a constant to a language” for any doctrine, and “adding an axiom to a theory” for a primary doctrine. These constructions are used to find a possible …
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Second-Order Algebraic Theories
Second-order universal algebra and second-order equational logic respectively provide a model theory and a formal deductive system for languages with variable binding and parameterised metavariables. This dissertation completes the algebraic foundations of second-order languages from the viewpoint …
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Logical and algebraic structures from Quantum Computation
… in Chapter 2 we will review some basics of universal algebra and functional analysis. In Chapters 3 through 6 the fundamentals of quantum gate theory will be produced. In Chapter 7 we will introduce quasi-MV algebras, a formal study of a suitable selection of algebraic operations associated …
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A general theory of syntax with bindings
… for the general theory. We start by taking a “universal algebra” approach, modelling syntaxes via algebraic-style binding signatures, which we employ in a substantial case study on formal reasoning: Church-Rosser and standardization theorems for lamda-calculus. This solution proves itself too …
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A mathematical formulation of intelligent agents and their activities
… use techniques and concepts from fields such as universal algebra, order theory, domain theory and topology. As part of the formulation we also present a case study to demonstrate how the formulation could be applied.
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A study of the computations done by grade 9 learners in a Western Cape high school when simplifying algebraic expressions involving the negative symbol
… computations that learners do when simplifying algebraic expressions are multiple and diverse, with some determined by reasoning aligned with mathematics whilst others rely on idiosyncratic constructs like mnemonics or solution templates. Research in mathematics education highlights symbol sense …
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Amalgamation in varieties of algebras
… of the most successful approaches to research in universal algebra has been the study of varieties, initiated by Garett Birkhoff in the 1930's. Examples of varieties include many classes of algebras such as groups, semigroups, lattices and Boolean algebras. In 1927, O. Schreier showed that for any …
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Congruence Relations in Direct Product Algebras
No abstract prepared.
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Cartesian closed bicategories: type theory and coherence
… and exponentials---arise in logic, categorical algebra, and game semantics. However, calculations in such bicategories quickly fall into a quagmire of coherence data. I show that there is at most one 2-cell between any parallel pair of 1-cells in the free cartesian closed bicategory on a set and …
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On Loop Commutators, Quaternionic Automorphic Loops, and Related Topics
<p>This dissertation deals with three topics inside loop and quasigroup theory. First, as a continuation of the project started by David Stanovský and Petr Vojtĕchovský, we study the commutator of congruences defined by Freese and McKenzie in order to create a more pleasing, equivalent definition …
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Computing congruences and endomorphisms for algebras of type (2m, 1n)
… que são mais próximas das empregadas na Álgebra Universal do que daquelas usadas em grupos. Existem maneiras de construir álgebras a partir das existentes (produtos diretos etc.), mas a operação inversa é crítica: decompor uma dada álgebra em outras menores. Este tipo de decomposição é …