UBC Theses and Dissertations

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UBC Theses and Dissertations

Applications of a natural deduction set theory Tsiknis, George Konstantinos


The goal of this thesis is to demonstrate the versatility and suitability of a logic and set theory NaDSet for providing logical foundations to disparate areas of mathematics and computer science. Category theory has been chosen as the area of mathematics, while programming language semantics and semantics for the lambda calculus are the areas of computer science. In each of the three areas NaDSet provides a logical foundation using exactly the same "logistic" method: Basic concepts are defined as terms of the logic and then the logic is used to derive all theorems; no assumptions in the form of additional axioms or rules of deduction are needed. The thesis demonstrates the ease and directness with which this can be done for the three areas, suggesting that in other, as yet unexplored areas, NaDSet may prove to be equally useful.

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