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A Categorical Approach to Logics and Logic Homomorphisms
, 2007
"... This master’s thesis presents a number of important concepts in logic such as models, entailment, and proof calculi within the framework of category theory. By describing these concepts as categories, a tremendous amount of generality and power is gained. In particular, this approach makes it possib ..."
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This master’s thesis presents a number of important concepts in logic such as models, entailment, and proof calculi within the framework of category theory. By describing these concepts as categories, a tremendous amount of generality and power is gained. In particular, this approach makes it possible to reason about maps from one logic to another in a consistent and convenient manner. By a consistent map is meant that the truth stays invariant, that is, a statement true in the source logic is mapped to a similarly true statement in the target logic. Conversely, a statement false in the source logic is mapped to a statement false in the target logic. While the thesis focuses on the theoretical notions outlined above, a brief coverage of two practical applications is given as a means to illustrate the utility of these notions. Concluding the text is a chapter containing a discussion and a section wherein possible future work is presented. In an effort to make the text mostly selfcontained, concepts beyond basic discrete mathematics are duly introduced with definitions and examples. These include, for