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Field: Mathematical Logic
Supervisor: Steffen Lewitzka
University: Universidade Federal da Bahia (UFBA)
"Increasing the expressiveness of a logical system is a goal of many fields in Computer Science such as Formal Systems, Knowledge construction, Linguistics, Universal Logic and Model Theory. The increasing of this expressiveness can be reached by the use of non-Fregean Logic, a non-classical logic. In non-Fregean Logic, formulas with the same truth value can have different denotations or meanings (also called situations). This concept breaks the Frege Axiom, the reason for the name non-Fregean Logic. Recently, it was shown that there is an equivalence between Boolean pre-algebras and non-Fregean logic models. This fact linked fields which were already using Boolean pre-algebras to represent their semantic models. In this thesis, an investigation on this equivalence is done and applications are exposed in the fields of Modal Logic, Truth Theory, Logic with Quantifiers and Epistemic Logic."
The full thesis can be found at http://repositorio.ufba.br/ri/handle/ri/1938