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Date added: 18.4.2015

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The scientific area this thesis belongs to is many-valued logics: this meanslogics in which, from the semantical point of view, we have intermediatetruth-values, between 0 and 1 (which in turns are designated to represent, respectively, the falseMoreThe scientific area this thesis belongs to is many-valued logics: this meanslogics in which, from the semantical point of view, we have intermediatetruth-values, between 0 and 1 (which in turns are designated to represent, respectively, the false and the true).The classical logic (propositional, for simplicity) is based on the fact thatevery statement is true or false: this is reflected by the excluded middle law, that is a theorem of this logic. However, there are many reasons that suggestto reject this law: for example, intuitionistic logic does not satisfy it, sincethis logic reflects a constructive conception of mathematics (see Hey71, Tro69]). On Some Axiomatic Extensions of the Monoidal T-Norm Based Logic Mtl: An Analysis in the Propositional and in the First-Order Case by Matteo Bianchi