Banca de DEFESA: FELIPE HENRIQUE ALVES MAGALHAES

Logic of Sufficiency

Modal logic, material implication, sufficient operator, doctrine of causality, principle of sufficient reason.

This thesis is an investigation into the formal concept of sufficiency. In algebraic terms, there is an important relationship between the operator of sufficiency and that of necessity. Through the representation theorem, it is known that propositional logic is isomorphic to Boolean algebra. By observing the behavior of modal operators, a logic with this new modal operator of sufficiency was defined. Its syntax and semantics were then explored. An analysis of the definition of the term was also carried out in certain contexts related to the notions of necessary and sufficient conditions in factual scenarios involving modalities. One of the results presented here is the observation that ”suffici- ent”behaves differently for each type of truth. In addition to the more formal topics concerning the notion of sufficiency, this thesis also briefly presents a historical-philosophical discussion of the notion of cause and the principle of sufficient reason, drawing on key philosophers such as Aristotle and Leibniz.