Pluralismo lógico e combinações de lógicas

Abstract

Logical pluralism, the claim that there is more than one correct logic, and logical realism, the claim that logic describes a reality independent of beliefs, practices, or language, appear to be antagonistic perspectives. This thesis presents a pluralistic approach compatible with a realist perspective on Classical Logic, in which non-classical logics can be justified by anti-realist perspectives so as not to compete with Classical Logic. Such an approach is represented here by modal logics, where we embed non-classical logics into classical modal systems.Gödel proposed an embedding of Intuitionistic Logic (IN T ) into the modal logic S4,where ◻ means provability by any correct means, interpreted here as a kind of factive evidence. Fitting, on the other hand, proposed an embedding of the Basic Logic of Evidence (BLE) into the modal logic KX4, whose modal operator, represented hereby ⊡, is interpreted as non-factive evidence. Non-factive evidence does not guarantee the truth of the proposition, whereas factive evidence does. In this thesis, the modal systems S4 and KX4 are combined into a single system, SKX4+ , which can accommodate both embeddings and represent the deductive behavior of factive and non-factive evidence. In addition to the axioms of S4 andKX4, SKX4+ includes the conclusivity principle (CP ), which connects the opera-tors ◻ and ⊡: ◻A → ¬ ⊡ ¬A. (CP ) expresses the idea that factive evidence for A cancels non-factive evidence for ¬A.