Paraconsistent logics emerged to reason with inconsistent information without collapsing into triviality. Formally, a logic is said to be paraconsistent if its consequence relation rejects the principle of explosion. Several such logics have been proposed [1-2]. In this talk, we focus on a paraconsistent logic that simultaneously captures evidence for and against a statement [3-4]. Since these two forms of evidence are not necessarily complementary, this approach allows us to capture different epistemic scenarios: vagueness, consistency, and contradiction. In addition, we will outline the underlying algebraic structures and their connection to bilattices [1], present the associated logical system, which yields a many-valued institution, and discuss some of its potential applications.

(Joint work with Alexandre Madeira and Luís S. Barbosa.)