Proof systems for Geometric theories (PROGEO) - Pimentel, Elaine (Anais do Workshop Brasileiro de Lógica (WBL), 2020)
We plan to study the problem of finding conservative extensions of first order logics. In this project we intend to establish a systematic procedure for adding geometric theories in both intuitionistic and classical logics, as well as to extend this procedure to bipolar axioms, a generalization of the set of geometric axioms. This way, we obtain proof systems for several mathematical theories, such as lattices, algebra and projective geometry, being able to reason about such theories using automated deduction.