8 papers
Glivenko's theorems from an ecumenical perspective
Luiz Carlos Pereira, Victor Barroso-Nascimento, Elaine Pimentel
In this paper, we revisit Glivenko's theorems, foundational results relating classical and intuitionistic logic, from an ecumenical perspective. We begin by discussing the historic…
Bilateralism with incompatible proofs and refutations
Victor Barroso-Nascimento, Maria Osório, Elaine Pimentel
Logical bilateralism challenges traditional concepts of logic by treating assertion and denial as independent yet opposed acts. While initially devised to justify classical logic,…
Effects of the Strict-Tolerant Approach on Intuitionistic and Minimal Logic
Victor Barroso-Nascimento, German Mejia
This paper extends the literature on the strict-tolerant logical approach by applying its methods to intuitionistic and minimal logic. In short, the strict-tolerant approach modifi…
Higher-order Kripke models for intuitionistic and non-classical modal logics
Victor Barroso-Nascimento
This paper introduces higher-order (``nested") Kripke models, a generalization of Kripke models that is remarkably close to Kripke's original idea -- both mathematically and concep…
Bilateral base-extension semantics
Victor Barroso-Nascimento, Maria Osório
Bilateralism is the position according to which assertion and rejection are conceptually independent speech acts. Logical bilateralism demands that systems of logic provide conditi…
A Sequent Calculus Perspective on Base-Extension Semantics (Technical Report)
Victor Barroso-Nascimento, Ekaterina Piotrovskaya, Elaine Pimentel
We define base-extension semantics (Bes) using atomic systems based on sequent calculus rather than natural deduction. While traditional Bes aligns naturally with intuitionistic lo…
A Proof-Theoretic Approach to the Semantics of Classical Linear Logic
Victor Barroso-Nascimento, Ekaterina Piotrovskaya, Elaine Pimentel
Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in on…
An ecumenical view of proof-theoretic semantics
Victor Nascimento, Luiz Carlos Pereira, Elaine Pimentel
Debates concerning philosophical grounds for the validity of classical and intuitionistic logics often have the very nature of logical proofs as one of the main points of controver…