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math.LO2024
On the Various Translations between Classical, Intuitionistic and Linear Logic
Gilda Ferreira, Paulo Oliva, Clarence Lewis Protin
Several different proof translations exist between classical and intuitionistic logic (negative translations), and intuitionistic and linear logic (Girard translations). Our aims i…
math.LO2024
Herbrandized modified realizability
Gilda Ferreira, Paulo Firmino
Realizability notions in mathematical logic have a long history, which can be traced back to the work of Stephen Kleene in the 1940s, aimed at exploring the foundations of intuitio…
math.LO2019
The Russell-Prawitz embedding and the atomization of universal instantiation
José Espírito Santo, Gilda Ferreira
Given the recent interest in the fragment of system F where universal instantiation is restricted to atomic formulas, a fragment nowadays named system F_at, we study directly in sy…