Tuesday, April 5, 20162:00 pmComputational Logic SeminarGraduate Center, rm. 4422

Gödel/Artemov-Style Analyses for Variants of Intuitionistic Logic

Thomas Ferguson

CUNY Graduate Center, Department of Philosophy

Thomas Ferguson

Kurt Gödel’s provability interpretation of intuitionistic logic and Sergei Artemov’s Logic of Proofs (LP) have jointly shed a great deal of light on the inner machinery of intuitionistic logic. In this talk, I will give Gödel/Artemov-style analyses to several variants of intuitionistic logic: Cecylia Rauszer’s Heyting-Brouwer Logic (HB) and David Nelson’s Logics of Constructible Falsity (N3 and N4). Heinrich Wansing has sketched out Gödel-style provability interpretations of these systems by distinguishing between categories of justification, e.g., proof and refutation. I will show that identifying these categories with distinct agents in Tatyana Yavorskaya-Sidon’s two-agent Logic of Proofs LP^2 permits salient Gödel/Artemov-style translations of HB and N3 into extensions of LP^2. Finally, we will discuss the prospects for a similar analysis of N4, considering proposals of Melvin Fitting and Che-Ping Su and a conjecture concerning a translation of N4 into the modal logic S4.

Thomas Ferguson is a Ph.D. student of Philososphy at the CUNY Graduate Center. He has authored 11 publications in refereed outlets, gave seven invited talks. His interests include philosophical and mathematical logic; philosophies of logic, mathematics, and computation.