Axioms as rules in intuitionistic logic

ABSTRACT

Over the past few decades, research in structural proof theory has made significant advances in converting axioms into inference rules, aiming to preserve the structural properties and proof-theoretic behaviour of a given logical calculus. This transformation is especially relevant for sequent calculi, where the addition of axioms as initial sequents would affect desirable properties such as cut elimination or analyticity. In this talk, we examine this conversion within the framework of intuitionistic logic, offering both a comparative analysis with the classical setting and novel extensions of the methodology. [Joint work with Matteo Tesi]

SHORT BIO:

Sara Negri is a Professor (it.: Professore Ordinario) of Mathematical Logic at the University of Genova. During 2015-2019, she held the chair of Theoretical Philosophy at the Philosophy Unit of the Department of Philosophy, History and Culture of the University of Helsinki. Previously, she was a Researcher/Senior Researcher since 1996 and Logiikan Dosentti (Adjunct Professor in Logic) since 1998 in the same department (a title resumed in 2021), and a research fellow at the Helsinki Collegium for Advanced Studies from 2014 to 2015. She obtained a Master’s degree in Mathematics in 1991 and a Ph.D. in Mathematics in 1996, both from the University of Padova. Other positions include Research Associate at the Department of Computing of the Imperial College in London, Humboldt Fellow at the Department of Mathematics of LMU in Munich, and Visiting Scientist at the Mittag-Leffler mathematical research institute in Stockholm as well as at the Hausdorff Research Institute for Mathematics in Bonn. In addition, she visited various universities, such as Amsterdam, Chalmers, St Andrews, and Toulouse.

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