Suprastructural logics

PAILOS, FEDERICO MATÍAS

Madrid

Taller; Taller Complutense de Filosofía Analítica; 2024

Universidad Complutense de Madrid

Over the last decades, considerable attention has been paid to substructurallogics, that is, logical systems that forego at least one of the structural principlessanctioned by classical logic. However, little or no attention has been paid to thedual notion of a suprastructural logic, that is, a system that sanctions at least onestructural principle that classical logic foregoes. In the present paper we explorethis notion and present different types of systems where at least one classicallyinvalid structural metainference holds. We introduce two families of contrastructural logics: Boolean logics and Strong-Kleene logics. Afterwards, we present somestrictly suprastructural logics. We show that LP and K3 are strictly suprastructural from a global perspective. We then introduce some metainferential logics thatare strictly suprastructural from a local perspective, and show that some of themare also supraclassical. This leads us to consider two different notions of suprastructurality: one that focuses on metainferences and the other that focuses on closureproperties.