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Petr Cintula - Substructural Logics: A Logical Glimpse at Residuated Lattices

Petr Cintula: Substructural Logics: A Logical Glimpse at Residuated Lattices

Lattices equipped with a monoidal operation and its left and right residua have attracted recently a lot of attention. The magnus opus of this area of algebra is Galatos, Jipsen, Kowalski and Ono's book `Residuated Lattices: An Algebraic Glimpse at Substructural Logics', where the authors concentrate on the role these algebras play in the study of the so-called substructural logics (a prominent family of non-classical logics).

Their `glimpse' is made possible due to the existence of a profound relationship between logical systems and classes of algebraic structures (which goes way beyond these particular logics/algebras). To date, however, logic has profited most from this relationship. My goal in this talk is to first glimpse the other way round and present residuated lattices through the eyes of a logician and second to return the favor to algebra and show that certain algebraic
problems can be attacked by finding, and solving, their logical counterparts.

The presentation is based on the joint work with Carles Noguera.