The Structure of Residuated Lattices

Explore the intricacies of residuated lattices in this comprehensive seminar presented by Peter Jipsen, Ph.D., as part of the Orange County Inland Empire (OCIE) Seminar series in History and Philosophy of Mathematics. Delve into a brief yet informative introduction to the structural developments of residuated lattices over the past 25 years, tailored for graduate students in Philosophy and Physics. Begin with motivating examples related to groups, relation algebras, and Heyting algebras before progressing to structural results concerning MV-algebras, generalized BL-algebras, and Kripke frames for residuated lattices. The presentation may also cover recent work on the structure of locally integral involutive residuated lattices, conducted in collaboration with Melissa Sugimoto and José Gil-Férez.