Invited Speakers:
Speakers from Chapman Univeristy:
Local Organizer: Alexander Kurz
Relations in Point-Free Topology
We report on progress on a program of investigating relations on point-free topological spaces (locales). As the category of locales is order-enriched, a natural notion of a relation from X to Y is a jointly epi cospan X->C<-Y. Dualizing, these manifest as special spans on the category of frames. Namely, we see that they correspond to the familiar notion of weakening relations between frames that are compatible with the frame structure in an obvious way. Thus, the study of point-free relations is the study of these so-called frame relations.
In the talk today, we build some of the needed techniques to deal with frame relations systematically. As one application, we show that on any frame L, the preorder frame relations on L constitute another frame, dually isomorphic to the coframe of point-free subspaces of L. We then prove directly a known result of Plewe that this frame is ultraparacompact, and also that is satisfies a certain density result. Together, these two properties are strong, and appear to be very nearly characterizing frames that occur as frames of nuclei.
Using Prover9/Mace4 to Investigate Kripke Frames of Distributive Quasi Relation Algebras
Joint work with Andrew Craig and Claudette Robinson (University of Johannesburg)
A Formal Deductive System for Euclid's Elements (Book I)
The 'Blacktriangle' Calculus
Part of a project with Giuseppe Greco, Apostolos Tzimoulis, Brandon Laing
Logical Dynamics of Neural Network Learning
The Topology of Surprise
Articles by Alexandru Baltag, Nick Bezhanishvili, David Fernández-Duque:
Logic and Computation of Social Behaviour