Course on Many-Valued Logic at ILLC
Starting form the 1st of September 2014, I will teach a course on Many-Valued Logics at the University of Amsterdam. The webpage with all the details can be found here.
Tutorial on Dualities
These are the slides of my tutorial on Dualities at the $16^{th}$ Latin American Symposium on Mathematical Logic. 28th July – 1st August 2014. Buenos Aires, Argentina. A shorter version can be found here.
Slides on Duality (SLALM 2014)
Canonical formulas for k-potent residuated lattices
Here are the slides of my presentation at Logic, Algebra and Truth Degrees 2014 (LATD 2014), 16-19 July 2014, Vienna, Austria. The conference was part of the wonderful Vienna Summer of Logic.
Dualities and geometry
Finally I wrote some slides about the long-waiting article I am writing together with Olivia Caramello and Vincenzo Marra on adjunctions, dualities, and Nullstellensätze . These slides where presented at the AILA meeting in Pisa and at the Apllied Logic seminar in Delft.
Geometrical dualities for Łukasiewicz logic
This is the transcript of a featured talk given on the 15th of September 2011 at the XIX Congeresso dell’Unione Matematica Italiana held in Bologna, Italy. It is based on a joint work with Vincenzo Marra of the University of Milan that was published in Vincenzo Marra and Luca Spada. The dual adjunction between MV-algebras and Tychonoff spaces, Studia Logica 100(1-2):253-278, 2012. Special issue of Studia Logica in memoriam Leo Esakia (L. Beklemishev, G. Bezhanishvili, D. Mundici and Y. Venema Editors).
The article develops a general dual adjunction between MV-algebras (the algebraic equivalents of Łukasiewicz logic) and subspaces of Tychonoff cubes, endowed with the transformations that are definable in the language of MV-algebras. Such a dual adjunction restricts to a duality between semisimple MV-algebras and closed subspaces of Tychonoff cubes. Further the duality theorem for finitely presented objects is obtained from the general adjunction by a further specialisation. The treatment is aimed at emphasising the generality of the framework considered here in the prototypical case of MV-algebras.
Geometrical dualities for Łukasiewicz logic
