Tutorial on Lukasiewicz logic and MV-algebras at the summer school in Campinas.
Prior to the MaToMUVI conference Philosophy and Mathematics of Uncertainty and Vagueness organised at CLE (UniCamp, Brazil), there will be a summer school for young researchers and undergaduate students. I will give a short tutorial on MV-algebras (seen in a broad perspective). I (hand-wrote) some notes that can be downloaded here. Take it cum grano salis, they are just notes I have used to follow a line of thoughts, still I believe they can be useful to the audience as they contain both specific references to the results presented and some good books giving an updated account of the subject.
Forum of Mathematics, Pi and Forum of Mathematics, Sigma
The idea of having an open access, high level mathematical journal is very welcome. Still, I believe this can be done without charging the authors, nevertheless I wish them success.
Logica II per Informatica
This year I will teach the course “Logica II” for the M.sc. degree in Computer Science. I think I will follow Moore’s modified method for the course (see also the wikipedia entry for the original method).
There are some freely available notes, looking promising, I will use during the course.
Other reference (standard books) that may be used as sources of inspiration during the course are:
- Mendelson, E. Introduction to Mathematical Logic. Chapman & Hall 2009.
- Mundici, D. Logica – Metodo breve. Springer Verlag 2011.
- Asperti, A. and Ciabattoni, A. Logica a Informatica. McGraw-Hill 2003
Further information will follow on this website.
ManyVal12 in Salerno 4-7 July
I am glad to announce that the 2012 edition of the conference series ManyVal will be hosted in Salerno, on the occasion of Antonio Di Nola $65^{th}$ birthday. Further information on the website of the conference.
Duality, projectivity, and unification in Łukasiewicz logic and MV-algebras
We prove that the unification type of Lukasiewicz infinite-valued propositional logic and of its equivalent algebraic semantics, the variety of MV-algebras,is nullary. The proof rests upon Ghilardi’s algebraic characterisation of unification types in terms of projective objects, recent progress by Cabrer and Mundici in the investigation of projective MV-algebras, the categorical duality between finitely presented MV-algebras and rational polyhedra, and, finally, a homotopy-theoretic argument that exploits lifts of continuous maps to the universal covering space of the circle. We discuss the background to such diverse tools. In particular, we offer a detailed proof of the duality theorem for finitely presented MV-algebras and rational polyhedra – a fundamental result that, albeit known to specialists, seems to appear in print here for the first time.
Duality, projectivity, and unification in Łukasiewicz logic and MV-algebras
