Web pages of Luca Spada

Corso di “Algebra della Logica” alla scuola AILA 2017

This year I teach a course (12 hours) a the AILA summer school of logic.  Below one can find the slides of my first three lectures and some references.

• Lecture 1 (Classical propositional logic and Boolean algebras)
• Lecture 2 (Algebraic completeness of propositional calculus)
• Lecture 3 (Abstract Algebraic Logic)
• Lecture 4 (Dualities) lecture material:
  1. Pat Morandi’s notes on dualities,
  2. Tutorial in Buenos Aires.
• Lecture 5 and 6 (Non classical logic) references:
  1. Y. Venema, Algebras and Coalgebras, in: J. van Benthem, P. Blackburn and F. Wolter (editors), Handbook of Modal Logic, 2006, pp 331-426.
  2. R. L. O. Cignoli, I. M. L. D’Ottaviano e D. Mundici, Algebraic Foundations of Many-Valued Reasoning, Trends in Logic, Vol. 7 Springer, 2000.

Lecture notes by Guido Gherardi (Computability Theory).

Workshop on “Geometry and non-classical logics”

I am happy to announce that we will host a workshop on “Geometry and non-classical logics” at the campus of the University of Salerno, from the 5th to the 8th of September.

The workshop is one of the events planned within the EU-funded project SYSMICS.
Further information can be found at http://logica.dipmat.unisa.it/sysmics/geoNonLogic/

The Twelfth International Tbilisi Symposium on Language, Logic and Computation

The Twelfth International Tbilisi Symposium on Language, Logic and Computation will be held on 18-22 September 2017 in Kakheti, Georgia. The Programme Committee invites submissions for contributions on all aspects of language, logic and computation: https://easychair.org/conferences/?conf=tbillc2017. Submission deadline: 15 March 2017.

Tutorials:

Language: Jakub Szymanik (University of Amsterdam)
Logic: Sam van Gool (City College of New York)
Computation: Ana Sokolova (University of Salzburg)

Invited speakers:

Language:
Gemma Boleda (Universitat Pompeu Fabra)
Ruth Kempson (King’s College, London)
Logic:
Alexander Kurz (University of Leicester)
Eric Pacuit (University of Maryland)
Computation:
Dexter Kozen (Cornell University)
Alex Simpson (University of Ljubljana)

Further information at http://events.illc.uva.nl/Tbilisi/Tbilisi2017/

PhD Course on Category Theory (Jan-Feb 2017)

Page contents

• News
• Contents
• Course material
• Practicalities

News

Contents

• Categories and functors. Universal objects.
• Natural transformations.  Adjoint functors and equivalences.
• Dualities: Stone, Gelfand, Pontryagin.

Course material

• Harold Simmons. An Introduction to Category Theory. (2011) Cambridge University Press.
• Saunders Mac Lane. Categories for the Working Mathematician (Second edition). Springer.

Homework

• Homework set 1
• Homework 2: prove that the three definitions of adjoint functors are equivalent. Skip the easiest details.

Practicalities

• Lecturer: Luca Spada
• Length of the course: 10 hours.

Dates/rooms:

• Lectures will take place is Sala Riunioni, Department of Mathematics.
• Lectures will be scheduled as follows:
  • Tuesday 17 of January, from 11:00 to 13:00;
  • Thursday 19 of January, from 11:00 to 13:00;
  • Tuesday 24 of January, from 11:00 to 13:00;
  • Thursday 26 of January, from 11:00 to 13:00;
  • Tuesday 7 of February, from 11:00 to 13:00;

An expansion of Basic Logic with fixed points

Abstract: We introduce an expansion of Basic Logic (BL) with new connectives which express fixed points of continuous formulas, i.e. formulas of BL whose connectives are among {&,∨,∧}. The algebraic semantics of this logic is studied together with some of its subclasses corresponding to extensions of the above-mentioned expansion. The axiomatic extensions are proved to be standard complete.

Preprint