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% (find-angg "LATEX/2017vichy-workshop.tex") % (defun c () (interactive) (find-LATEXsh "lualatex -record 2017vichy-workshop.tex")) % (defun d () (interactive) (find-xpdfpage "~/LATEX/2017vichy-workshop.pdf")) % (defun e () (interactive) (find-LATEX "2017vichy-workshop.tex")) % (defun u () (interactive) (find-latex-upload-links "2017vichy-workshop")) % (find-xpdfpage "~/LATEX/2017vichy-workshop.pdf") % (find-sh0 "cp -v ~/LATEX/2017vichy-workshop.pdf /tmp/") % (find-sh0 "cp -v ~/LATEX/2017vichy-workshop.pdf /tmp/pen/") % file:///home/edrx/LATEX/2017vichy-workshop.pdf % file:///tmp/2017vichy-workshop.pdf % file:///tmp/pen/2017vichy-workshop.pdf % http://angg.twu.net/LATEX/2017vichy-workshop.pdf \documentclass[oneside]{book} \usepackage[colorlinks]{hyperref} % (find-es "tex" "hyperref") %\usepackage[latin1]{inputenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \input edrxheadfoot.tex % (find-dn4ex "edrxheadfoot.tex") \begin{document} {\bf Logics for Children - Unilog 2018, Vichy (proposal)} \url{http://www.uni-log.org/wk6-logic-for-children.html} \url{http://www.uni-log.org/workshops6.html?sessions=Workshops} \medskip When we explain a theorem to children --- in the strict sense of the term --- we focus on concrete examples, and we avoid generalizations, abstract structures and infinite objects. When we present something to ``children'', in a wider sense of the term that means ``people without mathematical maturity'', or even ``people without expertise in a certain area'', we usually do something similar: we start from a few motivating examples, and then we generalize. One of the aims of this workshop is to discuss techniques for {\it particularization} and {\it generalization}. Particularization is easy; substituing variables in a general statement is often enough to do the job. Generalization is much harder, and one way to visualize how it works is to regard particularization as a projection: a coil projects a circle-like shadow on the ground, and we can ask for ways to ``lift'' pieces of that circle to the coil continously. {\it Projections} lose dimensions and may collapse things that were originally different; {\it liftings} try to reconstruct the missing information in a sensible way. There may be several different liftings for a certain part of the circle, or none. Finding good generalizations is somehow like finding good liftings. The second of our aims is to discuss {\it diagrams}. For example, in Category Theory statements, definitions and proofs can be often expressed as diagrams, and if we start with a general diagram and particularize it we get a second diagram with the same shape as the first one, and that second diagram can be used as a version ``for children'' of the general statement and proof. Diagrams were for a long time considered second-class entities in CT literature ([2] discusses some of the reasons), and were omitted; readers who think very visually would feel that part of the work involved in understanding CT papers and books would be to reconstruct the ``missing'' diagrams from algebraic statements. Particular cases, even when they were the motivation for the general definition, are also treated as somewhat second-class --- and this inspires a possible meaning for what can call ``Category Theory for Children'': to start from the diagrams for particular cases, and then ``lift'' them to the general case. Note that this can be done outside Category Theory too; [1] is a good example. Our third aim is to discuss {\it models}. A standard example is that every topological space is a Heyting Algebra, and so a model for Intuitionistic Predicate Logic, and this lets us explain {\sl visually} some features of IPL. Something similar can be done for some modal and paraconsistent logics; we believe that the figures for that should be considered more important, and be more well-known. \bigskip References: [1]: Jamnik, Mateja: Mathematical Reasoning with Diagrams: From Intuition to Automation. CSLI, 2001. [2]: Krömer, Ralf: Tool and Object: A History and Philosophy of Category Theory. Birkhäuser, 2007. \bigskip {\bf Call for papers} Topics of interest to the workshop include but are not limited to: \begin{itemize} \item Ways to visualize logics or other algebraic structure \item (The many roles of) diagrams in Category Theory \item Translations between digrammatical languages and formal languages \end{itemize} \bigskip Organizers of the workshop: Eduardo Ochs - Universidade Federal Fluminense (UFF), Rio das Ostras, RJ, Brazil eduardoochs@gmail.com, \url{http://angg.twu.net/math-b.html} \medskip Fernando Lucatelli Nunes - Centro de Matemática da Universidade de Coimbra, Coimbra, Portugal lucatellinunes@student.uc.pt, \url{http://fernandolucatelli.wordpress.com/} \bigskip \bigskip \bigskip My (E. Ochs) papers related to diagrams and things for children (note: these papers motivated me to propose this workshop, but their links won't appear in the page of the workshop; this is just for the keynote speakers): \medskip Planar Heyting Algebras for Children (2017, submitted): \url{http://angg.twu.net/math-b.html\#zhas-for-children-2} \medskip Internal Diagrams and Archetypal Reasoning in Category Theory (2013, Logica Universalis): \url{http://angg.twu.net/math-b.html\#idarct} \end{document} % Local Variables: % coding: utf-8-unix % End: