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% (find-angg "LATEX/2017puc-abstract.tex") % (defun c () (interactive) (find-LATEXsh "lualatex -record 2017puc-abstract.tex")) % (defun d () (interactive) (find-xpdfpage "~/LATEX/2017puc-abstract.pdf")) % (defun e () (interactive) (find-LATEX "2017puc-abstract.tex")) % (defun u () (interactive) (find-latex-upload-links "2017puc-abstract")) % (find-xpdfpage "~/LATEX/2017puc-abstract.pdf") % (find-sh0 "cp -v ~/LATEX/2017puc-abstract.pdf /tmp/") % (find-sh0 "cp -v ~/LATEX/2017puc-abstract.pdf /tmp/pen/") % file:///home/edrx/LATEX/2017puc-abstract.pdf % file:///tmp/2017puc-abstract.pdf % file:///tmp/pen/2017puc-abstract.pdf % http://angg.twu.net/LATEX/2017puc-abstract.pdf % % https://mail.google.com/mail/ca/u/0/#sent/15bfa10172153bfd % \documentclass[oneside]{book} \usepackage[colorlinks]{hyperref} % (find-es "tex" "hyperref") \begin{document} \noindent {\bf Intuitionistic Logic (and Planar Heyting Algebras) for Children} \noindent Eduardo Ochs - UFF (Rio das Ostras) \bigskip In this talk we will see a way to interpret Intuitionistic Logic {\sl visually}. One great way to make the expression ``for children'' precise in mathematical titles is to define ``children'' as ``people without mathematical maturity'', in the sense that they are not able to understand structures that are too abstract straight away --- they need particular cases first. The structures in which we can interpret operations like `and', `or' and `implies' and they obey the rules of intuitionistic logic are called Heyting Algebras. It turns out that finite, planar Heyting Algebras (``ZHAs'') can be drawn as subsets of rectangles, and we will see how the operations `and', `or' and `implies' can be calculated visually on them, and why they have to behave in that way. We will also see how ZHAs can be a tool for understanding Heyting Algebras in general and several other related concepts, like deduction trees, simply typed lambda-calculus, and categories. (Note: this material has been tested on real children --- young Computer Science students! --- and they liked it a lot) \bigskip Paper, slides and links: \url{http://angg.twu.net/math-b.html#ebl-2017} \url{http://angg.twu.net/math-b.html#zhas-for-children-2} \end{document} % Local Variables: % coding: utf-8-unix % End: