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\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}
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