Monday 5th of December 2022, 14:00-15:00 in HG03.085
Grégoire Marc
The Logic of Topoi.
Classical logic is intimately linked to set theory. If \(X\) is a set, the
set \(P(X)\) of subsets of \(X\) has a structure of Boolean algebra which is
strongly related to the one of truth values \(\{0,1\}\) of classical logic. As
a consequence, the value of any propositional formula in classical logic
can be determined only using the structure of \(P(X)\).
During this talk, we will see how it is possible to create new kind of
propositional logics by replacing the category of sets by any topos. To
this end, we will only deal with examples, and you don’t need to know
anything about topos theory and even category theory to understand this
talk. More precisely, we will investigate the propositional logic of
oriented graphs and of sets endowed with an action of the positive integers.