# Towards a Proof Theory of Analogical Reasoning

## Matthias Baaz

In this lecture we compare three types of analogies based on
generalizations and their instantiations:

- Generalization w.r.t. invariant parts of proofs (e.g., graphs of rule
applications etc.)
- Generalization w.r.t. an underlying meaning. (Here proofs and
calculations are considered as trees of formal expressions. We
analyze the well known calculation attributed to Euler demonstrating
that
the 5th Fermat number is compound.)
- Generalization w.r.t. the premises of a proof. (This type of
analogies
is especially important for juridical reasoning.)