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M. Baaz:
"Towards a Proof Theory of Analogical Reasoning";
Talk: Logic Seminar in Semester II AY 2015/16, National University of Singapore, School of Computing (invited); 2016-04-25.

In this lecture we compare three types of analogies based on generalizations and their instantiations: 1. Generalization w.r.t. to invariant parts of proofs, for example, graphs of rule applications.

2. Generalization w.r.t. to 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, i.e., that Fermat's claim is false, that all Fermat numbers are primes.

3. Generalization w.r.t. to the premises of a proof: This type of analogies is especially important for juridical reasoning.
The interested reader is referred to the article Generalizing proofs in monadic languages by Matthias Baaz and Piotr Wojtylak for further studies.