Modal Logic for Induction

Giulio Fellin, Sara Negri, Peter Schuster
2020 Advances in Modal Logic  
We use modal logic to obtain syntactical, proof-theoretic versions of transfinite induction as axioms or rules within an appropriate labelled sequent calculus. While transfinite induction proper, also known as Noetherian induction, can be represented by a rule, the variant in which induction is done up to an arbitrary but fixed level happens to correspond to the Gödel-Löb axiom of provability logic. To verify the practicability of our approach in actual practice, we sketch a fairly universal
more » ... tern for proof transformation and test its use in several cases. Among other things, we give a direct and elementary syntactical proof of Segerberg's theorem that the Gödel-Löb axiom characterises precisely the (converse) well-founded and transitive Kripke frames.
dblp:conf/aiml/FellinNS20 fatcat:wasffz56b5fxtdhzm7kmnarayy