From Tarski to Hilbert

Gabriel Braun (1) , Julien Narboux (1)

1 IGG

In this paper, we report on the formal proof that Hilbert's axiom system can be derived from Tarski's system. For this purpose we mechanized the proofs of the first twelve chapters of Schwabauser, Szmielew and Tarski's book: Metamathematische Methoden in der Geometrie. The proofs are checked formally within classical logic using the Coq proof assistant. The goal of this development is to provide clear foundations for other formalizations of geometry and implementations of decision procedures.

Keywords: formalization; Hilbert; Coq; Tarski; formal proof; geometry

Domains: Logic in Computer Science [cs.LO]

Gabriel Braun, Julien Narboux. From Tarski to Hilbert. Automated Deduction in Geometry 2012, Jacques Fleuriot, Sep 2012, Edinburgh, United Kingdom. pp.89-109, ⟨10.1007/978-3-642-40672-0_7⟩. ⟨hal-00727117v2⟩