Section: New Results

Proof theory

We believe that our work on proof-checking and automated theorem proving cannot be separated from a more theoretical research on proof theory.

Together with Denis Cousineau, Gilles Dowek and Olivier Hermant have related semantic criteria for proof normalization and admissibility of the cut rule in Deduction modulo [17] , [26] .

Gilles Dowek has proposed a new way to define classical connectives in a constructive framework [46] .

Together with Murdoch J. Gabbay (Heriot Watt), Gilles Dowek has proposed a new nominal logic that handles binders in terms [16] and a new semantics for predicate logic [29] .

During her visit in the team, Cecilia Englander has studied the correspondence between natural deduction and sequent calculus.

Together with Ying Jiang (Beijing), Gilles Dowek has defined a logic for finite structures. Kailiang Ji is currently investigating the use of proof search algorithms in Deduction modulo to automatically prove theorems in this theory.