Jean-Baptiste Joinet

On the linear decoration of intuitionistic derivations

SummaryWe define an optimal proof-by-proof embedding of intuitionistic sequent calculus into linear logic and analyse the (purely logical) linearity information thus obtained.

Strong Normalization for All-Style LK

We prove strong normalization of tq-reduction for all standard versions of sequent calculus for classical and intuitionistic (second and first order) logic and give a perspicuous argument for the completeness of the focusing restriction on sequent derivations.

Proofs, Reasoning and the Metamorphosis of Logic

With the “mathematical watershed”, Logic had been transformed into a foundational theory for mathematics, a theory of truth and proofs—far away from its philosophical status of theory of the intellectual process of reasoning. With the recent substitution of the traditional proofs-as-discourses paradigm by the proofs-as-programs one, Logic is now becomming a foundational theory for computing. One could interpret this new watershed as being “yet another technological drift”, bringing Logic always closer to practical ingeneering, always further from the human intellectual process of reasoning. This article promotes the dual point of view: enlightened by the contemporary analysis of the dynamic of proofs, which bring us to a new understanding of the semantic counterpart of processes operationality (including the links between semantic dereliction due to inconsistency and computational exuberance), Logic has never appeared so close to being, finally, the theory of reasoning.

Calculus of structures and proof-nets

Abstract The Calculus of Structures is a new logical formalism developped by A. Gugliemi, L. Strassburger et al. Using the central idea of CS, namely local rewritings of proofs at any depth, but directly in the formalism of Proof-Nets, I will give an alternative characterisation of the Multiplicative fragment of Multiplicative Linear Logic Proof Nets.