Categorical Semantics of Linear Logic Paul-André

Proof Theory is the result of a tumultuous history, developed on the periphery of mainstream mathematics. Hence, its language is often idiosyncratic: sequent calculus, cutelimination, subformula property, etc. This survey is designed to guide the novice reader and the itinerant mathematician on a smooth and engaging path through the subject – focused on the symbolic mechanisms of cut-elimination, and their transcription as coherence diagrams in categories with structure. This spiritual journey at the meeting point of linguistic and algebra is demanding at times, but unusually rewarding: to date, no language (formal or informal) has been studied as thoroughly in mathematics as the language of proofs. We start the survey by a short introduction to Proof Theory (Chapter 1) followed by an informal explanation of the principles of Denotational Semantics (Chapter 2) analogous to a Representation Theory for proofs, generating invariants modulo cutelimination. After describing in full detail the cut-elimination procedure of linear logic (Chapter 3), we explain how to transcribe it into the language of categories with structure. We review two alternative constructions of a ∗-autonomous category, or monoidal category with duality (Chapter 4). After giving a 2-categorical account of lax and colax monoidal adjunctions (Chapter 5) and recalling the notions of monoids and monads (Chapter 6) we relate four different categorical axiomatizations of propositional linear logic appearing in the litterature (Chapter 7)

Generix never gives up

We prove conjugacy and generic disjointness of generous Carter subgroups in groups of finite Morley rank. We elaborate on groups with a generous Carter subgroup and on a minimal conterexample to the Genericity Conjecture.

Do R and D subsidies stimulate or displace private R and D ? Evidence from Israel

Etabli dans le cadre du programme CNRS : 'Les enjeux economiques de l'innovation'.SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : DO 7603 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Building program evaluation into the design of public research support programs

Etabli dans le cadre du programme CNRS : 'Les enjeux economiques de l'innovation'.SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : DO 7601 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc