On the Algebra of Structural Contexts

Article dans revue scientifique avec comité de lecture.We discuss a general way of defining contexts in linear logic, based on the observation that linear universal algebra can be symmetrized by assigning an additional variable to represent the output of a term. We give two approaches to this, a syntactical one based on a new, reversible notion of term, and an algebraic one based on a simple generalization of typed operads. We relate these to each other and to known examples of logical systems, and show new examples, in particular discussing the relationship between intuitionistic and classical systems. We then present a general framework for extracting deductive system from a given theory of contexts, and prove that all these systems have cut-elimination by the means of a generic argument

Multiplicative Linear Logics and Fibrations

Colloque avec actes et comité de lecture. internationale.International audiencewe define a notion of fibration on generalized operads that automatically gives the categorical axiomatizion of a large class of multiplicative deductive systems we described in a previous paper. We illustrate it by showing examples taken from previously descirbed logics. Also we show interesting properties of the ctegory of structas, including the fact that it contains many well-known categories as subcategories, including the category of categories