Showing papers by "Jean-Yves Girard published in 1996"

TL;DR: A denotational semantics based on Banach spaces is presented, inspired from the familiar coherent semantics of linear logic, the role of coherence being played by the norm: coherence is rendered by a supremum, whereas incoherence isrendered by a sum, and cliques are rendered by vectors of norm at most 1.

TL;DR: All logical rules are now defined only on the main formulas of rules, as operations on ℙ-cliques, and soundness and completeness are then easily established for closed π1-formulas, i.e. second-order propositional formulas without existential quantifiers.