First order in Ludics

Authors:
Marie-Renee Fleury;Myriam Quatrini
Affiliations:
Institut de Mathématiques de Luminy, UPR 9016 C.N.R.S., Université de la Méditerranée, 163, avenue de Luminy – Case 907, 13288 Marseille Cedex 9 – France Email: mrd ...;Institut de Mathématiques de Luminy, UPR 9016 C.N.R.S., Université de la Méditerranée, 163, avenue de Luminy – Case 907, 13288 Marseille Cedex 9 – France Email: qua ...
Venue:
Mathematical Structures in Computer Science
Year:
2004

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Abstract

In Girard (2001), J.-Y. Girard presents a new theory, The Ludics, which is a model of realisibility of logic that associates proofs with designs, and formulas with behaviours. In this article we study the interpretation in this semantics of formulas with first-order quantifications and their proofs. We extend to the first-order quantifiers the full completeness theorem obtained in Girard (2001) for $MALL_2$. A significant part of this article is devoted to the study of a uniformity property for the families of designs that represent proofs of formulas depending on a first-order free variable.