Designs, Disputes and Strategies

Important progresses in logic are leading to interactive and dynamical models. Geometry of Interaction and Games Semantics are two major examples. Ludics, initiated by Girard, is a further step in this direction. The objects of Ludics which correspond to proofs are designs. A design can be described as the skeleton of a sequent calculus derivation, where we do not manipulate formulas, but their location (the address where the formula is stored). To study the traces of the interactions between designs as primitive leads to an alternative presentation, which is to describe a design as the set of its possible interactions, called disputes. This presentation has the advantage to make precise the correspondence between the basic notions of Ludics (designs, disputes and chronicles) and the basic notions of Games semantics (strategies, plays and views).