Linear Logic and Applications

Games for Linear Logic Andrea Schalk, Cambridge University We draw attention to a number of constructions which lie behind many concrete models for linear logic; we develop an abstract context for these and describe their general theory. Using these constructions we give a model of classical linear logic based on an abstract notion of game. We derive this not from a category with built-in computational content but from the simple category of sets and relations. To demonstrate the computational content of the resulting model we make comparisons at each stage of the construction with a standard very simple notion of game. Our model provides motivation for a less familiar category of games (played on directed graphs) which is closely reflected by our notion of abstract game. We briefly indicate a number of variations on this theme and sketch how the abstract concept of game may be refined further. Proof Search in Multiplicative Linear Logic Bertram Fronhöfer, Institut für Informatik, Technische Universität München In [1] we gave a characterization of theoremhood in terms of the Connection Method for the multiplicative fragments of Affine (Contraction-Free) and Linear Logic. Such matrix characterisations constitute a basis for the adaption of the classical proof search procedures to the just mentioned logics.