In this talk, we introduce a new game semantics framework for concurrency based on event structures, extending the work of Rideau and Winskel. In this framework, we can extend the notions of innocence and well-bracketing to the concurrent (and non-deterministic) case, generalizing the so-called “Abramsky cube”.

This talk focuses on the deterministic case. I will first introduce the concurrent strategies and their composition, in the existing linear setting. I will then present our extension to nonlinearity using copy indices and symmetry to represent uniformity. I will then present our notions of concurrent innocence & well-bracketing, to finish on our result of intensional full abstraction for PCF. Time permitting, I will discuss extensions of this result to non-angelic nondeterminism and probabilities.