On the semantics of Strategy Logic

With the proliferation of computerised devices, software verification is more prevalent than ever. Since the 80's, multiple costly software failures have forced both private and public actors to invest in software verification. Among the main procedures we find the model-checking, developed by Clarke and Emerson in the 80's. It consists in abstracting both the system into a formal model and the property of expected behaviour in some logical formalism, then checking if the property's abstraction holds on the system's abstraction. The difficulty lies in finding appropriate models and efficient algorithms. In this thesis, we focus on one particular logical formalism: the Strategy Logic SL, used to express multi-objectives properties of multi-agents systems. Strategy Logic is a powerful and expressive formalism that treats strategies (i.e. potential behaviours of the agents) like first-order objects. It can be seen as an analogue to first-order logic for multi-agents systems. Many semantic choices were made in its definition without much discussion. Our main contributions are relative to the possibilities left behind by the original definition. We first introduce SL and present some complexity results (including some of our owns). We then outline some other semantic choices within SL's definition and study their influence. Third, we study the logic's behaviour under quantitative multi-agents systems (games with energy and counter constraints). Finally, we address the problem of dependencies within SL[BG], a fragment of SL.