Separation Logic is used as an assertion language for Hoare-style proof systems about programs with pointers, and there is an ongoing quest for understanding its complexity and expressive power. Alternatively, there are a lot of activities to develop verification methods with decision procedures for fragments of practical use.

Actually, there exist many versions or fragments of Separation Logic that can be viewed as fragments of Second-Order Logic, as well as variants of Modal or Temporal Logics in which models can be updated dynamically (as in Public Announcement Logic).

In this talk, after introducing first principles on Separation Logic, issues related to decidability, computational complexity and expressive power are discussed. We provide several tight relationships with Second-Order Logic, Interval Temporal Logic or Data Logics, depending on the variants of the logic and on the syntactic resources available.

Results presented during the talk span from standard ones about Separation Logic to more recent ones, some of them obtained in collaboration with Dr. Morgan Deters (NYU, CIMS).