Towards Parametric Causal Semantics in pi-calculus

In a concurrent setting, causally-consistent reversibility relates causality and reversibility. In this note we overview three causal semantics for π-calculus: two classical and a recent one used for a reversible variant of π-calculus. We show the differences between them via examples, and discuss how to revise the classical one in order to be used as the underlying machinery for a reversible calculus. We propose a reinterpretation of such notions in particular when it comes to silent actions and names extrusion. Our ultimate goal is to devise a general reversible framework parametric into the underlying notion of causality.