Abramsky’s logical formulation of domain theory is extended to encompass the domain theoretic model for picalculus processes of Stark and of Fiore, Moggi and Sangiorgi. This is done by defining a logical counterpart of categorical constructions including dynamic name allocation and name exponentiation, and showing that they are dual to standard constructs in functor categories. We show that initial algebras of functors defined in terms of these constructs give rise to a logic that is sound, complete, and characterises bisimilarity. The approach is modular, and we apply it to derive a logical formulation of pi-calculus. The resulting logic is a modal calculus with primitives for input, free output and bound output.
M. Bonsangue and A. Kurz, “Pi-Calculus in Logical Form,” in 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007), Wroclaw, Poland, 2007, pp. 303–312.