Relating Reasoning Methodologies in Linear Logic and Process Algebra

We show that the proof-theoretic notion of logical preorder coincides with the process-theoretic notion of contextual preorder for a CCS-like process calculus obtained from the formula-as-process interpretation of a fragment of linear logic. The argument makes use of other standard notions in process algebra, namely simulation and labeled transition systems. This result establishes a connection between an approach to reason about process specifications, the contextual preorder, and a method to reason about logic specifications, the logical preorder. Support for this research was provided by the Qatar National Research Fund under NPRP grant 09-1107-1-168, by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the Carnegie Mellon Portugal Program under Grant NGN-44, and by an X10 Innovation Award from IBM. Yuxin Deng would also like to acknowledge the support of the Natural Science Foundation of China under grant 61173033 held by Shanghai Jiao Tong University.