Propositional Dynamic Logics for Communicating Concurrent Programs with CCS’s Parallel Operator ∗ Mario R. F. Benevides † L. Menasch´ e Schechter ‡ December 18, 2013 Abstract This work presents three increasingly expressive Dynamic Logics in which the programs are described in a language based on CCS. Our goal is to build dynamic logics that are suitable for the description and verification of prop- erties of communicating concurrent systems, in a similar way as PDL is used for the sequential case. In order to accomplish that, CCS’s operators and constructions are added to a basic modal logic. Doing this, the semantics of CCS’s parallel operator allows us to build dynamic logics that support communicating and concurrent programs. We build a simple Kripke seman- tics for these logics, provide complete axiomatizations for them and show that they have the finite model property. This contrasts with other dynamic logics with parallel operators presented in the literature, such as Peleg’s Concurrent PDL with Channels, where either the parallel programs cannot communicate, or at least one of the properties mentioned above (simple Kripke semantics, complete axiomatization and finite model property) is missing. Keywords: Dynamic Logic, Concurrency, Kripke Semantics, Axiomatization, Completeness 1 Introduction Propositional Dynamic Logic (PDL) [7] plays an important role in formal specifica- tion and reasoning about sequential programs and systems. PDL is a multi-modal logic with one modality 〈π〉 for each program π. The logic has a set of basic pro- grams and a set of operators (sequential composition, iteration and nondeterminis- tic choice) that are used to inductively build the set of non-basic programs. PDL has been used to describe and verify properties and behavior of sequential programs and systems. A Kripke semantics can be provided, with a frame F =(W, {R π } π∈Π ), where W is a non-empty set of possible program states and, for each program π ∈ Π, R π is a binary relation on W such that (s,t) ∈ R π if and only if there is a computation of π starting in s and terminating in t. * This work was supported by the Brazilian research agencies CNPq, CAPES and FAPERJ. † Department of Computer Science and Systems and Computer Engineering Program, Federal University of Rio de Janeiro, Brazil. E-mail: mario@cos.ufrj.br. ‡ Department of Computer Science, Federal University of Rio de Janeiro, Brazil. E-mail: luisms@dcc.ufrj.br. Corresponding author. 1