A Generalization of ACP Using Belnap's Logic

An overview is given of ACP with conditional composition (i.e., if-then-else) over Belnap's four-valued logic. The interesting thing is that much of ACP can be analyzed using this logic. For example, both the choice operation + and δ (deadlock) can be seen as instances of conditional composition, and the axiom x+δ=x follows from this perspective. Furthermore, parallel composition can be generalized to conditional parallel composition, which has sequential composition as an instance, next to common parallel composition, pure interleaving and synchronous ACP.This article is an extended abstract of [A. Ponse, M.B. van der Zwaag. A generalization of ACP using Belnap's logic. Submitted to Journal of Logic and Algebraic Programming]. The full article contains all proofs and some examples on parallel scheduling in GACP.