A generalization of ACP using Belnap’s logic

ACP is combined with Belnap’s four-valued logic via conditional composition (if–then–else). We show that the operators of ACP can be seen as instances of more general, conditional operators. For example, both the choice operator + and δ (deadlock) can be seen as instances of conditional composition, and the axiom x + δ = x follows from this perspective. Parallel composition is generalized to the binary conditional merge ϕ∥ψ where ϕ covers the choice between interleaving and synchronization, and ψ determines the order of execution. The instance B∥B is ACP’s parallel composition, where B (both) is the truth value that models both true and false in Belnap’s logic. Other instances of this conditional merge are sequential composition, pure interleaving and synchronous merge. We investigate the expression of scheduling strategies in the conditions of the conditional merge.