We describe a logical calculus for process synthesis applying reaction rules for consuming, transforming and producing products at costs. Unlike common logical calculi, which deal with propositions supported by truth semantics, the process synthesis calculus deals with products (in a concrete or abstract sense) and their costs, and creation of products by the composing of appropriate reaction assemblies from a database of reactions or transactions. As such the calculus may be understood as a resource logic akin to linear logics. The calculus appeals to means-end backwards reasoning using a derivative of definite clause logic. Although rather general in scope, as an interesting case in this paper the calculus is applied to chemical retro-synthesis – in particular with the notoriously difficult Solvay cluster designs.