This paper presents the Logical Process Calculus (LPC), a formalism that supports heterogeneous system specifications containing both operational and declarative subspecifications. Syntactically, LPC extends Milner's Calculus of Communicating Systems with operators from the alternation-free linear-time μ-calculus (LTμ). Semantically, LPC is equipped with a behavioral preorder that generalizes Hennessy's and De Nicola's must-testing preorder as well as LTμ's satisfaction relation, while being compositional for all LPC operators. From a technical point of view, the new calculus is distinguished by the inclusion of (i) both minimal and maximal fixed-point operators and (ii) an unimplementability predicate on process terms which tags inconsistent specifications. The utility of LPC is demonstrated by means of an example highlighting the benefits of heterogeneous system specification.