The flexible and efficient support of the process of product design and production requires combined expertise from many aspects of the product life-cycle, and the management and use of this knowledge in turn increasingly requires sophisticated computer-based advice systems. In this chapter we present a constraint-based approach to making the full First-Order Predicate Calculus available for knowledge representation purposes in intelligent networked colocation advice systems for concurrent engineering. Domain knowledge is represented as a theory written in a first-order logical language. The set of models of the language under which the theory is satisfied is the set of solutions of a constraint network. Solutions to the network are computed by a hierarchical and opportunistic constraint inference method. Galileo4, an implemented language and companion run-time system based on these ideas is discussed and its efficacy is demonstrated by presenting applications in which high problem-solving versatility is provided by concise and readable programs.