The paper presents a formal representation for modeling function structure graphs in a consistent, grammatically controlled manner, and for performing conservation-based formal reasoning on those models. The representation consists of a hierarchical vocabulary of entities, relations, and attributes, and 33 local grammar rules that permit or prohibit modeling constructs thereby ensuring model consistency. Internal representational consistency is verified by committing the representation to a Protégé web ontology language (OWL) ontology and examining it with the Pellet consistency checker. External representational validity is established by implementing the representation in a Computer Aided Design (CAD) tool and using it to demonstrate that the grammar rules prohibit inconsistent constructs and that the models support physics-based reasoning based on the balance laws of transport phenomena. This representation, including the controlled grammar, can serve, in the future, as a basis for additional reasoning extensions.

The purpose of this paper is to investigate if early stage function models of design can be used to predict the market-value of a commercial product. In previous research, several metrics of complexity of graph-based product models have been proposed and suitably chosen combinations of these metrics have been shown to predict the time required in assembling commercial products. By extension, this research investigates if this approach, using new sets of combinations of complexity metrics, can predict market-value. To this end, the complexity values of function structures for eighteen products from the Design Repository are determined from their function structure graphs, while their market values are procured from different vendor quotes in the open market. The complexity and value information for fourteen samples are used to train a neural net program to define a predictive mapping scheme. This program is then used to predict the value of the final four products. The results of this approach demonstrate that complexity metrics can be used as inputs to neural networks to establish an accurate mapping from function structure design representations to market values to within the distribution of values for products of similar type.

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This paper validates that a previously published formal representation of function structure graphs actually supports the reasoning that motivated its development in the first place. In doing so, it presents the algorithms to perform those reasoning, provides justification for the reasoning, and presents a software implementation called Concept Modeler (ConMod) to demonstrate the reasoning. Specifically, the representation is shown to support constructing function structure graphs in a grammar-controlled manner so that logical and physics-based inconsistencies are prevented in real-time, thus ensuring logically consistent models. Further, it is demonstrated that the representation can support postmodeling reasoning to check the modeled concepts against two universal principles of physics: the balance laws of mass and energy, and the principle of irreversibility. The representation in question is recently published and its internal ontological and logical consistency has been already demonstrated. However, its ability to support the intended reasoning was not validated so far, which is accomplished in this paper.