In engineering design, the end goal is the creation of an artifact, product, system, or process that fulfills some functional requirements at some desired level of performance. As such, knowledge of functionality is essential in a wide variety of tasks in engineering activities, including modeling, generation, modification, visualization, explanation, evaluation, diagnosis, and repair of these artifacts and processes. A formal representation of functionality is essential for supporting any of these activities on computers. The goal of Parts 1 and 2 of this Special Issue is to bring together the state of knowledge of representing functionality in engineering applications from both the engineering and the artificial intelligence (AI) research communities.

This paper is an informal description of some recent insights about what a device function is, how it arises in response to needs, and how function arises from the structure of a device and the functions of its components. These results formalize and clarify a set of contending intuitions about function that researchers have had. The paper relates the approaches, results, and goals of this stream of research, called functional representation (FR), with the functional modeling (FM) stream in engineering. Despite the occurrence of the term function in the two streams, often the results and techniques in the two streams appear not to have much to do with each other. I argue that, in fact, the two streams are performing research that is mutually complementary. FR research provides the basic layer for device ontology in a formal framework that helps to clarify the meanings of terms such as function and structure, and also to support representation of device knowledge for automated reasoning. FM research provides another layer in device ontology, by attempting to identify behavior primitives that are applicable to subsets of devices, with the hope that functions can be described in those domains with an economy of terms. This can lead to useful catalogs of functions and devices in specific areas of engineering. With increased attention to formalization, the work in FM can provide domain-specific terms for FR research in knowledge representation and automated reasoning.

Functional reasoning (FR) enables people to derive and explain function of artifacts in a goal-oriented manner. FR has been studied and employed in various disciplines, including philosophy, biology, sociology, and engineering design, and enhanced by the techniques borrowed from computer science and artificial intelligence. The outcome of FR research has been applied to engineering design, planning, explanation, and learning. A typical FR system in engineering design usually incorporates representational mechanisms of function concept together with description mechanisms of state, structure, or behavior, and explanations and reasoning mechanisms to derive and explain functions. As for representation, philosophers have long argued whether function of an artifact is a genuine property of it. As for explanation and reasoning, they have produced theories for functional ascription by an external viewer as part of an explanation. To build an FR-based system, the theory based on which the system is built and the underlying assumptions must be explicitly identified. This point is not always clear in the engineering of FR-based systems. Understanding the underlying assumptions, logical formulation, and limitations of FR theories will help developers assessing their systems correctly. The purpose of this paper is to review various FR theories and their underlying assumptions and limitations. This later serves as a benchmark for comparing various FR techniques.

The need to model and to reason about design alternatives throughout the design process demands robust representation schemes of function, behavior, and structure. Function describes the physical effect imposed on an energy or material flow by a design entity without regard for the working principles or physical solutions used to accomplish this effect. Behaviors are the physical events associated with a physical artifact (or hypothesized concept) over time (or simulated time) as perceived by an observer. Structure, the most tangible concept, partitions an artifact into meaningful constituents such as features, Wirk elements, and interfaces in addition to the widely used assemblies and components. The focus of this work is on defining a model for function-based representations that can be used across various design methodologies and for a variety of design tasks throughout all stages of the design process. In particular, the mapping between function and structure is explored and, to a lesser extent, its impact on behavior is noted. Clearly, the issues of a function-based representation's composition and mappings directly impact certain computational synthesis methods that rely on (digitally) archived product design knowledge. Moreover, functions have already been related to not only form, but also information of user actions, performance parameters in the form of equations, and failure mode data. It is essential to understand the composition and mappings of functions and their relation to design activities because this information is part of the foundation for function-based methods, and consequently dictates the performance of those methods. Toward this end, the important findings of this work include a formalism for two aspects of function-based representations (composition and mappings), the supported design activities of the model for function-based representations, and examples of how computational design methods benefit from this formalism.

Inspiration is useful for exploration and discovery of new solution spaces. Systems in natural and artificial worlds and their functionality are seen as rich sources of inspiration for idea generation. However, unlike in the artificial domain where existing systems are often used for inspiration, those from the natural domain are rarely used in a systematic way for this purpose. Analogy is long regarded as a powerful means for inspiring novel idea generation. One aim of the work reported here is to initiate similar work in the area of systematic biomimetics for product development, so that inspiration from both natural and artificial worlds can be used systematically to help develop novel, analogical ideas for solving design problems. A generic model for representing causality of natural and artificial systems has been developed, and used to structure information in a database of systems from both the domains. These are implemented in a piece of software for automated analogical search of relevant ideas from the databases to solve a given problem. Preliminary experiments at validating the software indicate substantial potential for the approach.