There is a difference of opinion in the research community regarding the meaning function and behavior; no standardized, consistent model of these terms exists. Some researchers consider function as a description of the actions a product can perform (e.g. [25]), while others treat it as a description of a subset of behaviors (i.e. intended behavior or ``purpose'', as in [31]). Various other definitions are given in [9,8].
The current author defines behavior as the response of a system to predefined inputs which are not necessarily quantified; it describes the role played by a product in a larger system. The behavioral perspective takes the product being designed to be a ``black box'' whose internal function is not visible (or even known); the inputs, outputs, and operational environment of the product, on the other hand, are ``transparent'' (see Figure 3.2b). Insofar as behavior describes the response of a product, it is seen as answering the question ``What does the product do?'' Behavior is described without commitment to the form of the product.
Function, on the other hand, is a description of how a product works rather than what it does (Figure 3.2a), where the environment is now opaque, and the product is ``transparent,'' and is composed of a series of black box subsystems whose interaction describes how the product comes to exhibit a certain behavior, but without necessarily making commitments about product form.
These perspectives are meant to demark the different kinds of tasks that can be performed with functional/behavioral information. At the behavioral level, design is systems-based, concerned with identifying functional requirements to be met by a product. At the functional level, on the other hand, design consists of a configuring components and their interrelationships. So-called ``top-down'' design proceeds by alternating between behavioral and functional perspectives at ever increasing levels of details. Identifying these perspectives is used below to demonstrate that behavioral and functional descriptions are essentially the same; they are just viewed in different contexts.
It is noted here that the definitions of function and behavior adopted by the other are the opposite of those commonly used in the literature. While the need for terminological consistency is aknowledged, the author believes his definitions are more in keeping with those conventionally implied by practicing engineers. In any event, it matters little in the long run since the distinction between function and behavior is shown (below) to be an artificial one only.
In order to explore this matter further, consider the following three statements:
Any of these statements in isolation can be considered a behavior of a refrigerator. If statement 1 is considered a behavior, then we may ask How is this behavior achieved? The answer involves the functions of a refrigerator (isolating a region of space, transferring heat from that space by some means, etc.). However, we may also ask Why does the refrigerator keep food cold? One answer to this question is statement 3. Now, considering statements 1 and 3 together, statement 1 is a function rather than a behavior. Thus ,whether the statements are taken as functional or behavioral, context plays a crucial role in (a) providing terminological information about the words appearing in the statements, and (b) implying information about the operating environment. For example, in statement 1, the terms ``cold'' and ``keeps'' are relative to the context of refrigerators.
Function and behavior are thus relative to the reference frame of an agent making assertions about a product; that is, they are not intrinsic properties of designed products. Nonetheless, functional and behavioral information about a product is very important, especially during the product's design. Therefore it is essential that it be representable in the author's system.
It is often possible to represent both functions and behaviors in single natural language clauses that seem quite intuitive to humans (e.g. ``...to support a load in bending....''); both behavior (``to support a load'') and function (``in bending'') are intimately connected in a single phrase. The fact that both the behavior and function can be described in a single natural language statement only obscures their distinction. This constitutes, in the author's opinion, a significant problem with the use of natural language, or any other informal language, to precisely define the nature of designed products. Natural language is used herein only for expository purposes; the author intends this research to lead eventually to a more formal specification of functional/behavioral information.
In order to avoid this confusion while maintaining a sense of connection between them, the author uses the term predicative description to include both function and behavior descriptions. This term captures the sense of activity, as well as the complexity of the concepts.
The basic relation that connects function and behavior is the ``how/why'' relation: given a function, the why relation describes its behavior; and given a behavior, the how relation describes the function that results in it. The how/why relations are disjoint and intransitive with other relations, particularly with respect specialization. In figure 2 four predicative statements about a refrigerator are given, and both the how/why and specialization/generalization relations are shown. It may be argued that the why relation is a kind of generalization: in comparing statements 1 and 3 in the figure, it is sensible to think of ``preserving food'' as a generalization of ``keeping food cold''. But this is a generalization based on the intent the statement as a whole, rather than one associated with the components of the statements. A similar argument can be made about the specialization and how relations. The key differences between function and behavior in the author's work can be summarized as in the table in Table 1.
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Predicative descriptions are complex in that their expression tends to be formed as predicate clauses consisting of verb/object pairs (VOPs). That is, they describe actions performed by an entity upon some other entity, independent of the phrasing in natural language.
This apparent verb/object structure of both functions and behaviors has been used as the root of various formalizations, such as in [32]; the current author also employs this approach. Consider again the statements in Figure 2: statements 1 and 3 are related through how/why relations. Statement 2 is related to statement 1 by generalization on the object of the VOP. A similar generalization carried out on statement 2 (yielding statement 4) is virtually meaningless. The author believes that generalizations will not generally transfer through how/why relations; in other words, abstraction relations and predicative relations are not transitive. Also, that the abstraction occurred only on the object part of the VOP suggests that in the general case, abstraction can occur on either the verb or the object parts independently.
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The key to abstraction of predicative relations is the verb part of the VOPs. But since a VOP can be both a functional and a behavioral description (depending on the context), any generalization rules for the verb parts of VOPs must be based on the definition of the verb term itself rather than on its functional or behavioral connotations.
Finally, these definitions of function and behavior deal only with the reactions expected of products for given sets of inputs; that is, no notion of intended, or designed-in, function or behavior, or of purpose is implied.
