As described in Table 1, definitional knowledge refers to knowledge
gained by defining ideas or concepts such that their definitions are not
uncontroversial or readily accepted by stakeholders. For definitional
knowledge, Kclm = Kprv andKinf = ∅. Since such pieces of knowledge
correspond to mere definitions of ideas, they are always true
(tautology). From an epistemological sense, such knowledge qualifies as
analytic a priori knowledge, as described in Section 2. This type of
knowledge can be further explained using examples discussed in the
section 4.
Deductive knowledge implies knowledge gained by establishing
relationships among definitional knowledge with the aid of a logical
process called deduction. Mathematically,
\(Deduction:\ \left(A\rightarrow B\right)\land\left(A\right)\vdash B,\ \ \left(\left(A\rightarrow B\right)\land\left(B\rightarrow C\right)\right)\vdash\left(A\rightarrow C\right)\)(2)
In the above equation, A , B , and C are, by
definition, true entities; that is, they qualify as definitional
knowledge.
Thus, from the viewpoint of deductive knowledge,Kclm ≠ Kprv ,Kinf = Deduction , andKprv represent pieces of definitional knowledge.
From an epistemological sense, deductive knowledge refers to synthetic a
priori knowledge or relations of ideas, as described in section 2. There
exist two categories of deductive knowledge—(a ) primary
relation of ideas and (b ) secondary relation of ideas—as
exemplified in section 4.
Inductive knowledge refers to knowledge gained by experiencing the world
with the aid of a logical process called induction. Mathematically,
\(Induction:\ \left(O_{1},\ldots,O_{n}\right)\vdash\left(A\rightarrow B\right)\)(3)
In the above expression,O 1,…,On refer to
finite observations, experimental results, experiences, and data.
Entities A and B are consistent with objects related toO 1,…,On . Thus, from
the viewpoint of inductive knowledge, Kclm ≠Kprv , Kinf =Induction , and Kprv correspond to pieces
of data and/or observations; that is,O 1,…,On , as
described above. Based on the nature of induction, inductive knowledge
can be classified into three main categories—(a )
informal-induction-based knowledge; (b )
relation-of-ideas-assisted inductive knowledge; and (c )
complex-induction-based knowledge. These categories have also been
exemplified in section 4.
Formulation of creative knowledge is caused by creative activities or
pragmatic preferences. In this case, there exists no formal provenance;
i.e., Kprv = ∅, and the logical process involved
most likely corresponds to abduction; that is,Kinf = Abduction (e.g., introducing
plausible causes (A 1, A 2,…) for achieving a
given effect (B ).
\(Abduction:\ \left(Unknow\ A\rightarrow B\right)\land\left(B\right)\vdash
Plausable\ A1,\ A2,\ldots\)(4)
It is remarkable that the truthiness of A 1, A 2,… is
neither true nor false until a new piece of deductive or inductive
knowledge is available. The truthiness may refer to Kantian categories
of judgment, as described in section 2. Creative knowledge can be
categorized into three types—(a ) analytic a-priori-based;
(b ) synthetic a-priori-based; and (c ) synthetic a
posteriori-based—as exemplified in section 4.
Knowledge types and their categories, except definitional knowledge,
cannot exist independently. As a result, knowledge chains form. A
knowledge chain manifests itself a concept map or network, or a set of
concept maps or networks. In other words, when a concept map or network
is studied, its contents boil down to definitional, deductive,
inductive, and/or creative knowledge. Consequently, while constructing
concept maps for use in desired purposes (e.g., human learning or
learning in human–cyber-physical systems), their contents can be
organized and analyzed in terms of knowledge types and categories
presented above.
4. Exemplifications
This section presents examples that describe the types and categories of
knowledge presented in Section 3. Most of the examples are relevant to
arbitrary scenarios underlying engineering design and manufacturing. In
all examples, a knowledge graph (concept map) represents knowledge claim
(Kclm ), and in some cases, the concept maps
directly point to relevant knowledge provenance
(Kprv ). In other cases,Kprv is either shown partially or not shown at
all. Knowledge inference (Kinf ) refers to an
equation out of equations (2)–(4), as appropriate, and it is not
explicitly shown in respective concept maps.
4.1. Definitional Knowledge
As already mentioned, definitional knowledge is created by
uncontroversial definitions of ideas or concepts, and it does not rely
on formal inference per se. At the same time, knowledge provenance
cannot be separated from knowledge claim. For example, consider an
illustration of turning (a widely used manufacturing process) and the
corresponding concept map depicted in Figures 1(a ) and
1(b ), respectively. The concept map captures a portion of the
knowledge underlying the scenario. It boils down to the following
statements—(1) Force acting along the cutting direction is called
cutting force; (2) Cutting speed refers to the speed at which the
workpiece makes contact with the cutting tool while turning; (3) Turning
is a manufacturing process that removes materials from a workpiece via
chip formation; and (4) If the cutting force equals zero, no chip
formation occurs. Since these statements define the concepts of cutting
speed and cutting force during the material-removal process called
turning, they can only be considered pieces of definitional knowledge.
Thus, the above statements can be considered knowledge claim and
provenance simultaneously. Without these definitions, other types or
categories of knowledge underlying turning (described below) do not make
sense.