As already described, deductive knowledge comes into being owing to the
inference called deduction (equation (2)), wherein knowledge claim and
knowledge provenance need not be identical. Instead, knowledge
provenance herein refers to pieces of definitional knowledge. There
exist two categories of deductive knowledge—primary relation of ideas
and secondary relation of ideas. For example, consider the concept map
depicted in Figures 2 that underlies the scenario described in Figure
1(a ). The concept map boils down to following statements—(1)
The manufacturing process called turning entails cutting power
(Pc ), material-removal rate (MRR ), and
specific cutting energy (Kc ); (2) Cutting power
(Pc ) can be expressed as \(P_{c}=F_{c}v_{c}\);
(3) Material-removal rate (MRR ) is given by\(\text{MRR}=a_{p}\text{fv}_{c}\); (4) Specific cutting energy
(Kc ) is given by\(K_{c}=\frac{P_{c}}{\text{MRR}}\); and (5)\(P_{c}=F_{c}v_{c}\),\(\text{MRR}=a_{p}\text{fv}_{c}\), and\(K_{c}=\frac{P_{c}}{\text{MRR}}\) yield\(K_{c}=\frac{F_{c}}{\left(a_{p}f\right)}\). The first statement
does not qualify as a piece of deductive knowledge; it is rather a piece
of informal-induction-based knowledge, as described in the next
subsection. Statements (2), (3), and (4) are examples of primary
relation of ideas, whereas the last statement exemplifies secondary
relation of ideas, because it has been derived from statements (2), (3),
and (4) using deduction.
Statement (2) entails three pieces of definitional knowledge—cutting
power, cutting force, and cutting speed—thereby collectively referring
to knowledge provenance. That is, “when force is multiplied by speed,
it yields power.” This provenance as well as the definitional knowledge
pertaining to the cutting force and cutting speed are not explicitly
described in the concept map (Figure 2). Figure 1(b ), on the
other hand, explicitly describes the definitional knowledge. Therefore,
knowledge can be made more meaningful from a user’s point of view by
integrating the concept maps depicted in Figures 1(b ) and 2 with
abovementioned provenance. Statement 3 entails four pieces of
definitional knowledge—material-removal rate, depth of cut, feed rate,
and cutting speed—which collectively refer to the provenance that
“material removal rate refers to the volume of material removed in unit
time.” Once again, this provenance and associated definitional
knowledge (depth of cut, feed rate, and cutting speed) are not
explicitly described in the concept map (Figure 2). Figure 1(b ),
on the other hand, depicts a portion of the relevant definitional
knowledge (cutting speed). Thus, by adding definitions of the depth of
cut and feed rate to the concept map depicted in Figure 1(b ) and
subsequently integrating it with the concept map depicted in Figure 2
and abovementioned provenance would make knowledge representation more
meaningful. A similar argument is true for statement 4.