260
and in particular an intensional definition,
1
which is “preferable to other types of
definitions and should be used whenever possible as [it] most clearly reveal[s] the
characteristics of a concept within a concept system” (ISO, 2009: 6.2). This
Appendix proposes a basic concept system of measurement with weaker terminological constraints, which allows us to provide for each relevant concept a term and
a characterization, sometimes in the form of explanation rather than a definition,
2
thus summarizing what is presented and discussed in the book.
As is common in top-level/upper ontologies, we use the term “entity” to refer to
the most generic concept, hence as a synonym of “object” in the sense of ISO
1087-1:2000: 3.1.1: “anything perceivable or conceivable”, so as to make it possible
to use “object” for any entity that carries a property (hence in this sense properties
are entities but are not objects). Together with “entity”, many other non-measurement-specific terms are used here with their usual meaning.
1 A structural strategy for building a concept system is top-down: some generic concepts are
assumed without a definition—called “primitive concepts” or simply “primitives”—and other concepts are subsequently derived from them according to a conjunctive logic:
X Y
Y n
:=
…
1 and
and
where the set {Y i } of the defining concepts is called the intension of the defined concept X. For
example, the VIM definition of, “process of experimentally obtaining one or more
values that can reasonably be attributed to a quantity” (JCGM, 2012: 2.1), can be understood as a
rephrasing of the following: measurement (X) is a process (Y 1 ) and (the process) is an experimental
obtainment of values (Y 2 ) and is a reasonable attribution of (these) values to a quantity (Y 3 ), i.e., X
≔ Y 1 and Y 2 and Y 3 . Evidently, for such a definition to be well formulated the defining concepts
(, , ) must have been previously defined. In a concept system built according to this top-down
strategy, definitions are means of specification: through definitions the system is built by progressive knowledge specification, where the relation between the defined concept X and each of the
defining concepts Y i is then species-genus, or, according to the ISO standards on terminology
work, subordinate-superordinate (hence in the definition mentioned above is a
species/subordinate of the genus/superordinate: measurement is a (species of/kind of)
process). In an intensional definition (ISO, 2000: 3.3.2), one defining concept Y 1 is singled out as
the superordinate, with the remaining Y 2 , …, Y n being its delimiting characteristics (ISO, 2000:
3.2.7). This leads to the template
defined concept superordinate concept
d elimiting
such that
:=
c characteristics
that can be read as
X
Y
Y
Y n
is a
such that
and
and
1
2
⊃
so that, for example, a measurement (X) is a process (Y 1 ) such that it is an experimental obtainment of values (Y 2 ) and is a reasonable attribution of these values to a quantity (Y 3 ).
2 In particular, the explanations in this concept system allow some circularities; that is, the explanation of the concept X includes a reference to the concept Y, and the explanation of Y includes a
reference to X. The substitution principle forbids this in a definition (ISO, 2009: 6.3.4). In other
words, these explanations include both a (n informal) definition and some possible notes.
Appendix A: A basic concept system of measurement
and in particular an intensional definition,
1
which is “preferable to other types of
definitions and should be used whenever possible as [it] most clearly reveal[s] the
characteristics of a concept within a concept system” (ISO, 2009: 6.2). This
Appendix proposes a basic concept system of measurement with weaker terminological constraints, which allows us to provide for each relevant concept a term and
a characterization, sometimes in the form of explanation rather than a definition,
2
thus summarizing what is presented and discussed in the book.
As is common in top-level/upper ontologies, we use the term “entity” to refer to
the most generic concept, hence as a synonym of “object” in the sense of ISO
1087-1:2000: 3.1.1: “anything perceivable or conceivable”, so as to make it possible
to use “object” for any entity that carries a property (hence in this sense properties
are entities but are not objects). Together with “entity”, many other non-measurement-specific terms are used here with their usual meaning.
1 A structural strategy for building a concept system is top-down: some generic concepts are
assumed without a definition—called “primitive concepts” or simply “primitives”—and other concepts are subsequently derived from them according to a conjunctive logic:
X Y
Y n
:=
…
1 and
and
where the set {Y i } of the defining concepts is called the intension of the defined concept X. For
example, the VIM definition of
values that can reasonably be attributed to a quantity” (JCGM, 2012: 2.1), can be understood as a
rephrasing of the following: measurement (X) is a process (Y 1 ) and (the process) is an experimental
obtainment of values (Y 2 ) and is a reasonable attribution of (these) values to a quantity (Y 3 ), i.e., X
≔ Y 1 and Y 2 and Y 3 . Evidently, for such a definition to be well formulated the defining concepts
(
strategy, definitions are means of specification: through definitions the system is built by progressive knowledge specification, where the relation between the defined concept X and each of the
defining concepts Y i is then species-genus, or, according to the ISO standards on terminology
work, subordinate-superordinate (hence in the definition mentioned above
species/subordinate of the genus/superordinate
process). In an intensional definition (ISO, 2000: 3.3.2), one defining concept Y 1 is singled out as
the superordinate, with the remaining Y 2 , …, Y n being its delimiting characteristics (ISO, 2000:
3.2.7). This leads to the template
defined concept superordinate concept
d elimiting
such that
:=
c characteristics
that can be read as
X
Y
Y
Y n
is a
such that
and
and
1
2
⊃
so that, for example, a measurement (X) is a process (Y 1 ) such that it is an experimental obtainment of values (Y 2 ) and is a reasonable attribution of these values to a quantity (Y 3 ).
2 In particular, the explanations in this concept system allow some circularities; that is, the explanation of the concept X includes a reference to the concept Y, and the explanation of Y includes a
reference to X. The substitution principle forbids this in a definition (ISO, 2009: 6.3.4). In other
words, these explanations include both a (n informal) definition and some possible notes.
Appendix A: A basic concept system of measurement