=Paper=
{{Paper
|id=None
|storemode=property
|title=Local Qualities, Quality Fields, and Quality Patterns: A Preliminary Investigation
|pdfUrl=https://ceur-ws.org/Vol-1007/paper5.pdf
|volume=Vol-1007
|dblpUrl=https://dblp.org/rec/conf/shapes/Guarino13
}}
==Local Qualities, Quality Fields, and Quality Patterns: A Preliminary Investigation==
https://ceur-ws.org/Vol-1007/paper5.pdf
Local Qualities, Quality Fields, and Quality
Patterns: A Preliminary Investigation
Nicola GUARINO
ISTC-CNR Laboratory for Applied Ontology, Trento
Abstract
Abstract. When we describe the shape of certain entities, like a vase or a river, we refer to their qualities in
different ways. A river has usually a definite length, but its width varies with the distance from the source,
typically getting higher towards the end. Similarly, a vase has a definite height, but its width may vary,
reflecting a certain pattern that often marks a particular style. So, at least for certain entities, quality kinds
such as length, height and width don’t behave in the same way: length or height just inhere to these objects
with no need of further qualification, while width requires a spatial localization in order to be determined.
In this paper I would like to explore the way qualities of things behave with respect to the parts of such
things. Building on the notion of individual quality introduced in the DOLCE ontology, I will introduce the
new notions of local quality, quality field and quality pattern, stressing their cognitive role in many practical
situations. I will argue that an expression like “the river’s width” or “the depth of the sea” actually refers to a
quality field, and not to an individual quality. Quality fields will be used to introduce the further notion of
quality pattern, and to analyze the distinction between variation and change.
Keywords. Ontology, quality, local quality, global quality, property, field, pattern
1. Introduction
When we describe the shape of certain entities, like a vase or a river, we refer to their
qualities in different ways. A river has (more or less) a definite length, but its width
varies with the distance from the source, typically getting higher towards the end.
Similarly, a vase has a definite height, but its width may vary, reflecting a certain
pattern that often marks a particular style. So, at least for certain entities, quality kinds
such as length, height and width don’t behave in the same way: length or height just
inhere to these objects with no need of further qualification, while width requires a
spatial localization in order to be determined.
We shall say that length and height, in these examples, behave as global qualities,
while width behaves as a local quality. A local quality of a certain object is a quality
which actually inheres to a part of that object, but, despite this fact, is somehow
considered, from the cognitive point of view, as a quality of the whole object: so, we
rarely say “the width of this river stretch is 100 meters”, but we prefer to say “the
river’s width is 100 meters here”. Analogously, we say “the depth of the Adriatic Sea
is much higher along the Croatian coast than along the Italian coast”, referring to “the
river’s width” or “the sea’s depth” as one single entity, although, so to speak, spread
out in space. Indeed, in many simple cases, we describe the qualitative shape of a
certain object in terms of the behavior of a local spatial quality along a certain
dimension.
Of course, the distinction between global and local qualities is very general, and
goes much beyond purely spatial qualities: consider for instance the mass or volume of
a physical object vs. its density or its temperature, or the duration of a rain vs. its
intensity. In all these cases, we observe different ways qualities of things behave with
respect to the parts of such things. The main purpose of this paper is to explore this
phenomenon, which I will call mereological behavior of qualities (or, more in general,
of properties, as we shall see), providing a formal account of local qualities and
analyzing its practical implications.
75
2. Inclusive and exclusive properties
Looking at the philosophical literature, the phenomenon we have described appears to
be connected to a more general one, concerning the mereological behavior of
properties. A classic distinction in this respect is that between homoeomerous and
anomoeomerous properties, based on whether or not a property holding for a whole
also holds for all its parts, and discussed in particular by Armstrong [1]. Ingvar
Johansson [2] builds on this work in the light of the Johnson’s distinction between
determinates and determinables [3], focusing his attention to the case of determinate
properties belonging to the same determinable, and to the ontological nature of patterns
like for instance a distribution of colored areas on a surface [4]. This is, at least in my
knowledge, one of the few works addressing in some detail the mereological behavior
of what I call qualities1 (i.e. colors, lengths, temperatures), and not just that of generic
properties, so I think it is a good starting point in our analysis2. Johansson proposes the
following distinction among determinates:
(1) A determinate property is inclusive if and only if each possible part of its
instances instantiates some other property under the same determinable.
(2) A determinate property is exclusive if and only if each possible part of its
instances instantiates this very same property (under the same determinable).
As an example of inclusive property, Johansson brings a volume-determinate: if an
object has a volume of 100 cm3, then all its (proper) parts must have a different
volume. So every instance of an inclusive determinate necessarily includes other
(different) determinates for its parts3. On the contrary, he notes that a color-determinate
is exclusive: if an object is (homogeneously) red, different determinates (under the
same determinable) are excluded.
In my view, the homogeneity proviso in the latter example is illuminating, since it
gives evidence of a peculiarity of some determinables (like color, density, or
temperature): they are prone to have their determinates arbitrarily distributed in the
region they are defined. They have therefore a local behavior. This makes it difficult to
understand the meaning of simple statements like this car is red, or the room’s
temperature is 20 °C, so that, in many cases, the ascription of such determinates to an
extended object is the result of an implicit convention (the car color is the body’s color)
or an average operation, and very rarely results from an homogeneous distribution.
To account for possible non-homogeneous distributions of determinates under the
same determinable, Johansson introduces a variant to (2):
(3) A determinate property is semi-exclusive if and only if some possible part of its
instances instantiates this very same property (under the same determinable).
So, if we admit that the red determinate is semi-exclusive, then an object can be
globally red (as a result of some convention) if it just has one red part while being
locally yellow somewhere else, or it may be also the case that it has multiple local
colors with no definite global color. We can conjecture therefore that semi-exclusivity
is a formal property which is associated with local behavior.
1
Note however that Johansson’s notion of quality is different from mine, as will be clear in the following,
since he adopts a realist ontology according to which qualities are conceived as universals, and include both
substances and properties.
2
To complete the picture, we should also consider the distinction between extensive and intensive properties,
which has many variants in the literature. I will discuss it in the next section, since I believe that Johansson’s
work helps to understand it.
3
For the sake of simplicity, I will assume there are no atoms in the domain, so every object has some proper
parts.
76
Consider now the width of a river. Like for the color case, we can have a river
stretch whose width is homogeneous, or another whose width is not definite, since it
varies along the river flow. So width-determinates are semi-exclusive. However,
differently from colors, we can’t say that widths can distribute freely for all the parts of
the river stretch, since the longitudinal parts are constrained to have a width lower than
that of the river stretch. Indeed, besides being semi-exclusive, according to Johansson
widths are also semi-inclusive:
(4) A determinate property is semi-inclusive if and only if some possible part of its
instances instantiates some other property under the same determinable.
This means that, in practice, there is a direction (across the river flow) according to
which each part contributes to the width of the whole, but there is another direction
(along the flow) according to which there is no such contribution. As we shall see, this
observation will be useful to define the notion of local quality. For the time being,
however, we must say that semi-exclusivity, alone, is not enough to fully capture the
intuition behind the notion of local behavior, mainly because, according to the
definitions above, semi-inclusivity and semi-exclusivity are not disjoint.
3. Extensive and intensive properties
In physics and chemistry, an extensive property (like having a certain volume) is such
that, if it holds for a whole, every single part necessarily contributes to this fact, while
an intensive property (like having a certain temperature or color) is not necessarily
affected by the parts of its instances. In his book, Johansson uses the terms ‘extensive’
and ‘intensive’ in a different sense, based on Kant’s distinction between extensive and
intensive magnitudes. He observers that for Kant ‘extensive’ is synonymous of
‘inclusive’, but ‘intensive’ means just quantifiable, so that it is not opposite to
‘extensive’4. I don’t think this understanding of ‘intensive’ is useful for our purposes,
so I will stick to the previous (still informal) definition.
I will rather suggest the following definition:
(5) A determinate property is extensive if and only if it is necessarily semi-
inclusive. A property is intensive otherwise.
Under this definition, an intensive property is just a property which does not
impose any inclusivity constraints on its mereological behavior. All exclusive
properties turn out to be intensive, as well as all semi-exclusive properties which are
not also semi-inclusive5. An important aspect of this definition is its modal nature. A
property is extensive or intensive depending on whether or not, because of its very
nature, it forces the proper parts of its instances to be different. To me, this definition
of intensivity finally captures our intuitions concerning the local behavior of a
determinable: only intensive determinables (i.e., all of whose determinates are
intensive) can admit arbitrary distributions within the parts of a given object.
As a final note, someone may observe that (5) is neutral with respect to an aspect
usually considered as characteristic of extensive properties, namely additivity.
Additivity however only concerns quantifiable properties, and I agree with Johanssson
that the basic distinction we are aiming at should be more general. In particular,
4
In other words, on one hand ‘intensive’ is understood as opposite to ‘extensive’, while on the other hand it
is understood as ‘capable of having an intension’.
5
In addition, a property like mean temperature of 20° C, which is neither semi-exclusive nor semi-inclusive
(since it can hold both when all the proper parts of its instances have the same temperature and when no
proper part has the same temperature), turns out to be intensive.
77
Johansson makes a very interesting example of a semi-inclusive determinable, namely
shape, which is not additive but still would count as extensive under our definition.
4. Local qualities
Let us now shift from determinates and determinables to individual qualities and
quality kinds. Independently from any deep metaphysical commitments, I think that
this move is pragmatically useful not only to provide an analysis consistent with the
DOLCE ontology [5], [6], but also to better clarify our intuitions concerning local
qualities. In DOLCE we distinguish between individual qualities, which inhere to
specific individuals, and qualia, which are abstract entities representing what exactly
resembling individual qualities have in common. Qualia resulting from comparable
individual qualities are organized in quality spaces. We refer to individual qualities
with expressions such as the color of my car, while we refer to qualia with simple
terms like red. So the color of my car is different from the color of your car, even if
they have exactly the same shade of red, i.e., they have the same quale6. If I paint my
car in blue, the term the color of my car still denotes the same quality, but its quale is
now different. So, in general, the relationship between qualities and qualia is
temporalized.
From now on, I shall simply use the term quality to refer to an individual quality. In
DOLCE, qualities are organized in quality kinds, i.e. maximal classes of comparable
qualities. Color and volume are examples of quality kinds. Their instances are
individual colors or individual volumes. The objects to which such qualities inhere are
instances, respectively, of the has-color and has-volume determinables. So there is a
correspondence between determinables and quality kinds, but quality kinds are not
determinables. Similarly, there is a correspondence between determinates and qualia, in
the sense that the objects whose qualities have the same quale inhere are instances of
the same determinate.
In terms of individual qualities and quality kinds, (1) can be reformulated as
follows7:
(6) A quality q of kind Q with quale ql inhering to an object x is inclusive iff every
proper part y of x has a quality q’ of kind Q with quale ql’ different from ql.
The definitions (2)-(4) above can be reformulated analogously, and will be omitted
here for the sake of brevity. (5) however makes little sense at the level of individual
qualities, and much more sense at the level of quality kinds, or, more in general, to
classes of qualities belonging to the same kind:
(7) A quality kind (or a class o qualities belonging to the same kind) is extensive iff,
necessarily, all its instances (i.e., its individual qualities) are semi-inclusive. It is
intensive otherwise.
Let us now go back to our initial question: what is a local quality? A first conjecture
we can make is that a local quality is an instance of an intensive quality kind. So,
looking back at our original example, the color of each part of the vase, being an
instance of an intensive quality kind (color), appears to be a local quality.
6
I must say I have no clear understanding about the best way to name the relationship existing between
individual qualities and their qualia. In this paper I will simply use “has”. Probably a more informative name
would be “manifests as”.
7
For the sake of conciseness, I will abstract from time in these definitions, since time is not relevant to
understand their rationale. Extending them to the temporal version is however a simple matter, taking into
account that in DOLCE the part-of and the has-quale relation are temporalized when they concern endurants.
78
However, things are not so simple, since we want also to account for the local
behavior of a river’s width, and width is not an intensive quality kind, since it is semi-
inclusive. Moreover, a fundamental question arises: local to what? Given a particular
object, how can we tell what are its local qualities? For instance, think of our river
example. Arguably, the river has many local widths, each inhering to a particular river
stretch. But also each possible longitudinal part of the river has a width. Is that width a
local quality of the river, or just of a strange part of it? From the cognitive point of
view, I say it is not a local width of the river. Think of another example, perhaps more
vivid: a vase with a handle. The vase has many local widths (at the top, at the bottom,
in the middle…), as well as the handle has many local widths, but none of the local
widths of the handle is a local width of the vase, despite the fact that the handle is a
part of the vase.
To address this issue, let us first clarify that each local quality of an object inheres to
some proper part of the object, but not to the object itself. So, when we say that a vase
has many local widths, this is because of an indirect inherence relation, similar to the
one holding in DOLCE between an event and the spatial location of its participants.
The point now is that this indirect relation existing between the quality of a part and the
whole doesn’t hold for all parts: as we have seen, not every width of a part of the vase
is a local width of the vase. I think there is a simple cognitive mechanism that explains
this situation. When we consider a (non-inclusive) quality kind such as width as applied
to a river, we implicitly introduce a set of canonical parts (namely those cut across the
river flow, corresponding to river stretches) whose width counts as a local width of the
river. Because of the way canonical parts are constructed, the class of all local widths
of a river turns out to be intensive, despite the quality kind ‘width’ is not.
Similarly, when we apply ‘width’ to a vase, we consider as canonical parts those
concerning the internal cavity, excluding the handle. Finally, when we apply ‘color’ to
a car, we only consider the external parts of the body as canonical parts, while when we
apply it to the vase we may consider as canonical all the (external) parts of the vase,
including those of the handle.
In sum, we can conclude that local qualities are instances of quality classes,
constructed ad hoc with the cognitive mechanism described above as a specialization of
non-inclusive quality kinds. In general, such classes are not rigid, using OntoClean’s
terminology: the color of a part of the vase will keep its identity when the part is
removed, although it will not be a local color of the vase any more. Local qualities
don’t form a new ontological category. Locality, for qualities, is just a special way to
describe a whole (especially its shape) with reference to the qualities of its parts.
5. Quality fields and quality patterns
Consider now all local qualities of a certain kind that a certain object has, at a given
time. For instance, think of all the local depths of the Adriatic Sea. I say that the
mereological sum of these local qualities is a quality field. While a single local depth
does not inhere to the whole Adriatic Sea, the whole depth field does, it inheres to it.
Quality fields form therefore a new ontological category in the vast class of dependent
entities. We are able to define them thanks to the introduction of the notion of local
quality.
Once we introduce quality fields, we can give an exact denotation to expressions
like “the river’s width” or “the depth of the sea” which don’t usually refer to an
individual quality, unless we conventionally pick up a specific individual quality (say
the maximal depth). I will say that these expressions denote a quality field. Indeed, on
the basis of our previous analysis, we can safely assume that an expression of the form
79
“the Q of X” denotes a quality field if Q is not an extensive quality kind, unless a
special convention is introduced for certain kinds of X.
Let us bring time into account, using the notion of quality field to analyse the
distinction between variation and change. Synchronically, at a specific time, we can
observe variations in the Adriatic Sea’s depth field when shifting our focus of attention
from one part (e.g., the depth of the Italian side) to an other (e.g., the depth of the
Croatian side). The whole quality field can also genuinely change in time, keeping its
identity, when some of its individual qualities change their qualia. This is what
happened in the last 2000 years, since the depth of the Italian coast is much lower than
it used to be in the Roman age.
Consider now the Adriatic Sea’s depth field at the Roman age. It exhibits an
individual spatial pattern, which is different from the pattern we can observe today.
Such pattern reflects the specific qualia distribution of the individual qualities forming
the depth field at that time. I define a individual pattern as an emerging entity
constituted by (a part of) a quality field. It differs from a quality field since the actual
qualia distribution is an essential property of the pattern, and is not essential to the
quality field (whose qualia distribution can change in time). So individual patterns are
frozen, they don’t change, although they can exhibit variations. Note that I am insisting
using the term individual pattern to make it clear they are not abstract entities: two
things may have exactly resembling, although distinct, individual patterns. In this case,
I say that they will have the same shape, but this is another story.
Let us finally shift the attention to perdurants. They can have both global and local
qualities, inhering to each temporal part. The duration of a rain is a global quality,
while its intensity is a quality field. When we say “the rain intensity is high now” we
are referring to the whole intensity field, whose value happens to be low in the present
time interval, exactly like the width of the river happens to be high in a certain place.
So, the introduction of local qualities and fields can help understanding apparent
“changes” in events and processes, like those described in [7], without the need of
introducing a new entity which is the subject of such change: a speed variation during a
run or an increase in the river flow will be simply considered as a variation of a local
quality (the run speed or the water flow) along the temporal dimension. This move may
also eliminate (at least for these examples) the need to introduce so-called relators [8]
in addition to events exemplifying a binary relation like marriage: a change in the
peacefulness of the marriage will be simply described as a variation of a local quality
of the marriage itself, with no need to introduce a separate relating entity.
In conclusion, the introduction of local qualities, fields and patterns seems to be a
simple and powerful extension to the Dolce’s notion of quality, which allows us to
formally account for the way we deal with spatial and temporal quality distributions.
This is still not enough to fully account for the different shapes such distributions may
exhibit, but I believe it contributes to understand what shapes are.
References
[1] D. M. Armstrong, Universals and Scientific Realism, Volume 2: A Theory of
Universals. Cambridge University Press, 1978, pp. 1–169.
80
[2] I. Johansson, Ontological Investigations. An Inquiry into the Categories of Nature,
Man and Society. Routlege, 1989.
[3] W. E. Johnson, “Logic - Part I,” Cambridge University Press, pp. 1–304, 1921.
[4] I. Johansson, “Pattern as an ontological category,” N. Guarino, Ed. Formal
Ontology in Information Systems Amsterdam, Oxford, Tokyo, Washington,
DC: IOS Press (Frontiers in Artificial Intelligence and Applications), 1998,
pp. 86–94.
[5] S. Borgo and C. Masolo, “Foundational choices in DOLCE,” in Handbook on
ontologies, S. Staab and R. Studer, Eds. Springer, 2009, pp. 361–381.
[6] C. Masolo, “The DOLCE Ontology,” WonderWeb Deliverable D18, Dec. 2003.
Available at http://www.loa.istc.cnr.it/Papers/D18.pdf.
[7] A. Galton and R. Mizoguchi, “The water falls but the waterfall does not fall: New
perspectives on objects, processes and events,” Applied Ontology, vol. 4, no.
2, pp. 71–107, 2009.
[8] G. Guizzardi, Ontological foundations for structural conceptual models. University
of Twente, CTIT PhD Thesis Series, no. 05-74, 2005.
81