The conceptual space defines a metric space that
can be used to compute the proximity between any
two entities, and between entities and prototypes. To
compute the distance between two points p
1
, p
2
we
apply a distance metrics based on the combination of
the Euclidean distance and the angular distance inter-
vening between the points. Namely, we use Euclidean
metrics to compute within-domain distance, while for
dimensions from different domains we use the Man-
hattan distance metrics, as suggested in (G¨ardenfors,
2000; Adams and Raubal, 2009). Weights assigned to
domain dimensions are affected by the context, too,
so the resulting weighted Euclidean distance dist
E
is
computed as follows
dist
E
(p
1
, p
2
,k) =
s
n
∑
i=1
w
i
(p
1,i
− p
2,i
)
2
,
where i varies over the n domain dimensions, k is the
context that indicates the set of weights associated to
each domain, and w
i
are dimension weights.
We represent points as vectors (with as many
dimensions as required by the considered domain),
whose components correspond to the point coordi-
nates, so that a natural metrics to compute the simi-
larity between them is cosine similarity. In the metric
space being defined, the distance between an individ-
ual and prototypes is computed with the Manhattan
distance, enriched with information about context k.
Also, the distance between any two concepts can be
computed as the distance between two regions in a
given domain Also, we can compute the distance be-
tween any two region prototypes, or the minimal dis-
tance between their individuals, or we can apply more
sophisticated algorithms. Further details about tech-
nical issues can be found in (Ghignone et al., 2013).
Inference in conceptual spaces is mostly per-
formed on incomplete and/or noisy information: that
is, it is frequent the case that only partial information
is available to categorize a given input individual, and
some points are not defined for one or more dimen-
sions. Conceptual spaces are robust to this sort of lack
of information, which is conversely a decisive factor
in the context of formal ontologies. In these cases we
restrict to considering domains that contain points in
the input individual: if the description for a given in-
dividual does not contain points of some domains, the
distance for those domains is set to a default value.
The basic representational structure processed by
the system is named genericDescription; it encodes
the salient aspects of the entities being considered. A
genericDescription is a super-domain that hosts infor-
mation about physical and non physical features ar-
ranged into nine domains: size, shape, color, loca-
tion, feeding, locomotion, hasPart, partOf, manRela-
tionship. The size of entities is expressed through
the three Euclidean dimensions; the shape allows ex-
pressing that an object has circular, square, spherical,
cubic, etc., shape. The color space maps object’s fea-
tures onto the
L
⋆
a
⋆
b
⋆
color space.
L
⋆
(0 ≤ L ≤ 100)
is the correlate of lightness,
a
⋆
(−128 ≤ a ≤ 127) is
the chromaticity axis ranging from green to red, and
b
⋆
(−128 ≤ b ≤ 127) is the chromaticity axis ranging
from blue to yellow.
The location space indicates the place where the
object being modeled can be typically found. It actu-
ally results from the combination of five dimensions,
and namely: humidity, indicated as a percentage; tem-
perature, ranging in [−40
◦
,50
◦
]; altitude, ranging in
[−11000,8848]; vegetation, ranging in [0,100]; time.
In turn, time contains a partitioning of the hours of the
day into sunrise (4–6 AM), morning (6–12 AM), af-
ternoon (12–5 PM), evening (5–10 PM) and night (10
PM–4 AM).
The domain feeding is currently specific to ani-
mals, and it allows mapping an element over two di-
mensions, typeOfFood and amountOfFood. The type-
OfFood is associated to an integer indicating 1: her-
bivore, 2: lectivore, 3: detritivore, 4: necrophage,
5: carnivore. The underlying rationale is that close
elements (e.g., necrophage and carnivore, that are
one step apart in the proposed scale) are represented
as close in this space due to their proximity under
an ethological viewpoint, whilst different categories
(e.g., herbivore and carnivore) are featured by larger
distances in the considered scale (Getz, 2011).
Similar to the previous one, also the locomotion
domain combines two dimensions: the former dimen-
sion is used to account for the type of movement (1:
swim, 2: dig, 3: crawl, 4: walk, 5: run, 6: roll, 7:
jump, 8: fly), and the latter one is used to account
for the speed, expressed in km/h (Bejan and Marden,
2006). Finally, the manRelationship space is used to
grasp entities as related to man by function (both a
train and a horse can be used as ‘transport’), product
(chicken produce ‘eggs’, and ‘chicken’ per se are a
food product), symbol (‘lion’ can be used as a symbol
for ‘strength’ and ‘royalty’). A simplified example of
the
lion
prototype information is reported below.
<object name="lion">
<genericPhysicalDescription>
<feeding>
<foodType>5</foodType>
<foodQuantity>100</foodQuantity>
</feeding>
</genericPhysicalDescription>
<manRelationship>
<symbol id="08153437">royalty</symbol>
<symbol id="05036872">strength</symbol>
</manRelationship>
</object>
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