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fall roughly in three different classes: (i) proposals that employ classical ontological
theories of parthood (
Mereologies
). In this class, there is a number of works in the
literature that employ the ontological theory put forth by the philosopher Mario
Bunge [5] typically accessed through its most popular adaptation termed the BWW
ontology [6,7]; (ii) proposals that are based on research from linguistics and cognitive
science in which different sorts of
Meronymic
relations are elaborated. Most contribu-
tions in this class are based on the theory developed by Winston , Chaffin and
Herrmann (henceforth WCH) [8]. An example of a pioneering article in this class is
[9]; (iii) proposals which define a number of so-called
secondary properties
which
have been used to further qualify parthood relations [6]. These include distinctions
which reflect different
modal aspects
of parthood reflecting different relations of
dependence (e.g., generic versus existential dependence). An example is the distinc-
tion between
essential
and
inseparable
parthood in [2].
Despite their important contributions, there are significant shortcomings in the cur-
rent scenario considering the aforementioned approaches. On the one hand, accounts
of parthood solely based on WCH suffer from many difficulties inherited from the
original theory. As discussed in [10,11], WCH's original taxonomy turned out to be
overly linguistically motivated, focusing on the linguistic term
part-of
(and its cog-
nates). In fact, as demonstrated by these authors, the six linguistically-motivated types
of part-whole relation originally proposed in WCH give rise to only four distinct
ontological types, namely: (a)
subquantity-quantity
: modeling parts of an amount of
matter (e.g., alcohol-wine, gin-Martini, Chocolate-Toddy); (b)
member-collective
:
modeling a collective entity in which all parts play an equal role w.r.t. the whole (e.g.,
tree-forest, card-deck, lion-pack); (c)
subcollective-collective
: modeling a relation
between a collective and the subcollectives that provide further structure to the former
(e.g., the north part of the black forest-black forest, the underage children of John-the
children on John); (d)
component - functional complex
: modeling an entity in which
all parts play a different role w.r.t. the whole, thus, contributing to the functionality of
the latter (e.g., heart-circulatory system, engine - car).
On the other hand, conceptual modeling accounts of parthood based on BWW
inherit the limitations of Bunge's original treatment of parthood in its most basic core.
Mereology is a mature discipline with well-defined and formally characterized theo-
ries. These in fact form a lattice of theories such that there is not one single formal
meaning of part in mereology but several alternative axiomatizations of parthood that
extend each other. Mapping modeling primitives representing part-whole relations to
these theories can indeed provide an important contribution to conceptual modeling.
Firstly, in a direct manner because these theories can provide sound and fully charac-
terized formal semantics for these relations. But, also because nowadays several au-
thors have proposed codifications of different mereological theories by mapping them
to different Description Logics, hence, providing a mechanism for automated reason-
ing with
partonomies
in conceptual models [12,13]. The negative point here is that
Bunge's theory of parthood corresponds to the weakest theory in mereology. In fact a
theory which is even considered to be too weak to count as a characterization for a
true part-whole relation [14].
Finally, most current approaches limit themselves to analyze the relation between
the whole and its parts. However, as discussed in [15], a conceptual theory of
parthood should also countenance a
theory of wholes
, in which the relations that tie
