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mereological

Mereology is the branch of philosophy and formal ontology that studies part–whole relations. It seeks to understand how objects can be composed of parts, and how the whole relates to its parts. Central notions include part and proper part, overlap, disjointness, and the fusion or sum of a collection of parts. In formal theories, parthood is typically treated as a primitive relation with the aim of deriving logical laws that govern composition and inference about wholes.

The term and the first systematic development of the theory are associated with Stanisław Leśniewski in the

In extensional mereology, the parthood relation is usually taken to be reflexive, transitive, and antisymmetric: every

Variants include non-extensional applications and debates over topics such as mereological nihilism (only simples exist) versus

early
20th
century,
who
introduced
a
dedicated
Mereology
as
one
of
his
three
logical
systems.
His
approach
presents
parthood
and
fusion
as
fundamental
notions
that
do
not
reduce
to
set-theoretic
membership.
Modern
mereology
continues
to
explore
parthood
as
a
partial
order
and
investigates
how
sums
of
parts
form
wholes,
and
how
overlaps
constrain
composition.
object
is
a
part
of
itself;
if
x
is
part
of
y
and
y
is
part
of
z,
then
x
is
part
of
z;
and
if
x
is
part
of
y
and
y
part
of
x,
then
x
and
y
are
identical.
A
proper
part
is
a
part
that
is
not
identical
to
the
whole.
The
sum
or
fusion
of
a
family
of
objects
is
the
smallest
object
that
has
all
members
as
parts.
Overlap
means
there
exists
some
part
common
to
both
x
and
y.
universalism
(everything
is
part
of
something).
Mereology
is
widely
used
in
analytic
philosophy
and
in
knowledge
representation
to
model
complex
part–whole
hierarchies
in
biology,
geography,
and
engineered
systems.