Mereology

Synonyms

Aggregation relation; Part-whole relation; Theory of parthood

Definition

In Ontology, the theory of how a part relates to the whole.

Various mereological theories exist, which are more or less expressive. Commonly, the part-of relation is taken as a primitive relation (i.e., not defined but only its properties are characterized) and other relations are defined using this primitive relation, such as proper-part-of (1) and overlap (2). The part-of relation is reflexive (3), antisymmetric (4), and transitive (5), and the proper-part-of relation is irreflexive (6), asymmetric (7), and transitive (8):

• 1. ∀x∀y(proper-part-of(x,y) = _def part-of(x,y) ∧ ¬part-of(y,x))

• 2. ∀x∀y(overlap(x,y) = _def ∃z(part-of(z,x) ∧ part-of(z,y)))

• 3. ∀x(part-of(x,x))

• 4. ∀x∀y((part-of(x,y) ∧ part-of(y,x)) → x = y)

• 5. ∀x∀y∀z((part-of(x,y) ∧ part-of(y,z)) → part-of(x,z))

• 6. ∀x¬proper-part-of(x,x)

• 7. ∀x∀y(proper-part-of(x,y) → ¬proper-part-of(y,x))

• 8. ∀x∀y∀z((proper-part-of(x,y) ∧ proper-part-of(y,z)) → proper-part-of...