I have been working towards proposing definition for my proposed spatial inclusion relation enveloped_by. After quite a lot of readings and discussions, the following two possible definitions are proposed. One is by using the tangential proper part relation and the other is by using covered by relation.

Proposal definition 1:
enveloped_by(b,a) / envelopes(a,b) = TPP(a,b) and SCOINC(a,b)

enveloped_by(b,a)= a is tangentialproperpartof b and two boundaries of
a and b coincide at all points such that:
b is a closed material object (whether sphere, or cylindrical),
a is a material object,
the outer boundary of b and the inner boundary of a coincide with each
other at all points (i.e. the boundaries of b and a co-exist with each
other)

SCOINC(a,b) — if two (spatial) boundaries a and b coincide, a and b
cannot spatially exist independently or cannot be located farther from
each other

Proposal definition 2:
enveloped_by(b,a) / envelopes(a,b) = (bCOVERED_BYa) and (aSCOINCb)

enveloped_by(b,a)= b is coveredby a and two boundaries of a and b
coincide at all points such that:
b is a closed material object (whether sphere, or cylindrical),
a is a material object, and
the outer boundary of b and the inner boundary of a coincide with each
other (i.e. the boundaries of b and a co-exist with each other)

SCOINC(a,b) — if two (spatial) boundaries a and b coincide, a and b
cannot spatially exist independently or cannot be located farther from
each other

Properties: Intransitive and assymetric

Cardinality: one to one

Relations:
nucleus is enveloped_by nuclear membrane
mitochondria is enveloped_by double layered membrane
animal cell is enveloped_by cell membrane

Enveloped_by / envelopes = enclosed_by / encloses

Enveloped_by notequalto surrounded_by because in surrounded_by the boundaries of a and b do not coincide and a and b can spatially exist independently or can be located farther from each other.

References: RO, GFO, FMA, Point-Set Topological Relations, Region Connection Calculus

I have proposed these two definitions in the OBO-discuss and OBO-Relations mailing lists for further discussions and comment from the community. Let us see.

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