Examples of the Partial Order Properties

Isa is reflexive:

A bear is a bear.

-> Isa(bear, bear)

Isa is antisymmetric:

A bear is a wowie, and a wowie is a bear.

Therefore, bear and wowie represent the same things.

Isa(bear, wowie) & Isa(wowie, bear) -> bear = wowie

Isa is transitive:

A grizzly is a bear, and a bear is a mammal.

Therefore, a grizzly is a mammal.

Isa(grizzly, bear) & Isa(bear, mammal) -> Isa(grizzly, mammal)