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The horizontal relations in an analogy are the relations of similarity (and difference) in the mapping between domains, while the vertical relations are those between the objects, relations and properties within each domain.
The "categories" you're seeing listed when you search are those common objects that the systems are trained to look for.
On an inclusivist or expansive conception, architectural objects are those designed objects ranging over the whole of the built environment; on an exclusivist conception, the range describes only some coherent subset of the whole of the built environment.
The first photographs in the grid are those of objects or locations closest to you.
Outside the mainstream campaigns are those who object to the referendum not offering PR as a choice.
There are those who believe the objects left behind by the dead hold a certain residual power.
The denotations of 'cloud' and 'that' according to a precisification P are those concepts and objects that are the most natural according to P of the concepts and objects that we could be denoting by those terms, for all one can tell from the way the terms are used.
We must again affirm that the only objects which can be seen by us in the skies, (setting aside the planets and a few other bodies in the solar system,) are those objects which are self-luminous in consequence of their intensely high temperature.
With a few exceptions, those are also the objects with the highest abundances of short-lived radionuclides.
When those layers are lifted off, "the objects are so pristine", Knight said, "it's as if 3,000 years never happened.
There are, then, acts of intellect, but there are no separate inner concepts that are the objects of those acts.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com