> A common use of be is to express set membership rather than identity
Google for "logical "is a" vs logical "is"".
Google AI answers this:
> "is" typically represents an equality relation
Rest is from the AI response:
In logic, "is" typically represents an equality relation, while "is a" (or "is of the type") represents an inclusion relation. "Is" indicates that two things are the same or identical, while "is a" indicates that one thing is a member of a larger class or set of things.
Logical "is" (equality):
Meaning:
"A is B" means that A and B are the same thing, or have the same properties.
Example:
"The Eiffel Tower is in Paris" (the Eiffel Tower and the thing in Paris are the same thing).
Logical "is a" (inclusion or type):
Meaning: "A is a B" means that A belongs to the category or class of things that are B.
Example: "A dog is an animal" (dogs are a type of animal).
"silk is cloth" is not true except for the colloquial interpretation that infers "silk can sometimes be a cloth". Given the clarifications, it seems the OP is intending to say it's an exact equality and not a colloquial definition that actually means "subset".
I'll note, I have not asked any questions other than (paraphrasing): "what do you mean precisely?" To which, I have not gotten any answers other than trolling and flaming; and examples that all conveniently swap "is" with "is a".
Google for "logical "is a" vs logical "is"".
Google AI answers this:
> "is" typically represents an equality relation
Rest is from the AI response:
In logic, "is" typically represents an equality relation, while "is a" (or "is of the type") represents an inclusion relation. "Is" indicates that two things are the same or identical, while "is a" indicates that one thing is a member of a larger class or set of things.
Logical "is" (equality):
Logical "is a" (inclusion or type):