Possession using first order logic

Question

How does one express possession using only first order logic?
For example:
Let D be the set of all dogs. Let H be the set of all humans.
Then how would "dog d belongs to human h" be expressed in first order logic?

Answer 1

Possession is a binary relation here . So you need a two-place relational predicate to express it. "$B$" perhaps, so that "$Bdh$" expresses the claim -- as it might be -- that Duke belongs to Henry (if "$d$" denotes Duke and "$h$" denotes Henry)

If you want to say explicitly that Duke is a dog and Henry a human and Duke belongs to Henry you'll need something like "$Dd \land Hh \land Bdh$" with the one-place predicates "$D$" and "$H$" having the obvious interpretations.

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But having said all that, your question is perhaps indicating that you should read a decent entry-level book on first order logic. Nick Smith's introductory book is excellent, but there are others with many virtues. E.g. mine is now freely downloadable from https://www.logicmatters.net/ifl -- you should find its detailed chapters on translating in and out of FOL helpful.