Originally Posted by

**mosesquine** There are some ways of regimenting plural quantificational statements like "There are some apples on the table" as:

(∃xx)(∀u)(xx ≤ u → Au & Tu)

which translates into "There exist some xx such that for every u, if xx is *part of *u, then u is an apple, and u is on the table" in semi-formal language mixed with logic and English.

The symbol '≤' means '...is part of...', that is, the parthood relation. I think that the symbol of parthood must have inference rules like other logical symbols have.

**My question is "What are the inference rules of parthood relation symbol?**??"