# What is the term for a phrase that connects two objects with some relation?

In mathematics, we usually see symbols that join two objects: numbers, sets, etc. The more familiar one is the equality symbol "=" which in a formal standpoint means "is logically identical to." My question is what are these types of terms called? Terms that connect two objects with some relation. Sorry, I'm not very familiar or knowledgeable about the field and concepts of linguistics, correct me if the question is too vague.

• Are you looking for "predicate"? For example, in "cats hunt mice", "hunt" is a binary predicate that connects the entities "cats" and "mice".
– Draconis
Aug 3, 2022 at 4:52
• Especially, are you looking for commutative predicates like marry? There are some, but very few. Every English predicate (function analog) has its own set of possible arguments, forbidden constructions, optional transformations, modifications when inside negative, modal, or quantifier scopes, plus selected short subjects. You're safe to think of them as largely unstudied special functions like zeta or gamma. Aug 3, 2022 at 17:13
• If you want to see how predicates become verb phrases, try the logic guide and the verb phrase guide. Aug 3, 2022 at 17:15

The operator `=` is a two-place predicate. We can think of a think of this as a function that takes two arguments and returns True if the two arguments are equal to other. Equivalently, we think of it as a function that takes one argument, and returns a function which itself takes another argument and return True if the two are the same.
This functional nature of predicates can be somewhat obscured by the fact that we write operators like `=` and verbs like "saw" in infix notation, i.e. between their arguments. Instead, we could imagine writing them in prefix notation like we would in math, i.e. `f(x)`. In this way, we could think of the equality predicate as a function `((= (x)) y)` where the expression `(= x)` is a function that takes in some argument and returns True if it's equal to `x`. Similarly, we can imagine "saw" as a predicate in prefix notation, i.e. `((saw (Mary)) John)` where "saw" is a function that takes in an object, i.e. Mary, and returns a function. That function `(saw Mary)` is then a function that takes in a subject and returns True if and only if that subject indeed saw Mary.