Binary relations are obvious, and I see the need to have 3-ary relations such as "being in between things". Are there natural language examples of relations greater 3?
Edit: without combining binary or tertiary relations
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If you're asking about predicate valency then there are a few examples of tritransitive/quadrivalent verbs with four arguments. For example:
I1 bet you2 five dollars3 that it would rain4.
I can't quickly think of ones very obviously corresponding to a word in a natural language (such as "between" for ternary). The best I can think of is "surrounded by", since presumably (living on a two-dimensional surface) one needs at least three things to be surrounded by -- one step up from between!
In principle one could make up a word for all kinds of quaternary relations such as:
A list of more than three items could be viewed as a relationship where each item in the list is connected by "and". For example,
"Today I spent $20 on food, $40 on housing, $10 on entertainment and $30 dollars on transportation."
I could symbolize my spending (S) as one part for food (f), one part for housing (h), one part for entertainment (e) and one part for transportation (t) and then write the relation S with variables as S(f,h,e,t).
I could break this up into four unary relations all connected by "and", but from a natural language perspective if I were telling someone what I spent, I would likely combine them into a 4-ary relation.