C.S. Peirce studied ternary (and higher-order, n-ary logic, too) logic in the context of which he called semiosis,
an action, or influence, which is, or involves, a coöperation of three subjects, […], this tri-relative influence not being in any way resolvable into actions between pairs.
Has any logician applied ternary logic to understand the intricacies of human relationships among three (or more) people?
or "Love Polyhedra" for the higher-order analogue: