adj. 1. (Logic) (of a relation) never holding between a pair of elements in one order when it holds between them in order, except when x = y; that is, ordered pairs of elements 〈x, y〉 and 〈y, x〉 can not both have the relation unless the relata are identical. For example, less than or equal to (≤), and no younger than are antisymmetric relations. Any asymmetric relation is a fortiori antisymmetric, as is any empty relation. Compare non-symmetric, symmetric. 2. (of a matrix) another term for skew-symmetric.