An ornamental, split-rail fence that does not enclose any land is only a “fence” in the sense that the material is normally used to create an installation that has at least four sides and actually encloses something.  A pair of split-rail posts (or more than 2 posts, even) with some horizontal members attached is likely more intended to evoke a rustic look that complements a residence instead of actually enclosing the residence or a portion of land adjacent to the residence, and it would not be considered a “fence” that violates your restrictions.

 

Words in restrictions are given their ordinary meanings, and the most common definition of “fence” in the sense it is used in your restrictions is “a barrier enclosing or bordering a field, yard, etc., usually made of posts and wire or wood, used to prevent entrance, to confine, or to mark a boundary.” Even though the fence referred to may mark part of a boundary, it does not necessarily  occur on a boundary line and is not a violation because it does not prevent entrance or confine anything.