(≤k)-reconstructible binary relations

A relation R is ( ≤ k ) -reconstructible ( k a positive integer) if it is isomorphic with any relation S on the same vertex set with the property that the relations induced by R and S on any set of at most k vertices are isomorphic; it is ( ≤ k ) -self dual if every restriction to at most k vertices is self dual, i.e.  isomorphic to its dual relation (the relation obtained by reversing its arcs). In particular, relying on the description of ( ≤ k ) -self dual binary relations, we characterize, for each k ≥ 4 , all ( ≤ k ) -reconstructible binary relations: A binary relation is ( ≤ k ) -reconstructible if and only if its modules that are chains are finite and its ( ≤ k ) -self dual modules are self dual.