Tangle Insertion Invariants for Pseudoknots, Singular Knots, and Rigid   Vertex Spatial Graphs
  The notion of a pseudoknot is defined as an equivalence class of knot diagrams that may be missing some crossing information. We provide here a topological invariant schema for pseudoknots and their relatives, 4-valent rigid vertex spatial graphs and singular knots, that is obtained by replacing unknown crossings or vertices by rational tangles. 
Allison Henrich and Louis H. Kauffman
math.GT