  Classical knots in $\mathbb{R}^3$ can be represented by diagrams in the
plane. These diagrams are formed by curves with a finite number of transverse
crossings, where each crossing is decorated to indicate which strand of the
knot passes over at that point. A pseudodiagram is a knot diagram that may be
missing crossing information at some of its crossings. At these crossings, it
is undetermined which strand passes over. Pseudodiagrams were first introduced
by Ryo Hanaki in 2010. Here, we introduce the notion of a pseudoknot, i.e. an
equivalence class of pseudodiagrams under an appropriate choice of Reidemeister
moves. In order to begin a classification of pseudoknots, we introduce the
concept of a weighted resolution set, an invariant of pseudoknots. We compute
the weighted resolution set for several pseudoknot families and discuss notions
of crossing number, homotopy, and chirality for pseudoknots.
