  In analogy with non-degenerate involutive set-theoretic solutions of the
Yang-Baxter equation and braces, we define non-degenerate involutive partial
set-theoretic solutions and partial braces. We define the structure group and
the structure inverse monoid of such a solution and prove that if the partial
solution is square-free, then its structure inverse monoid embeds into the
restricted product of a commutative inverse monoid and an inverse symmetric
monoid. Furthermore, we show that there exists a square-free, non-degenerate
involutive partial solution with structure group isomorphic to Thompson's group
$F$.
