  We define a new family of open Gromov-Witten type invariants based on
intersection theory on the moduli space of pseudoholomorphic curves of
arbitrary genus with boundary in a Lagrangian submanifold. We assume the
Lagrangian submanifold arises as the fixed points of an anti-symplectic
involution and has dimension 2 or 3. In the strongly semi-positive genus 0
case, the new invariants coincide with Welschinger's invariant counts of real
pseudoholomorphic curves. Furthermore, we calculate the new invariant for the
real quintic threefold in genus 0 and degree 1 to be 30.
