conic Lagrangian submanifold with boundary

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I'm reading through the paper "Lagrangian Intersection and the Cauchy Problem" by Melrose and Uhlmann, and I'm having trouble with the definition of intersecting pair of Lagrangian manifolds.

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I am aware of the definition of conic Lagrangian manifold, but what is a conic Lagrangian manifold with boundary? Do we require the boundary to be isotropic or is it that if a conic Lagrangian submanifold has boundary then the boundary is always isotropic, or do we just define it to be such that the interior is a conic Lagrangian submanifold?