Dr Quickly: That's not a sandwich.
Rabot: Sure it is, a soft tortilla tuna salad roll. Part of our "try our many sandwiches" promotion.
Dr Quickly: BAH!
Dr Quickly: Bring me a REAL sandwich!
<< SPLUT >>
Rabot: A "pizza pocket"!
Dr Quickly: NO!!
Rabot: A crimped shut grilled cheese on white rye.
Dr Quickly: That's great!
Rabot: Open-face PB&J...
Dr Quickly: Also excellent! Set it down!
Rabot: Okay I give up! What's your heuristic for sandwichness?!
Dr Quickly: A sandwich is "filling between"!
Dr Quickly: It doesn't have to be between slices of bread, either! A Bar Harbor Bar is a perfectly good sandwich! Mmm, cookies and ice cream. What a treat!
Dr Quickly: Calzone, panzerotti, stromboli, dumplings, pasties, and patties are all folded shut from a single sheet. They're all "filling inside", or stuffed, or rolled. Rolls and wraps are the same, just without being sealed shut.
Dr Quickly: But you can make a great sandwich out of two slices of pizza!
Dr Quickly: Sandwiches that become closed containers during the cooking process, like the crimped grilled cheese, still started out as proper sandwiches. A deep-fried Monte Cristo is still a sandwich, too.
Dr Quickly: Open face and double-decker sandwiches are degenerate special cases that prove the rule of Filling Between. Open face sandwiches have an implied top layer. Double-decker (and larger) sandwiches have an atypical filling.
Rabot: Something in the space separating two planes. From that... all sandwiches follow logically!