I actually covered this, long ago, so I'm just going to recap and skip to the end. Debt is of the form "A owes B to C". Where we disagree is that you think that the essence of debt is in the nouns A, B and C, while I think it is the verb, "owes".
Mortgage: A=homeowner, B=cash payment stream, C=bank (in reality C is usually investors via a MBS)
Mob favor: A=mob boss**, B=(ABSTRACT), C=poor shopkepper
Bearer bond: A=bond issuer, B=cash, C=(ABSTRACT)
Dollar: A=(ABSTRACT), B=(ABSTRACT), C=(ABSTRACT)
Ok, but then I can play that game too. "property of asset X by Y" is then:
A = ABSTRACT ; B = X ; C = Y
If I own a house, we can then say that abstractly one owes me a house, and I am enjoying the usage of that debt.
You can make it even more fun, and in fact define property as: A = Y, B = X, C = children:
if I possess a house, then in fact I owe a house to my children or who-ever comes after me when I will die :-)
What defines property then, is the debt I will have towards my children if I die right away (because they will inherit it then).
Once you start emptying a concept from its fundamental characteristics (you call it "abstract") you can just say anything !
What is essential to me in the concept of debt, is that A and B are not abstract, and that punishment of some kind follows if it is not honored. Otherwise it is not distinguishable from other concepts.