What are monotonic and non monotonic access structures in ABE ? While reading Attribute Based Encryption Schemes, I did not quite understand what a monotonic access structure or non monotonic access structures are. 

Is there a popular explanation of those terms ? any references ?
My understanding of this is as follows:


Monotonic access structure: if $\mathbb{A}$ is a set of attributes satisfying an access structure $T$, then any $\mathbb{A}'$ such that $\mathbb{A} \subset \mathbb{A}'$ also satisfies $T$. For example, consider $T = A \cap B$, then both $\mathbb{A}=\{A,B\}$ and $\mathbb{A}'=\{A,B,C\}$ satisfy $T$. 
Non-monotonic access structure: there exists $\mathbb{A}'$ such that $\mathbb{A} \subset \mathbb{A}'$ and $\mathbb{A}'$ does not satisfy $T$. For example, consider $T = A \cap \neg C$. Then in the previous example, only $\mathbb{A}$ satisfies $T$.