Is the particle entanglement a boolean property? That is, when we consider two given particles, is the answer to the question "are they entangled" always either "yes" or "no" (or, of course, "we are not sure if it's yes or no")? Is there such thing as partial entanglement?
Answer
No, it's not a Boolean property. Entanglement between two quantum systems (could be particles, or anything else) could be partial, and can be quantified using different measures. In the specific example of Bell states, the two systems (each of them with 2 states $|0\rangle$ and $|1\rangle$) are said to be maximally entangled with the entanglement entropy being 1 qubit.
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