If you are obliged by a rule or law you are metaphorically bound by it—that is, you are required to obey it. The idea of binding links the word to its Latin source, ligāre, meaning “to fasten, bind.”
Definition of obliged adjective in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
Obliged typically refers to a moral or legal obligation or responsibility. If you're being followed by an ambulance with its siren on, you are obliged to pull to the side of the road and let it pass.
To compel or require (someone) to do something, as by circumstance or legality: When the power went out, we were obliged to fetch water with a bucket. The contract obliges you to meet the deadline.
OBLIGED definition: 1. to be forced to do something or feel that you must do something: 2. used to thank someone and…. Learn more.
I'd be obliged for the other half. I'm obliged to you for all the trouble you've taken.
Adjective obliged (comparative more obliged, superlative most obliged) Under an obligation to do something.
Obligated and obliged are often confused. Obliged means to be in debt of gratitude because of a favor or service. Obligated means to compel someone to undertake a legal or moral duty.
Again, being obliged to do it unless and until someone else does it will solve the problem only where there is perfect communication.
In summary: The interplay of meaning and axiomatic machine mathematics, captured by the difference between $\models$ and $\vdash$, is a subtle and interesting thing.