Yes. Or at least you could in 3rd ed. A Sense of Duty compels you to behave in certain strictly defined ways under certain circumstances -- it restricts your freedom to choose courses of action. A Duty is a service you are required to perform -- in GURPS this is long-term, like being career Army or the guardian of a child. The two can complement each other, but are really not dependent upon or exclusive of each other.
-- Bob
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Then the horns kicked in...
...and my shoes began to squeak.
-- Bob
---------
Then the horns kicked in...
...and my shoes began to squeak.