Synonyms for Responsibility (same or very similar meaning)
WordNet sense 1 (the proper sphere or extent of your activities):
provinceWordNet sense 2 (a form of trustworthiness; the trait of being answerable to someone for something or being responsible for one's conduct):
responsiblenessWordNet sense 3 (the social force that binds you to the courses of action demanded by that force):
duty, obligationFrom the ODE community, based on WordNetadd/edit