The Stable Roommates problem (SR) is characterized by the preferences of\nagents over other agents as roommates: each agent ranks all others in strict\norder of preference. A solution to SR is then a partition of the agents into\npairs so that each pair shares a room, and there is no pair of agents that\nwould block this matching (i.e., who prefers the other to their roommate in the\nmatching). There are interesting variations of SR that are motivated by\napplications (e.g., the preference lists may be incomplete (SRI) and involve\nties (SRTI)), and that try to find a more fair solution (e.g., Egalitarian SR).\nUnlike the Stable Marriage problem, every SR instance is not guaranteed to have\na solution. For that reason, there are also variations of SR that try to find a\ngood-enough solution (e.g., Almost SR). Most of these variations are NP-hard.\nWe introduce a formal framework, called SRTI-ASP, utilizing the logic\nprogramming paradigm Answer Set Programming, that is provable and general\nenough to solve many of such variations of SR. Our empirical analysis shows\nthat SRTI-ASP is also promising for applications. This paper is under\nconsideration for acceptance in TPLP.\n