We consider the problem of finding relevant consistent concepts in a conversational AI system, particularly, for realizing a conversational socialbot. Commonsense knowledge about various topics can be represented as an answer set program. However, to advance the conversation, we need to solve the problem of finding relevant consistent concepts, i.e., find consistent knowledge in the "neighborhood" of the current topic being discussed that can be used to advance the conversation. Traditional ASP solvers will generate the whole answer set which is stripped of all the associations between the various atoms (concepts) and thus cannot be used to find relevant consistent concepts. Similarly, goal-directed implementations of ASP will only find concepts directly relevant to a query. We present the DiscASP system that will find the partial consistent model that is relevant to a given topic in a manner similar to how a human will find it. DiscASP is based on a novel graph-based algorithm for finding stable models of an answer set program. We present the DiscASP algorithm, its implementation, and its application to developing a conversational socialbot.