Humans understand language by extracting information (meaning) from sentences, combining it with existing commonsense knowledge, and then performing reasoning to draw conclusions. While large language models (LLMs) such as GPT-3 and ChatGPT are able to leverage patterns in the text to solve a variety of NLP tasks, they fall short in problems that require reasoning. They also cannot reliably explain the answers generated for a given question. In order to emulate humans better, we propose STAR, a framework that combines LLMs with Answer Set Programming (ASP). We show how LLMs can be used to effectively extract knowledge -- represented as predicates -- from language. Goal-directed ASP is then employed to reliably reason over this knowledge. We apply the STAR framework to three different NLU tasks requiring reasoning: qualitative reasoning, mathematical reasoning, and goal-directed conversation. Our experiments reveal that STAR is able to bridge the gap of reasoning in NLU tasks, leading to significant performance improvements, especially for smaller LLMs, i.e., LLMs with a smaller number of parameters. NLU applications developed using the STAR framework are also explainable: along with the predicates generated, a justification in the form of a proof tree can be produced for a given output.