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We propose a novel approach for answering and explaining multiple-choice science questions by reasoning on grounding and abstract inference chains. This paper frames question answering as an abductive reasoning problem, constructing plausible explanations for each choice and then selecting the candidate with the best explanation as the final answer. Our system, ExplanationLP, elicits explanations by constructing a weighted graph of relevant facts for each candidate answer and extracting the facts that satisfy certain structural and semantic constraints. To extract the explanations, we employ a linear programming formalism designed to select the optimal subgraph. The graphs' weighting function is composed of a set of parameters, which we fine-tune to optimize answer selection performance. We carry out our experiments on the WorldTree and ARC-Challenge corpus to empirically demonstrate the following conclusions: (1) Grounding-Abstract inference chains provides the semantic control to perform explainable abductive reasoning (2) Efficiency and robustness in learning with a fewer number of parameters by outperforming contemporary explainable and transformer-based approaches in a similar setting (3) Generalisability by outperforming SOTA explainable approaches on general science question sets.