Treewidth-Aware Complexity for Evaluating Epistemic Logic Programs

Logic programs are a popular formalism for encoding many problems relevant to knowledge representation and reasoning as well as artificial intelligence. However, for modeling rational behavior it is oftentimes required to represent the concepts of knowledge and possibility. Epistemic logic programs (ELPs) is such an extension that enables both concepts, which correspond to being true in all or some possible worlds or stable models. For these programs, the parameter treewidth has recently regained popularity. We present complexity results for the evaluation of key ELP fragments for treewidth, which are exponentially better than known results for full ELPs. Unfortunately, we prove that obtained runtimes can not be significantly improved, assuming the exponential time hypothesis. Our approach defines treewidth-aware reductions between quantified Boolean formulas and ELPs. We also establish that the completion of a program, as used in modern solvers, can be turned treewidth-aware, thereby linearly preserving treewidth.