Relevance-Driven Evaluation of Modular Nonmonotonic Logic Programs

Modular nonmonotonic logic programs (MLPs) under the answer-set semantics have been recently introduced as an ASP formalism in which modules can receive context-dependent input from other modules, while allowing (mutually) recursive module calls. This can be used for more succinct and natural problem representation at the price of an exponential increase of evaluation time. In this paper, we aim at an efficient top-down evaluation of MLPs, considering only calls to relevant module instances. To this end, we generalize the well-known Splitting Theorem to the MLP setting and present notions of call stratification, for which we determine sufficient conditions. Call-stratified MLPs allow to split module instantiations into two parts, one for computing input of module calls, and one for evaluating the calls themselves with subsequent computations. Based on these results, we develop a top-down evaluation procedure that expands only relevant module instantiations. Finally, we discuss syntactic conditions for its exploitation.