Recursive rules with aggregation: a simple unified semantics

Abstract Complex reasoning problems are most clearly and easily specified using logical rules, but require recursive rules with aggregation such as count sum for practical applications. Unfortunately, the meaning of has been a significant challenge, leading to many disagreeing semantics. This paper describes unified semantics aggregation, extending founded constraint negation. The key idea is support simple expression different assumptions underlying semantics, orthogonally interpret operations their usual meaning. We present formal definition prove important properties compare prior In particular, we an efficient inference over that gives precise answers all examples have studied from literature. also apply our wide range challenging examples, show matches desired results in cases. Finally, describe experiments on exhibiting unexpectedly superior performance well-known systems when they can compute correct answers.