Using ADFs for Inconsistency-Tolerant Query Answering with Existential Rules

We present a new reduction of inconsistency-tolerant query answering to acceptance in ADFs. In particular, we consider knowledge bases (KBs) that use existential rules, and consider common inconsistency-tolerant semantics based on maximal consistent subsets. While reductions of inconsistency-tolerant reasoning to argumentation frameworks have been considered before, we aim to obtain a reduction that reflects the inference structure of the KB on a fine-grained level, so that they can be used to explain query answers on the level of individual inference steps. In particular, in our ADFs, every node corresponds to a fact derived in the chase, and acceptance conditions are used to relate facts using inference rules and integrity constraints. We show that our reduction satisfies rationality postulates, and observe that common semantics of ADFs fail to fully reproduce inconsistency-tolerant query answering with our reduction. We introduce a new semantics as refinement of the preferred semantics, which solves this problem, and analyze the computational complexity of this new semantics in the general and in our case.