Causality and Minimal Supports in Recursive Datalog

2026-07-17

AI Summary

In recursive Datalog, minimal supports can grow exponentially, complicating causal explanation and robustness analysis. This work proposes a deletion-based explanation framework that constructs minimal support hypergraphs over endogenous facts, unifying for the first time the structural notion of minimal support with causal semantics and revealing a fundamental distinction between recursive and non-recursive queries at the explanatory level. The core contributions include proving that for positive-length reachability queries, minimal supports correspond precisely to simple directed paths; establishing that minimal support hypergraphs fully determine actual causality, counterfactual causality, responsibility scores, and deletion-based robustness; and showing that, in reachability settings, robustness is equivalent to the size of a minimum directed edge cut, with its threshold decision problem being NP-hard.

Abstract

Recursive rule evaluation can make explanation harder than in nonrecursive query answering. For fixed unions of conjunctive queries, each explanation is bounded by the query body. For recursive rules, the same answer may depend on large supports, and the number of minimal supports may be exponential in the input. We study this gap through deletion-based explanation, using inclusion-minimal endogenous input facts that entail the atom together with fixed background facts. We organize these supports as a hypergraph and prove that it determines actual causes, counterfactual causes, responsibility, and deletion robustness. The resulting view separates nonrecursive queries from recursive Datalog at the level of minimal input explanations. For positive-length reachability, minimal supports are exactly simple directed paths, and deletion robustness is the minimum directed edge cut. We also prove invariance under fixed-goal equivalent positive Datalog programs and an NP-hardness calibration for the robustness threshold problem.

Problem

• causality
• minimal supports
• recursive Datalog
• explanation
• deletion robustness

Innovation

• recursive Datalog
• minimal supports
• deletion-based explanation
• causality
• deletion robustness