{"paper":{"title":"Causality and Minimal Supports in Recursive Datalog","arxiv_id":"2607.16443","primary_cat":"cs.DB","submitted_at":"2026-07-17T18:45:49+00:00","version_compiled":"v2"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. 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body.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.44,"main_claim_p":0.07,"quantitative":true,"quantitative_p":0.84,"role_probabilities":{"gap":0.02,"method":0.0,"result":0.23,"background":0.75,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":0.52,"id":"s2","own":false,"role":"gap","text":"For recursive rules, the same answer may depend on large supports, and the number of minimal supports may be exponential in the input.","hedge":{"p":0.51,"label":"asserted"},"own_p":0.36,"main_claim_p":0.14,"quantitative":true,"quantitative_p":0.92,"role_probabilities":{"gap":0.52,"method":0.0,"result":0.1,"background":0.37,"limitation":0.01,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":3,"p":0.67,"id":"s3","own":true,"role":"contribution","text":"We study the gap through deletion-based explanation, using inclusion-minimal endogenous input facts that entail the atom together with fixed background facts.","hedge":{"p":0.95,"label":"asserted"},"own_p":0.89,"main_claim_p":0.11,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.01,"method":0.32,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.67,"interpretation":0.0}},{"i":4,"p":0.46,"id":"s4","own":true,"role":"result","text":"We organize these supports as a hypergraph and prove that it determines actual causes, counterfactual causes, responsibility, and deletion robustness.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.32,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.12,"result":0.46,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.41,"interpretation":0.01}},{"i":5,"p":0.61,"id":"s5","own":true,"role":"interpretation","text":"The resulting view separates nonrecursive queries from recursive Datalog at the level of minimal input 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