{"paper":{"title":"Causal Resolution of Undefined Answers in Datalog with Negation","arxiv_id":"2611.11756","primary_cat":"cs.DB","submitted_at":"2026-11-09T01:55:11+00:00","version_compiled":"v1"},"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. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"Unstratified negation may leave the answer to a Boolean Datalog query undefined under the well-founded semantics.","hedge":{"p":1.0,"label":"hedged_possibility"},"own_p":0.05,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":0.99,"id":"s1","own":true,"role":"contribution","text":"We study database causality in this setting by asking which fact insertions and deletions realize a prescribed transition and which other changes preserve the observed query answer while making a designated fact pivotal.","hedge":{"p":0.84,"label":"asserted"},"own_p":0.79,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.01,"limitation":0.0,"future_work":0.0,"contribution":0.99,"interpretation":0.0}},{"i":2,"p":0.52,"id":"s2","own":false,"role":"contribution","text":"Such a set of changes to other facts is a contingency for the designated fact and the prescribed transition.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.3,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.19,"result":0.01,"background":0.19,"limitation":0.0,"future_work":0.0,"contribution":0.52,"interpretation":0.09}},{"i":3,"p":0.97,"id":"s3","own":true,"role":"method","text":"Our game representation assigns one shared move to each mutable fact and preserves query values and intervention distances.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.92,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.22,"role_probabilities":{"gap":0.0,"method":0.97,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.03,"interpretation":0.0}},{"i":4,"p":0.83,"id":"s4","own":true,"role":"result","text":"Pairing source and target certificates characterizes all minimum contingencies for the six transitions among true, false, and undefined.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.24,"quantitative":true,"quantitative_p":0.75,"role_probabilities":{"gap":0.0,"method":0.04,"result":0.83,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.13,"interpretation":0.0}},{"i":5,"p":0.82,"id":"s5","own":true,"role":"method","text":"When inserting or deleting a move resolves a draw, a directed tree traces the newly winning and losing positions along alternating paths to the source of that move.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.87,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.08,"role_probabilities":{"gap":0.0,"method":0.82,"result":0.12,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.06,"interpretation":0.0}},{"i":6,"p":1.0,"id":"s6","own":true,"role":"result","text":"For the fixed one-rule win--move program, deciding whether a contingency of size at most $k$ exists is $\\mathrm{NP}$-complete for each transition, even on bounded-degree graphs.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.88,"main_claim_p":0.18,"quantitative":true,"quantitative_p":0.81,"role_probabilities":{"gap":0.0,"method":0.0,"result":1.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":7,"p":1.0,"id":"s7","own":true,"role":"result","text":"Computing the minimum size is $\\mathrm{FP}^{\\mathrm{NP}[\\log]}$-complete, and counting minimum contingencies is $\\#\\mathrm{P}$-hard under polynomial-time Turing reductions.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.86,"main_claim_p":0.17,"quantitative":true,"quantitative_p":0.56,"role_probabilities":{"gap":0.0,"method":0.0,"result":1.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":8,"p":0.81,"id":"s8","own":true,"role":"result","text":"When only one of true and false is reachable, the prime implicants of undefinedness satisfied at the observation cover every undefined state, and their supports induce nonempty subtrees of a common tree, we compute a minimum resolving intervention in polynomial time from the game instance.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.92,"main_claim_p":0.21,"quantitative":false,"quantitative_p":0.45,"role_probabilities":{"gap":0.0,"method":0.03,"result":0.81,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.16,"interpretation":0.0}},{"i":9,"p":0.48,"id":"s9","own":true,"role":"method","text":"From the explicit tree and these implicants, we construct an equally large family of disjoint supports, certifying optimality.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.12,"quantitative":true,"quantitative_p":0.77,"role_probabilities":{"gap":0.0,"method":0.48,"result":0.36,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.14,"interpretation":0.02}}]},"compiled":{"main_claim":{"p":0.44,"text":"When only one of true and false is reachable, the prime implicants of undefinedness satisfied at the observation cover every undefined state, and their supports induce nonempty subtrees of a common tree, we compute a minimum resolving intervention in polynomial time from the game instance.","location":"abstract s8","hedge_strength":{"p":1.0,"label":"asserted"}},"provenance":{"route":{"via":"TypeSafe API","model":"classifier-1.13.0","endpoint":"https://api.typesafe.ai/v1/systemone","provider":"TypeSafe"},"packing":"one request per 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