{"id":"W2137777810","doi":"10.1109/lics.2001.932495","title":"A second-order system for polytime reasoning using Gradel's theorem","year":2002,"lang":"en","type":"article","venue":"","topic":"Logic, Reasoning, and Knowledge","field":"Computer Science","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Bounded function; Order (exchange); Polynomial; Second-order logic; Polynomial hierarchy; Mathematics; Function (biology); Reverse mathematics; Discrete mathematics; Corollary; Class (philosophy); Time complexity; Combinatorics; Algebra over a field; Computer science; Pure mathematics; Description logic; Axiom; Artificial intelligence; Higher-order logic","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003362669,0.0001987612,0.000243917,0.00009941672,0.0003024539,0.0002697339,0.0007096336,0.00009648338,0.000241665],"category_scores_gemma":[0.00006861821,0.0001553467,0.000128131,0.0003930811,0.00003944489,0.0004275393,0.0001751367,0.0000971956,0.0001491565],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009601555,"about_ca_system_score_gemma":0.00003707792,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002260772,"about_ca_topic_score_gemma":0.0000126866,"domain_scores_codex":[0.9985622,0.00005827606,0.0002411892,0.0004735877,0.0001690041,0.0004957927],"domain_scores_gemma":[0.9989478,0.0001394483,0.0001049687,0.0005295052,0.0001408296,0.0001374234],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.000003583796,0.00005234056,0.0001811082,0.00006504964,0.00003356026,0.00001126908,0.001407777,0.00003847051,0.0005966944,0.9883016,0.002706425,0.006602107],"study_design_scores_gemma":[0.0006328626,0.00008039157,0.00006231586,0.00007494076,0.00001545365,0.0001761961,0.0001847278,0.9864447,0.002359486,0.001934948,0.007675793,0.0003581682],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.009273721,0.0005803616,0.8225567,0.0001349461,0.0005944644,0.0003109149,0.000002303931,0.0005630568,0.1659836],"genre_scores_gemma":[0.8630919,0.00000270451,0.128172,0.0001775571,0.0002156785,0.00002007443,9.244864e-7,0.00002018749,0.008298938],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.9864063,"threshold_uncertainty_score":0.6334856,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03144452859730704,"score_gpt":0.2425264978791249,"score_spread":0.2110819692818179,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}