{"id":"W2012135231","doi":"10.1093/jigpal/jzi021","title":"The Complexity of Propositional Proofs with the Substitution Rule","year":2005,"lang":"en","type":"article","venue":"Logic Journal of IGPL","topic":"Advanced Algebra and Logic","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematical proof; Substitution (logic); Propositional calculus; Computer science; Mathematical economics; Mathematics; Programming language","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":true,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004064605,0.00006803662,0.0001044276,0.00002315645,0.0002708054,0.00004373703,0.0006456665,0.00001950379,0.000008011687],"category_scores_gemma":[0.00002388843,0.00002619582,0.00005591822,0.0001550219,0.0004500614,0.0003055136,0.00005096695,0.0001811499,0.000005041429],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003200751,"about_ca_system_score_gemma":0.00009349699,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":9.061866e-7,"about_ca_topic_score_gemma":0.000008502916,"domain_scores_codex":[0.999171,0.00007090237,0.0002185669,0.00007462053,0.0003299727,0.0001349094],"domain_scores_gemma":[0.9991501,0.00008322257,0.000337798,0.000173887,0.0002203833,0.00003462107],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00003128361,0.00005129995,0.00003726607,0.000002377924,0.00001368452,0.000006756498,0.0001185603,0.00163833,0.0003758127,0.9889718,0.0001555005,0.008597283],"study_design_scores_gemma":[0.0008827207,0.000901084,0.0241567,0.00005944919,0.00002439776,0.001339535,0.0001288093,0.004379199,0.005975223,0.9502535,0.01172777,0.0001716137],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03452084,0.00122652,0.9192373,0.0310807,0.0001778354,0.0001864476,0.000001391364,0.00001960486,0.01354943],"genre_scores_gemma":[0.9630523,0.00002205709,0.03644745,0.0002816265,0.0001443757,0.000001640536,2.420225e-7,0.000001725143,0.00004856272],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9285315,"threshold_uncertainty_score":0.2082843,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0285264946244958,"score_gpt":0.2501613741698497,"score_spread":0.2216348795453539,"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."}}