{"id":"W4285130938","doi":"10.1007/978-981-19-0957-3_3","title":"The Principle of Inclusion and Exclusion","year":2022,"lang":"en","type":"book-chapter","venue":"Texts and readings in mathematics","topic":"History and Theory of Mathematics","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"","keywords":"Inclusion–exclusion principle; Inclusion (mineral); Inclusion and exclusion criteria; Calculus (dental); Mathematics; Philosophy; Sociology; Medicine; Political science; Gender studies; Law; Alternative medicine; Pathology","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.00218412,0.0003637055,0.0007388676,0.0001782839,0.0008518174,0.00002574906,0.0003499535,0.0002557335,0.0003150286],"category_scores_gemma":[0.0003986759,0.0002523343,0.00009893005,0.00004388734,0.0004692199,0.00006207304,0.001944059,0.0005378724,0.000004389318],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009562099,"about_ca_system_score_gemma":0.00004213062,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001849397,"about_ca_topic_score_gemma":0.00001290155,"domain_scores_codex":[0.9980339,0.00004148604,0.0008928502,0.000291028,0.0005131643,0.0002275932],"domain_scores_gemma":[0.9966074,0.001931722,0.000817575,0.0005152528,0.00005289752,0.00007517003],"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":[0.00001598224,0.00007245005,0.000001933581,0.001468503,0.00003446051,0.00001248497,0.007604504,3.042292e-7,0.00005117566,0.9879361,0.0003227864,0.002479254],"study_design_scores_gemma":[0.0002096037,0.00007260767,0.00000108824,0.0007509763,0.00007449524,0.00005374367,0.0001326859,0.0001732723,0.00003115847,0.8029616,0.1953133,0.0002254097],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.03704599,0.005692317,0.0003620633,0.0002732127,0.0003269948,0.001608677,0.00005305509,0.0001175276,0.9545202],"genre_scores_gemma":[0.0255651,0.009401824,0.02295835,0.00007093883,0.0001458912,0.00005770622,0.0000151866,0.0003449509,0.94144],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.1949906,"threshold_uncertainty_score":0.9999929,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02831790964430503,"score_gpt":0.2829817857305972,"score_spread":0.2546638760862922,"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."}}