{"id":"W2101249878","doi":"10.1016/j.apal.2006.04.001","title":"Frege systems for extensible modal logics","year":2006,"lang":"en","type":"article","venue":"Annals of Pure and Applied Logic","topic":"Logic, Reasoning, and Knowledge","field":"Computer Science","cited_by":15,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Propositional calculus; Propositional variable; Equivalence (formal languages); Intuitionistic logic; Well-formed formula; Mathematics; Modal; Modal logic; Calculus (dental); Mathematical proof; Propositional formula; Discrete mathematics; Intermediate logic; Zeroth-order logic; Logical equivalence; Algebra over a field; Computer science; Pure mathematics; Programming language; Multimodal logic; Description 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00312236,0.001215892,0.001334857,0.003370116,0.003287964,0.005654905,0.002692002,0.002384406,0.01504506],"category_scores_gemma":[0.007422471,0.001201193,0.002411744,0.002207228,0.004018527,0.01294173,0.006303594,0.005201523,0.002051838],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003095422,"about_ca_system_score_gemma":0.001290244,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.004108,"about_ca_topic_score_gemma":0.005977805,"domain_scores_codex":[0.9977247,0.0006894135,0.0001901198,0.0004566332,0.0005304146,0.000408727],"domain_scores_gemma":[0.997422,0.001353194,0.000152852,0.0005723532,0.0003533993,0.0001461549],"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":[0.00002654417,0.00001345127,0.00007845601,0.00002693587,0.00001285908,0.00004772773,0.000182111,0.00231523,0.0002675046,0.9873125,0.001100738,0.008615824],"study_design_scores_gemma":[0.000009495286,0.000005246276,0.00002869784,0.00001545682,0.00001062021,0.00002542047,0.00005513742,0.009326467,0.0001935307,0.9865597,0.003757261,0.00001291853],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03250916,0.002635363,0.9155447,0.001775127,0.0003286916,0.0001889629,0.0004456734,0.001386434,0.04518593],"genre_scores_gemma":[0.59272,0.002052156,0.3625562,0.0009312111,0.0005066459,0.00038549,0.001236376,0.0005314735,0.03908055],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01504506,"threshold_uncertainty_score":0.0503307,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04791883066781888,"score_gpt":0.2739468383898415,"score_spread":0.2260280077220226,"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."}}