{"lemma":"axiom","gloss":"a starting truth accepted for proof","pos":"NOUN","provenance_ids":["adr-0090:domain_seed:2026-05-21"],"definitional_atoms":["starting","truth","proof"],"predicates_invited":["grounds"],"definition_version":1}
{"lemma":"theorem","gloss":"a statement established by proof","pos":"NOUN","provenance_ids":["adr-0090:domain_seed:2026-05-21"],"definitional_atoms":["statement","established","proof"],"predicates_invited":["follows"],"definition_version":1}
{"lemma":"lemma","gloss":"a proved step used by another proof","pos":"NOUN","provenance_ids":["adr-0090:domain_seed:2026-05-21"],"definitional_atoms":["proved","step","proof"],"predicates_invited":["supports"],"definition_version":1}
{"lemma":"proof","gloss":"an ordered demonstration from premises to conclusion","pos":"NOUN","provenance_ids":["adr-0090:domain_seed:2026-05-21"],"definitional_atoms":["ordered","demonstration","conclusion"],"predicates_invited":["supports"],"definition_version":1}
{"lemma":"premise","gloss":"a statement used as a proof starting point","pos":"NOUN","provenance_ids":["adr-0090:domain_seed:2026-05-21"],"definitional_atoms":["statement","starting","proof"],"predicates_invited":["precedes"],"definition_version":1}
{"lemma":"conclusion","gloss":"the statement reached by inference","pos":"NOUN","provenance_ids":["adr-0090:domain_seed:2026-05-21"],"definitional_atoms":["statement","reached","inference"],"predicates_invited":["follows"],"definition_version":1}
{"lemma":"implication","gloss":"a relation where one statement entails another","pos":"NOUN","provenance_ids":["adr-0090:domain_seed:2026-05-21"],"definitional_atoms":["relation","statement","entails"],"predicates_invited":["precedes"],"definition_version":1}
{"lemma":"equivalence","gloss":"a relation where statements entail each other","pos":"NOUN","provenance_ids":["adr-0090:domain_seed:2026-05-21"],"definitional_atoms":["relation","entail","each"],"predicates_invited":["supports"],"definition_version":1}
{"lemma":"contradiction","gloss":"an inconsistency where claims cannot both hold","pos":"NOUN","provenance_ids":["adr-0090:domain_seed:2026-05-21"],"definitional_atoms":["inconsistency","claims","hold"],"predicates_invited":["contrasts_with"],"definition_version":1}
{"lemma":"negation","gloss":"an operator that denies a claim","pos":"NOUN","provenance_ids":["adr-0090:domain_seed:2026-05-21"],"definitional_atoms":["operator","deny","claim"],"predicates_invited":["contrasts_with"],"definition_version":1}
{"lemma":"set","gloss":"a collection treated as one object","pos":"NOUN","provenance_ids":["adr-0090:domain_seed:2026-05-21"],"definitional_atoms":["collection","one","object"],"predicates_invited":["has"],"definition_version":1}
{"lemma":"function","gloss":"a mapping from inputs to outputs","pos":"NOUN","provenance_ids":["adr-0090:domain_seed:2026-05-21"],"definitional_atoms":["mapping","input","output"],"predicates_invited":["causes"],"definition_version":1}
{"lemma":"domain","gloss":"the valid input space of a relation","pos":"NOUN","provenance_ids":["adr-0090:domain_seed:2026-05-21"],"definitional_atoms":["input","space","relation"],"predicates_invited":["belongs_to"],"definition_version":1}
{"lemma":"range","gloss":"the output space produced by a relation","pos":"NOUN","provenance_ids":["adr-0090:domain_seed:2026-05-21"],"definitional_atoms":["output","space","relation"],"predicates_invited":["follows"],"definition_version":1}
{"lemma":"identity","gloss":"a mapping or relation that preserves sameness","pos":"NOUN","provenance_ids":["adr-0090:domain_seed:2026-05-21"],"definitional_atoms":["mapping","preserve","sameness"],"predicates_invited":["supports"],"definition_version":1}
{"lemma":"composition","gloss":"combining mappings in sequence","pos":"NOUN","provenance_ids":["adr-0090:domain_seed:2026-05-21"],"definitional_atoms":["combine","mapping","sequence"],"predicates_invited":["precedes"],"definition_version":1}
