See De Morgan algebra in All languages combined, or Wiktionary
Download JSON data for De Morgan algebra meaning in English (3.6kB)
{
"etymology_text": "Named after British mathematician and logician Augustus De Morgan (1806–1871). The notion was introduced by Grigore Moisil.",
"forms": [
{
"form": "De Morgan algebras",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"head": "De Morgan algebra"
},
"expansion": "De Morgan algebra (plural De Morgan algebras)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "English entries with language name categories using raw markup",
"parents": [
"Entries with language name categories using raw markup",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "English terms with non-redundant non-automated sortkeys",
"parents": [
"Terms with non-redundant non-automated sortkeys",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Algebra",
"orig": "en:Algebra",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"examples": [
{
"ref": "1980, H. P. Sankappanavar, “A Characterization of Principal Congruences of De Morgan Algebras and its Applications”, in A. I. Arruda, R. Chuaqui, N. C. A. Da Costa, editors, Mathematical Logic in Latin America: Proceedings of the IV Latin American Symposium on Mathematical Logic, page 341",
"text": "Finally it is shown that the compact elements in the congruence lattice of a De Morgan algebra form a Boolean sublattice.",
"type": "quotation"
},
{
"ref": "2000, Luo Congwen, Topological De Morgan Algebras and Kleene-Stone Algebras: The Journal of Fuzzy Mathematics, Volume 8, Pages 1-524, page 268",
"text": "By a topological de Morgan algebra we shall mean an abstract algebra (A,#x5C;land,#x5C;lor,#x5C;',l) where (A,#x5C;land,#x5C;lor,l) is a de Morgan algebra,",
"type": "quotation"
},
{
"ref": "2009, George Rahonis, “Chapter 12: Fuzzy Languages”, in Manfred Droste, Werner Kuich, Heiko Vogler, editors, Handbook of Weighted Automata, Springer, page 486",
"text": "If (L,#x5C;le,#x7B;⁻#x7D;) is a bounded distributive lattice with negation function (resp. a De Morgan algebra), then (L#x5C;langle#x5C;#x21;#x5C;langleS#x5C;rangle#x5C;#x21;#x5C;rangle,#x5C;le,#x7B;⁻#x7D;) constitutes also a bounded distributive lattice with negation function (resp. a De Morgan algebra); for every r#x5C;inL#x5C;langle#x5C;#x21;#x5C;langleS#x5C;rangle#x5C;#x21;#x5C;rangle its negation #x5C;overline#x7B;r#x7D;#x5C;inL#x5C;langle#x5C;#x21;#x5C;langleS#x5C;rangle#x5C;#x21;#x5C;rangle is defined by (#x5C;overline#x7B;r#x7D;,s)#x3D;#x5C;overline#x7B;(r,s)#x7D; for every s#x5C;inS.",
"type": "quotation"
}
],
"glosses": [
"A bounded distributive lattice equipped with an involution (typically denoted ¬ or ~) which satisfies De Morgan's laws."
],
"hypernyms": [
{
"sense": "Ockham algebra",
"word": "distributive lattice"
}
],
"hyponyms": [
{
"sense": "Kleene algebra",
"word": "Boolean algebra"
}
],
"id": "en-De_Morgan_algebra-en-noun-iLDpBDyM",
"links": [
[
"algebra",
"algebra"
],
[
"bounded",
"bounded lattice"
],
[
"distributive lattice",
"distributive lattice"
],
[
"involution",
"involution"
],
[
"De Morgan's laws",
"De Morgan's laws"
]
],
"raw_glosses": [
"(algebra, order theory) A bounded distributive lattice equipped with an involution (typically denoted ¬ or ~) which satisfies De Morgan's laws."
],
"synonyms": [
{
"word": "de Morgan algebra"
}
],
"topics": [
"algebra",
"mathematics",
"order-theory",
"sciences"
],
"wikipedia": [
"Augustus De Morgan",
"De Morgan algebra",
"Grigore Moisil"
]
}
],
"word": "De Morgan algebra"
}
{
"etymology_text": "Named after British mathematician and logician Augustus De Morgan (1806–1871). The notion was introduced by Grigore Moisil.",
"forms": [
{
"form": "De Morgan algebras",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"head": "De Morgan algebra"
},
"expansion": "De Morgan algebra (plural De Morgan algebras)",
"name": "en-noun"
}
],
"hypernyms": [
{
"sense": "Ockham algebra",
"word": "distributive lattice"
}
],
"hyponyms": [
{
"sense": "Kleene algebra",
"word": "Boolean algebra"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English entries with language name categories using raw markup",
"English eponyms",
"English lemmas",
"English multiword terms",
"English nouns",
"English terms with non-redundant non-automated sortkeys",
"English terms with quotations",
"en:Algebra"
],
"examples": [
{
"ref": "1980, H. P. Sankappanavar, “A Characterization of Principal Congruences of De Morgan Algebras and its Applications”, in A. I. Arruda, R. Chuaqui, N. C. A. Da Costa, editors, Mathematical Logic in Latin America: Proceedings of the IV Latin American Symposium on Mathematical Logic, page 341",
"text": "Finally it is shown that the compact elements in the congruence lattice of a De Morgan algebra form a Boolean sublattice.",
"type": "quotation"
},
{
"ref": "2000, Luo Congwen, Topological De Morgan Algebras and Kleene-Stone Algebras: The Journal of Fuzzy Mathematics, Volume 8, Pages 1-524, page 268",
"text": "By a topological de Morgan algebra we shall mean an abstract algebra (A,#x5C;land,#x5C;lor,#x5C;',l) where (A,#x5C;land,#x5C;lor,l) is a de Morgan algebra,",
"type": "quotation"
},
{
"ref": "2009, George Rahonis, “Chapter 12: Fuzzy Languages”, in Manfred Droste, Werner Kuich, Heiko Vogler, editors, Handbook of Weighted Automata, Springer, page 486",
"text": "If (L,#x5C;le,#x7B;⁻#x7D;) is a bounded distributive lattice with negation function (resp. a De Morgan algebra), then (L#x5C;langle#x5C;#x21;#x5C;langleS#x5C;rangle#x5C;#x21;#x5C;rangle,#x5C;le,#x7B;⁻#x7D;) constitutes also a bounded distributive lattice with negation function (resp. a De Morgan algebra); for every r#x5C;inL#x5C;langle#x5C;#x21;#x5C;langleS#x5C;rangle#x5C;#x21;#x5C;rangle its negation #x5C;overline#x7B;r#x7D;#x5C;inL#x5C;langle#x5C;#x21;#x5C;langleS#x5C;rangle#x5C;#x21;#x5C;rangle is defined by (#x5C;overline#x7B;r#x7D;,s)#x3D;#x5C;overline#x7B;(r,s)#x7D; for every s#x5C;inS.",
"type": "quotation"
}
],
"glosses": [
"A bounded distributive lattice equipped with an involution (typically denoted ¬ or ~) which satisfies De Morgan's laws."
],
"links": [
[
"algebra",
"algebra"
],
[
"bounded",
"bounded lattice"
],
[
"distributive lattice",
"distributive lattice"
],
[
"involution",
"involution"
],
[
"De Morgan's laws",
"De Morgan's laws"
]
],
"raw_glosses": [
"(algebra, order theory) A bounded distributive lattice equipped with an involution (typically denoted ¬ or ~) which satisfies De Morgan's laws."
],
"topics": [
"algebra",
"mathematics",
"order-theory",
"sciences"
],
"wikipedia": [
"Augustus De Morgan",
"De Morgan algebra",
"Grigore Moisil"
]
}
],
"synonyms": [
{
"word": "de Morgan algebra"
}
],
"word": "De Morgan algebra"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.