Holomua Lālā paʻa hōʻailona helu. hōʻailona helu o ke kūpili. Oihana mua o ka makemakika ke kūpili

I keia la o ka honua mākou i increasingly hoʻohana i keʻano o nā machines a me nā Hāmeʻa. Aʻaʻole wale ia ia ka pono i ka pili literally kupaianaha maoli ikaika: ka neʻeʻana i ka haawe ana, e hoala mai au ia ia i ke kiʻekiʻe, mahi lōʻihi a me ka hohonu hale kaʻa, etc. Uhane i keia la ohi robots, ai ua moʻa Multivarki a me kula haʻahaʻaa makemakika hoʻomaulia paka m'kini helu ... More a oi pinepine mākou i lohe i ka hopuna'ōlelo "Lālā paʻa hōʻailona helu". Paha ua hiki mai ka manawa e maopopo i ke kūlana o ke kanaka i loko o ka hanaia ana o robots a me machines ka hiki e hoʻoponopono i ole wale makemakika, akā, i Logical pilikia.

kūpili

Ma Greek kūpili - he kauoha nenoaiu o ka manaʻo e hana i ka pilina ma waena o ka haawi aku ana, a e leie aku oe i ka e kuhi ka nānā 'ana ma luna o nā mea mahuʻi a me nā koho. Muli o kona kulana pinepine, ua noi aku kekahi i kekahi: "He Logical i" ka pane hōʻoia ana mākou nā mea mahuʻi paha criticizes i ka huakaʻi o ka manaʻo. Akā, i ke kaʻina hana 'aʻole e pau ana ma laila: mākou e hoʻomau e kamaʻilio.

I kekahi manawa, i ka helu o nā kūlana (hoʻokomo o) ka nui, a me ka pilina ma waena o ia mea ai i hookahuli ai a me ka luna 'ia ke kanaka lolo mea,ʻaʻole hiki iā "hōʻuluʻulu" a pau ma kahi hoʻokahi. Oe i Pono no i ka naʻauao o ka mea e hanaia aku ma mua o hoʻokahi mahina (hebedoma, makahiki). Akā, ke kālā no ke ola, aole ia e hāʻawi iā mākou i kēia manawaʻanuʻu e e hoʻoholo. A mākou Hawaii i ke kokua ana o kamepiula 'ē aʻe. A me ia mea iʻaneʻi i ka mea, he hōʻailona helu a me ke kūpili, a me kona kānāwai a me ka waiwai. Ma hope o ka hoʻoiliʻana a pau o ka palapala ikepili, ke ae i ke kamepiula, e ike i ka pili ma, e hoʻopauʻokoʻa, a no ka loaʻa i ke kupono pāʻoihana.

Makemakika a me ke kūpili

Famous Gotfrid Vilgelm Leybnits ua kālaiʻia i ka manaʻo o "makemakika kūpili", i hana, ua oluolu i ka maopopo wale heʻuʻuku pōʻai o ka poʻe puni hoʻonaʻauao. O ka pau hoihoi o ke kuhikuhi i ole i, a me ka waena o ka XIX kenekulia o ka makemakika kūpili ikeia ma ka poʻeʻuʻuku.

Ua nui ka hoihoi i loko o ka 'epekema kaiāulu ua kena ae la i kekahi hoopaapaa ma i ka Pelekāne Dzhordzh Bula hai mai i kona manao, e hookupaa aku i kekahi lālā o ka makemakika,ʻaʻole ka loaʻaʻohe mea hiki ana. E like me ka ua i mai ka mōʻaukala, i kēia manawa 'Imi ulu hanalima-i? Iecaianoaaiiuo, ua nui nā' ano o nā kākoʻo machines, ua i 'ole. E. All scientific discoveries he mea hiki kohoʻia.

Ke huli nei mua, ke i aku nei au i ka holomua Lālā paʻa hōʻailona helu - ka loa hoʻohana 'ia i loko o ke ao nei i keia la kekahi hapa o ka makemakika. No laila, i kou manaʻo hoʻopiʻi Buhl nalowale.

Dzhordzh Bula

Ke kanaka o ka mea kākau hewaʻiʻo kūikawā noonoo. Pela hoi, aole i haawiia mai ka mea i loko o ka hala kanaka la i mua o kākou, no ka mea, e kaulana e ia i loko o nā makahiki 16 o John. Buhl ao mai la ia ma ke kula kauhale, a me ka 20 makahiki wehe i kona mau kula ma Lincoln. Mathematician e akakaʻi ke kahu moku elima'ōlelo'ē, a me kona mau hoʻokoe manawa, i ka heluhelu i nā hana o Newton a me Lagrange. A me keia a pau - ma luna o ke keiki a ka maʻamau limahana o!

I ka makahiki 1839, Buhl hoouna mai i kona mau mua scientific na pepa ma ka Kamepelika makemakika Pai. Nä känaka 'epekema huli 24 makahiki. Boole ka hana mea ai pili lālā o ka Royal Society, ma ka makahiki 1844, ka mea loaa i ka mekala no kona makana i ka hooulu ana o ka makemakika Ka Ikepili. i ho'ākāka 'ia ma kekahi mau paʻi palapala ma i na kumu o ka makemakika kūpili, makemakika aeia ka mea'ōpiopio, e lawe i ke kia o Kumu i loko o ka College o Cork Kalana. ole ke hoole ia i ka hoʻonaʻauao loa Boole ua.

manaʻo

I ka rula, Lālā paʻa hōʻailona helu o loa mea. Aia nā māmala'ōlelo e hōʻike ana (Logical , ka 'aoʻao) i, mai ka wahi o ka Hawaii o ka makemakika, hiki wale nō e ho'ākāka' ia ma ka hua'ōlelo elua: "oiaio" a me "hoopunipuni". No kekahi laʻana, na laau ma ka pūnāwai ua pua i nā - i ka oiaio, ma ke kauwela ia snows - he wahahee. I ka nani o ka makemakika mea ia ia mea,ʻaʻole pololei e pono e hoʻohana wale helu. No ka hōʻailona helu hoopai loa e pono i kekahi olelo me ka hanana manaʻo.

Ke'ī mai, i ka hōʻailona helu o ke kūpili hiki ke hoʻohana literally wahi: ma ka haʻalele 'ana a me ka palapala aʻoʻia, Ka Ikepili o conflicting' ike e pili ana i ka hanana a me ka manao paa o ke kaʻina o nā hana. Ka mea nui wale - e ike i ka mea aole ia i mea pehea mākou ho oholo i ka oiaio a me falsity o māmala'ōlelo e hōʻike ana. Mai kēia mau "pehea" a me "ke kumu" e pono e kāpae'ōlelo. He aha nā nīnau mea wale nō i ka hoakaka ana o ka mea: i ka oiaio o ka wahahee.

O ka ihu, iaaiey i ka manaʻano nui o ka hōʻailona helu o ke kūpili mea i kākau me ka kūpono na hoailona a me nā hōʻailona. A aʻo ia - ka mea, 'o ia hoʻi, e aʻo i ka hou haole' ōlelo. ʻAʻohe mea hiki ole.

Hoʻokumu paʻa manaÿo a me ka wehewehena i

Me ka heleʻana i loko o ka hohonu, mākou e hana me ka terminology. No laila, Lālā paʻa hōʻailona helu presupposes:

• māmala'ōlelo e hōʻike ana;
• Logical ana;
• oihana a me nā kānāwai.

Māmala'ōlelo e hōʻike ana - kekahi affirmative 'aoʻao e hiki ke' ano ua mau-kuaiia. Ka mea, ua kākauʻia ma ka huina (5> 3) a ua kālaiʻia i nā hua'ōlelo (Elephant - ka nui aeaia ieaeiieoa?). Ma keia hihia, ka hopuna'ōlelo "ka giraffe ka ai mea ole" no hoi i ka pono, e ola ana, wale Lālā paʻa hōʻailona helu hoakaka ia me "he wahahee."

All māmala'ōlelo e hōʻike ana e e unambiguous, akā, ka mea, i e walaʻauʻana a me ka hui. Recent hoʻohana Logical pua. E. Ma ka hōʻailona helu māmala'ōlelo e hōʻike ana nā'ōlelo kūpaʻa i huiia i hanaʻia ma ka hou o ke kula haʻahaʻaa kūpili hana.

Holomua Lālā paʻa hōʻailona helu ana

E hoomanao mua i ka hana i loko o ka hōʻailona helu o nā'ōlelo kūpaʻa - Logical. E like me ka hōʻailona helu o nā helu ka hoʻohana 'ana i ka makemakika hana, e hui aku, unuhi, aole hoi e hoohalike helu, makemakika kūpili oihana mua ae e e eiiieaen māmala'ōlelo e hōʻike ana, e hoole paha, e hoʻomaulia i ka hopena hope loa.

Kūpili ana no ka formalization a me ka naau kupono i hoike ma ka haʻilula, maʻa iā mākou ma ka makemakika. Waiwai o Lālā paʻa hōʻailona helu nā helu kaulike e ka mea e hiki ai i ka palapala, a hoÿomaulia i ka IKE OLE IA. Logical hana e ana i kākauʻia e ka oiaioʻaina. Kona oihana mua hoakaka kolamu, a Me hana i ua hana ma luna o ia mau mea, a me na lalani hōʻike i ka hopena o ka ho.

Walaʻauʻana kūpili o ka hana

Ka loa, he pono ole i loko o ka holomua Lālā paʻa hōʻailona helu ana i negation (NOT), a me ka Logical AND a me OR. A he mea hiki ke wehewehe i kokoke a pau na anuu, ma ka hōʻailona helu hoʻoponoʻana. Mākou aʻo i loko o kēlā me kēia au mamuli o na hana ekolu.

Ke negation (ole) ua noi i hoʻokahi wale hehee ai (operand). No laila, ua kapaʻia ka hana he unary negation. E palapala i ka manaʻo o "i A" hoʻohana i ka hōʻailona: ¬A, he ole A !. Ma tabular palapala ia nana e like keia:

I ka hana o ka hōʻole typical o ia i hoakaka: inā A He oiaio, alaila, A - mea wahahee. No ka laʻana, i ka mahina revolves a puni ka Honua - i ka oiaio; Honua revolves a puni ka mahina - he wahahee.

Logical multiplication a me ka hou

Logical AND ana ua kapaia ka ka huipūʻana. He aha aʻole ia ke ano o? Mua, i ka mea hiki ke hoopili ia mau operands, 'o ia hoʻi, au - .. aeaie hana. Ka lua, ia mea wale nō i loko o ka hihia o ka oiaio o nā operands (o A a me B) ua oiaio, a me ka hōʻike iho. Ka nane, "ke ahonui, a me ka wahi kākoʻo 'ana o" hoʻohuʻu i elua wale kumumea ke kōkua i kekahi kanaka Makuakane me na pilikia.

hōʻailona i hoʻohana no ka hoʻopaʻa ': A∧B, A⋅B a A && B.

Ka huipūʻana mea i 'ano like e multiplication ma ka makemakika. I kekahi manawa, a me ka olelo - Logical multiplication. Inā e hoonui i ke kumu o na lalani o ka papaʻaina, kiʻi mākou i ka hopena i like i ka Logical manaʻo.

Disjunction mea he Logical OR hana. He oiaio ina ma ka liʻiliʻi loa kekahi o na olelo, he oiaio (kekahi A a B). Ua Ua palapala e like keia: A∨B, A + B a A || B. ka oiaioʻaina no kēia mau hana a pau:

Disjunction like makemakika hou. Logical hou ana i hoʻokahi wale kapu: 1 + 1 = 1. Akā, ke hoomanao ana i loko o ka mīkini waihona ua kaupalena 'i ka makemakika kūpili 0 a me 1 (kahi 1 - i ka oiaio, 0 - wahahee). No ka laʻana, ke hoakaka "i loko o ka iau 'oe ke' ike i ka masterpiece a loaʻa i ka poʻe maikaʻi" 'o ia hoʻi nā mea e hiki ke ike i na hana o ke akamai, a me ia mea hiki, e halawai me ka hoihoi' kanaka. I ka Ia manawa, mai noho aliʻi mai ka manawa kūpono o i ka wā hoʻokahi hoʻokō i nā hanana.

Oihana a me nā kānāwai

No laila, i ka mea a ka Logical hana hoʻohana Lālā paʻa hōʻailona helu mākou i kāinoa mua. Oihana e wehewehe i nā mea a pau i ka waiwai o na kumu o ka makemakika kūpili, a ua ae mai e Nohie luna 'hui māmala'ōlelo e hōʻike ana. I ka loa a me ka maopopo hemahema hoi ka mea i rejection waiwai o na nā mea loaʻa hana. Ma ka mea, ua maopopo nā mea loaʻa XOR, implication a me ka equivalence. mākou i heluhelu like wale me ka hoʻokumu paʻa hana, a laila, i ka waiwai o kekahi wale noonoo ia.

Associativity 'o ia hoʻi i loko o nā māmala'ōlelo e hōʻike ana e like me "o A a me B, a me B' kaʻina helu o na operands, aole ia i mea. Ua palapala ke haʻilula like penei:

(A∧B) ∧V = A∧ (B∧V) = A∧B∧V,

(A∨B) ∨V = A∨ (B∨V) = A∨B∨V.

E like me 'oe ke ike, i kēia mea,ʻaʻole kū hoʻokahi i ka ka huipūʻana akā, he disjunction.

Commutativity hoʻopaʻapaʻa i ka hopena o ka ka huipūʻana paha disjunction 'aʻole i hilinaʻi'ikamu ma i i noʻonoʻo ma ka outset:

A∧B = B∧A; A∨B = B∨A.

Distributivity apono 'hōʻike brackets ma luna' Logical, ka 'aoʻao. Na rula e like me ka puka parenthesis i loko o ka multiplication a me ka hou ma ka hōʻailona helu:

A∧ (B∨V) = A∧B∨A∧V; A∨B∧V = (A∨B) ∧ (A∨V).

Unit ka waiwai a me ka kūikawā, a hiki e kekahi o na operands mea i like me ka algebraic multiplication ma ka 'Aʻohe paha kekahi, a me ka hou ana o ka pa alima.

A∧0 = 0, A∧1 = A; A∨0 = A, A∨1 = 1.

Idempotency hai mai ia ina kŘpa a elua like operands i ka hopena o ka hana o ka ia, e hiki "kiola" ka oi complicate hoopaapaa ana operands. A me ka ka huipūʻana a me ka disjunction ana i idempotent.

B∧B = B; B∨B = B.

Āpana i apono mai e Nohie i ka helu kaulike. Omo hākālia nō i ka wā o ka 'aoʻao o ua noi ia kekahi operand, kekahi hana me ka ia hehee ai o ka hopena operand ua Komo' o ia hana.

A∧B∨B = B; (A∨B) ∧B = B.

kaʻina o nā hana

Ke kaʻina o nā hana i ka nui. Maoli, e like me ka hōʻailona helu, aia no he makakoho papa e hoʻohana i ka hōʻailona helu Lālā paʻa. Nā papakuhikuhi hiki ke Nohie malalo wale i ka manaʻo nui o ka hana. Kiʻekiʻe o ka loa nui i negligible, ua loaa i ka kēia kaʻina:

1. hōʻole.

2. ka huipūʻana.

3. ka disjunction, XOR.

4. E ka implication, equivalence.

Me oe e ike, wale i ka negation o ka ka huipūʻana, a maiʻaʻole i like makakoho. A makakoho o ka disjunction a me ka XOR e like, e like me na nā makakoho o implication a me ka equivalence.

Oihana o ka implication a me ka equivalence

E like me mākou i mai la, ma ka hou ana i ke kumu o Logical hana, makemakika kūpili a me ka pähola 'ana o algorithms hoʻohana' ana i nā mea loaʻa. He loa pinepine ka implication a me ka equivalence.

Ke implication a Logical no - i kēia'ōlelo, ma i kekahi hana o ke ana, a me ka mea 'ē aʻe - i ka hopena o kona manaʻo. Ma na olelo e ae, i kēia manaʻoi hāpai 'ia me ka pretext o "ina ... laila". "Ma hope o kaʻaina ahiahi hele mai i ka helu." E. No ka hoʻokukeʻana e e puakai ma ka maa aku ai i puʻu. Inā he mea ole makemake e hoʻoneʻe i lalo, mai ka mauna mai, a laila, kauo i ka maa aku ai i mea e pono. Ua palapala ai: A → B a A⇒B.

Equivalence hoʻohuʻu i ka upena ia ia lŘlŘ wale ka wā nā operands he oiaio. No ka laʻana, po, oia ke ala a hiki i ka lā laila (a wale laila), i ka wa a ka lā ma luna o ka moana lipolipo. Ma ka 'ōlelo o ka makemakika kūpili o keia olelo ua palapala like A≡B, A⇔B, A == B.

Other kānāwai o Lālā paʻa hōʻailona helu

Hōʻailona helu hoopai ana e hoʻomōhala ai, a me na mea he nui piliʻepekema e formulate hou kānāwai. Ua kaulana loa i manaoia postulates Hawaiian mathematician O. De Morgan. He i kekahi, a haawi mai la i ka wehewehena o ka waiwai i pili negation, hou a me ka papalua io.

Close hōʻole paipai i mua o ka parenthesis mea ole e hoole ana:ʻaʻole (A a B) = i A a me B. NOT

I ka wā o ka operand ua hooleia, nānā 'ole o kona waiwai, e olelo aku no hou:

B∧¬B = 0; B∨¬B = 1.

A eia ka mea hope, o ka waʻa negation iho compensates. Ie mua kekahi operand negation ke kino a koe hoʻokahi wale nō.

Pehea e hoʻoponopono i ho'āʻo ai i

Kūpili hoʻohuʻu simplification hoʻoholo ma mua nā helu kaulike. Iki e like ma ka Lie hōʻailona helu, ia mea pono e maximally kōkua mua ana (e pakele o ka huikau hoʻokomo o ana, a me ia), a laila, hoʻomaka e kakali ana no ka pane pololei.

He aha e hana ai i Nohie? Hoohuli i na nā mea loaʻa i loko o ka mea hana. A laila, wehe i na brackets (a Hope versa, e e na brackets e ho'ēmi i keia hehee ai). I kekahi anu u E e, e hoʻohana Lālā paʻa hōʻailona helu waiwai ma ka hoʻomaʻamaʻa (omo waiwai 'Aʻohe a me kekahi, a me ka' ole.).

Ultimately, ka helu kaulike e komo i ka palena iki helu o unknowns, hui me na mea hana. Ke easiest ala, e nana aku i ka pāʻoihana, ina oe e he nui helu o ka pili maikaʻi 'ole. A laila, e pukaaniani i ka pane like ina e iho.