Propositional logic

Txhais kom meej lub sij hawm "propositional logic", nws yog tsim nyog los nkag siab kom meej meej li cas yog ib tug "ntaub ntawv".

Yog li ntawd, cov nqe lus no yog ib tug kab lus, Ranked grammatically tseeb, thiab yog tsis muaj tseeb los yog muaj tseeb. Qhov no notion yuav tsum qhia ib tug tej yam ntsiab lus. Piv txwv li, cov kab lus "canary noog muaj ib tug" muaj xws li cov nram qab no Cheebtsam: "canary" thiab "noog".

Uas yog vim li cas ib tug ntawm cov tseem ceeb thawj cov ntsiab lus ntawm logic thiab yog hais tias. Cov tswv yim yuav tsum piav qhia txog ib tug hais li nyob rau hauv uas lub ntsiab lus yog tog twg los ib yam dab tsi los yog tsis kam muab.

Nws yog suav hais tias yuav tsum muaj ib tug yeej muaj tseeb daim ntawv qhia, yog hais tias tus twb tsis siv kab kev muaj tiag ntawm qhov teeb meem no thaum nws yog circumscribing. By lawv tus kheej, "cuav" thiab "muaj tseeb" txiav txim qhov tseeb ntawm cov nqe lus.

Propositional logic muaj tej yam yooj yim thiab complex kab zauv. Yog li ntawd, cia li xav hais tias cov nqe lus uas tsis muaj nyob rau hauv nws muaj pes tsawg leeg lwm kab zauv. Thiab mus rau lub complex muaj xws li kab zauv uas yog derived ntawm ib tug yooj yim, txawj kev cob cog rua cov nqe lus.

Classical propositional logic yuav sawv cev los ntawm cov kev tshawb xav ntawm txiav. Nws yog hais tias ib feem ntawm logic, uas piav tsis yog nyob ntawm seb cov nqe lus ntawm cov zajlus kom kev twb kev txuas ntawm tej yam yooj yim cov kab zauv.

Tsis hais lub conjunctions - ib tug yooj yim lub taub Tawvv tau los ntawm combining ob yooj yim kab zauv siv lo lus "thiab". Qhov tseeb ntawm qhov tau tshawb kom paub tseeb tias tag nrho cov nqe lus muaj nyob rau hauv nws cov qauv. Nyob rau hauv lub rooj plaub uas tsawg kawg yog ib tug ntawm cov tswv cuab ib tug tsis muaj tseeb, tag nrho cov tau yog ib tug kos npe rau ntawm "ib tug dag."

Nws tus kheej yog ib tug tau mus rau txoj cov nqe lus, uas yog raws li nyob rau hauv cov kev xav:

- tej kev qhia (thiab yooj yooj yim thiab complex) yuav tsum yog muaj tseeb los yog cuav;

- qhov tseeb ntawm lub complex utterances nyob ntawm qhov tseeb ntawm cov nqe lus muaj nyob rau hauv nws thiab cov zajlus kom mus nyob rau hauv nws.

Thaum uas txuas ob nqe lus siv lo lus "los yog" yog twb tau lub disjunction. Nyob rau hauv lub neej txhua hnub, cov tswvyim no yuav tau saib los ntawm lub foundations ntawm ob peb lub ntsiab. Ua ntej, nws yog uas tsis yog-kom kev txiav txim zoo, uas txhais tau tias qhov tseeb ntawm kev hais lus, tsis hais txog ntawm qhov muaj tseeb tiag qhia ntawm ib tug ntawm ob los yog lawv cov neeg ntawm lub ob. Ob txhais, xa lub siab asserts tias ib tug ntawm cov kab zauv yog muaj tseeb tiag, thiab rau lwm yam - yog tsis muaj tseeb.

Propositional qauv muaj tus cim tshwj xeeb. Yog li, nyob rau hauv lub disjunction cim V ntawd hais tias cov kev qhia no yeej muaj tseeb yog hais tias tus tseeb ntawm tsawg kawg yog ib tug ntawm cov nqe lus, thiab tsis tseeb yog tias tag nrho ob qho nws tsis muaj tseeb chaw mos.

Nyob rau hauv kev txiav txim implication muaj lub assertion uas yog lub hauv paus cov nqe lus yuav tsis tau tseeb rau cov tsis ncaj ncees lawm kev tshawb nrhiav. Nyob rau hauv lwm yam lus, cov tswvyim no implies dependence tseeb los yog falsity ntawm cov kev qhia ntawm tus nqi ntawm nws cov Cheebtsam thiab cov hau kev ntawm lawv kev sib raug zoo.

Txawm tias muaj tseeb hais tias cov implication yog heev pab tau rau tej hom phiaj, nws yog tsis heev raws li cov pa nkag siab txog ntawm kev sib txuas lus nyob rau hauv feem ntau. Yog li ntawd, thaum nws puag ncig lub ntaus ntawv ntau ntawm cov tseem ceeb nta ntawm cov zajlus kom coj tus cwj pwm ntawm cov nqe lus muab tswvyim tej zaum yuav tsis yog ib qho kev txaus hauj lwm ntawm nws.

Propositional logic tswj daws xws li ib tug central ua hauj lwm, raws li cov kev sib cais ntawm muaj tseeb thiab tsis yog circuits kev xav thiab systematization thawj. Yuav kom tau txais txoj cai tshwm sim, koj yuav tsum ua kom pom tseeb rau hauv lub cim tshwj xeeb uas yuav sawv cev rau ib tug los yog lwm daim ntawv. Li no qhia kev txaus siab nyob rau hauv xws seemingly insignificant lus xws li "los yog", "thiab," etc.

Logic nqe lus txawm nws muaj nws tus kheej cov lus, muaj raws ntawm cov nram qab no hais:

- tus thawj cim - variables, zajlus kom constants, thiab kev cim;

- cov qauv.

Rau ib tug zoo kev nkag siab txog tej yam tau hais tias koj yuav tsum mus rau kev piv txwv. Piv txwv li, lub tau siv lub cim &, disjunction - \ / los yog \ º /.