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<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/abstract>	"Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations between propositions, including the construction of arguments based on them. Compound propositions are formed by connecting propositions by logical connectives. Propositions that contain no logical connectives are called atomic propositions. Unlike first-order logic, propositional logic does not deal with non-logical objects, predicates about them, or quantifiers. However, all the machinery of propositional logic is included in first-order logic and higher-order logics. In this sense, propositional logic is the foundation of first-order logic and higher-order logic."@en .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://www.w3.org/2000/01/rdf-schema#comment>	"La l\u00F2gica proposicional \u00E9s una branca de la l\u00F2gica cl\u00E0ssica que estudia les proposicions o sent\u00E8ncies l\u00F2giques, les seves possibles avaluacions de veritat i, en el cas ideal, el seu nivell absolut de veritat. Les seves constants l\u00F2giques, anomenades connectives l\u00F2giques, representen operacions sobre proposicions, capaces de formar altres proposicions de complexitat superior."@ca .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://www.w3.org/2000/01/rdf-schema#comment>	"Kalkulus proposisional adalah sistem formal untuk menyatakan dan membuktikannya dengan cara menggabungkan dan operator logika. Beberapa contoh operator logika adalah: \n* (negasi) \n* (konjungsi) \n* (disjungsi) \n* (implikasi) \n* (ekuivalensi)"@in .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/abstract>	"Logika proposizionala, proposizioak eta horiek lotzen dituzten lokailuak osagaitzat hartzen dituen bat da. Logika proposizionalean \"hizkuntza\" edo proposizio konplexuak, proposizioak beraien artean lokailuen bitartez lotuz osatzen da. Premisa izeneko proposizio multzo batetik logikaz erator daitekeen ondoriozko proposiziora heltzea du helburu logika proposizionalak. Logika-sistema guztiak bezalaxe, logika proposizionalak ez du aztertzen proposizio bat errealitatean egiazkoa edo faltsua den, beste proposizioetatik deduzitzeko baliatu den prozesu logikoa edo argumentua zuzena den baizik. Logika proposizionala XIX. mendearen amaieran asmatu zuen Charles Sanders Peirce filosofoak eta XX. mendearen hasieran Ludwig Wittgenstein filosofoak osatu zuen, liburuan. Zehatzago, logika proposizionalak proposizio atomiko edo bakunak egiazkoak edo faltsuak diren hartzen du kontuan, ondoren egia-taula izenekoen bitartez proposizio konplexuen egia-balioa aztertzeko: proposizio bakunen egia-balio guztietarako proposizio konplexua egia bada, proposizio konplexua tautologia dela esaten da; proposizio bakunen egia-balio guztietarako proposizio konplexua faltsua bada, kontraesana izango da eta proposizio konplexuaren egia-balioa batzuetan egia eta beste batzuetan faltsua bada, orduan argumentua sendoa da kasu batzuetan. Aldi berean, logika proposizionalak inferentzia edo argumentuak deduzitzeko erregelak ematen ditu, proposizio bakun edo konplexuen multzo batetik deduzituz: premisak (proposizio atomikoak edo konposatuak) egiazkoak direnean, ondorioa egiazkoa bada, argumentua zuzena izango da. honetan bereizten da, logika proposizionala proposizio atomikoak egia eta gezurra izateko modu ezberdinak zehazten dituen arren, erabiltzen diren inferentzia aurauen arabera, logika modala egia modalitate ezberdinetik lan egiten du, egia absolutua, eta egia erlatiboa. Logika proposizionalak proposizio konplexuei egia eta faltsua balioez gainera, tarteko balioak ere esleitzen dizkio, inferentzia arauek proposizio atomikoen modu ezberdinak garatzen dituztenean. Adibidez, \"Jon altua da\" eta \"altuek azterketa aprobatzen dute\" proposizio atomikoek egiazkoak dira, baina subjektiboak, eta horrela proposizio konplexua eratzean logika proposizionalak, tarteko balioak izango ditu, \"Jon altua da eta azterketa aprobatuko du\" propiszioak probabilitate bat izan dezakeelako egia izateko."@eu .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://www.w3.org/2000/01/rdf-schema#comment>	"Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations between propositions, including the construction of arguments based on them. Compound propositions are formed by connecting propositions by logical connectives. Propositions that contain no logical connectives are called atomic propositions."@en .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/abstract>	"Satslogiken \u00E4r ett formellt logiskt system med v\u00E4ldefinierad syntax, avsett att symboliskt hantera spr\u00E5kliga satser, vilka uttrycker p\u00E5st\u00E5enden, och fr\u00E5n dessa med giltiga slutledningar, dra slutsatser. Att det satslogiska systemet \u00E4r formellt, inneb\u00E4r att dess teori, regler och definitioner inte h\u00E4nvisar till symbolernas eller de spr\u00E5kliga uttryckens betydelser, utan endast till relationer mellan de symboler av vilka de spr\u00E5kliga uttrycken \u00E4r uppbyggda. Satslogikens logiska syntax inneh\u00E5ller en systematisk framst\u00E4llning av giltiga slutledningsregler.Till grundl\u00E4ggarna av den formella logiken, s\u00E4rskilt satslogiken, r\u00E4knas George Boole, Gottlob Frege och Bertrand Russell. I vardagsspr\u00E5ket anv\u00E4nds en m\u00E4ngd olika ord f\u00F6r att sammanbinda (\"connect\") satser. Dessa ord kallas konnektiv. I satslogiken \u00E4r konnektiven v\u00E4ldefinierade och de fem, som f\u00F6retr\u00E4desvis anv\u00E4nds \u00E4r: icke, och, eller, om... s\u00E5... och om och endast om. Symbolerna f\u00F6r dessa uttryck \u00E4r respektive och . P\u00E5st\u00E5enden i form av atom\u00E4ra satser eller elementarsatser, betecknas med en bokstav. Den implikation, som f\u00F6rekommer i satslogiken och som symboliseras med tecknet, , \u00E4r en s\u00E5 kallad materiell implikation, vars inneb\u00F6rd ofta missf\u00F6rst\u00E5s. Det f\u00F6rtj\u00E4nar att p\u00E5pekas att satsen: om p s\u00E5 q, och som skrivs p q, inte \u00E4r en implikation i den bem\u00E4rkelsen att det skulle r\u00E5da n\u00E5got logiskt eller kausalt samband mellan p och q. Den kan heller inte tolkas s\u00E5, att q kan h\u00E4rledas fr\u00E5n p. Att en sats materiellt implicerar en annan, betyder i satslogiken endast att det icke \u00E4r s\u00E5, att den f\u00F6rsta satsen \u00E4r sann och den andra falsk. Emil L. Post visade att det satslogiska systemet PS med spr\u00E5ket P \u00E4r semantiskt fullst\u00E4ndigt. S\u00E5ledes \u00E4r varje tautologi A, i spr\u00E5ket P ett teorem i systemet PS, vilket symboliskt kan uttryckas enligt f\u00F6ljande: Om s\u00E5 .. Satslogiken har formaliserats till algebraisk kalkyl i den Booleska algebran."@sv .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/abstract>	"La logica proposizionale (o enunciativa) \u00E8 un linguaggio formale con una semplice struttura sintattica, basata fondamentalmente su proposizioni elementari (atomi) e su connettivi logici di tipo vero-funzionale, che restituiscono il valore di verit\u00E0 di una proposizione in base al valore di verit\u00E0 delle proposizioni connesse (solitamente noti come AND, OR, NOT...). La semantica della logica proposizionale definisce il significato dei simboli e di qualsiasi proposizione che rispetti le regole sintattiche del linguaggio, basandosi sui valori di verit\u00E0 associati agli atomi. Data una interpretazione (o modello) di una proposizione (in generale di un insieme di proposizioni), e cio\u00E8 una associazione tra le proposizioni elementari e le realt\u00E0 rappresentate, possiamo generare un insieme infinito di proposizioni con significato definito che riguardino quella realt\u00E0. Ciascuna proposizione si riferisce quindi a uno o pi\u00F9 oggetti della realt\u00E0 rappresentata (anche astratta, ovviamente) e permette di descrivere o ragionare su quell'oggetto, utilizzando i due soli valori \"Vero\" e \"Falso\"."@it .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://www.w3.org/2000/01/rdf-schema#comment>	"Em l\u00F3gica e matem\u00E1tica, uma l\u00F3gica proposicional (ou c\u00E1lculo sentencial) \u00E9 um sistema formal no qual as f\u00F3rmulas representam proposi\u00E7\u00F5es que podem ser formadas pela combina\u00E7\u00E3o de proposi\u00E7\u00F5es at\u00F4micas usando conectivos l\u00F3gicos e um sistema de regras de deriva\u00E7\u00E3o, que permite que certas f\u00F3rmulas sejam estabelecidas como teoremas do sistema formal. A linguagem de um c\u00E1lculo proposicional consiste em: Uma f\u00F3rmula bem formada (fbf) \u00E9 qualquer f\u00F3rmula at\u00F4mica ou qualquer f\u00F3rmula que pode ser constru\u00EDda a partir de f\u00F3rmulas at\u00F4micas, usando conectivos de acordo com as regras da gram\u00E1tica."@pt .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://www.w3.org/2000/01/rdf-schema#comment>	"De propositielogica is een tak van logica die zich bezighoudt met het redeneren met proposities. Proposities zijn uitspraken of beweringen die ofwel waar, ofwel onwaar zijn. Voorbeelden hiervan zijn De Winkler Prins is een encyclopedie en Wicky heeft een noormannenhelm op. In de propositielogica kunnen uitspraken alleen waar of onwaar zijn, dit in tegenstelling tot meerwaardige logica's waarbij uitspraken ook andere waarden kunnen hebben. In vergelijking met andere types van logica is de propositielogica eenvoudig van opbouw (structuur, grammatica) maar beperkt in uitdrukkingsmogelijkheid."@nl .
<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/abstract>	"Kalkulus proposisional adalah sistem formal untuk menyatakan dan membuktikannya dengan cara menggabungkan dan operator logika. Beberapa contoh operator logika adalah: \n* (negasi) \n* (konjungsi) \n* (disjungsi) \n* (implikasi) \n* (ekuivalensi)"@in .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/abstract>	"Die Aussagenlogik ist ein Teilgebiet der Logik, das sich mit Aussagen und deren Verkn\u00FCpfung durch Junktoren befasst, ausgehend von strukturlosen Elementaraussagen (Atomen), denen ein Wahrheitswert zugeordnet wird. In der klassischen Aussagenlogik wird jeder Aussage ein Element einer Booleschen Algebra als Wahrheitswert zugeordnet. Der Wahrheitswert einer zusammengesetzten Aussage l\u00E4sst sich ohne zus\u00E4tzliche Informationen mittels der Operationen der Booleschen Algebra aus den Wahrheitswerten ihrer Teilaussagen bestimmen."@de .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://www.w3.org/2000/01/rdf-schema#comment>	"Le calcul des propositions ou calcul propositionnel, (ou encore logique des propositions) fait partie de la logique math\u00E9matique. Il a pour objet l'\u00E9tude des relations logiques entre \u00AB propositions \u00BB et d\u00E9finit les lois formelles selon lesquelles les propositions complexes sont form\u00E9es en assemblant des propositions simples au moyen des connecteurs logiques et celles-ci sont encha\u00EEn\u00E9es pour produire des raisonnements valides. Il est un des syst\u00E8mes formels, piliers de la logique math\u00E9matique dont il aide \u00E0 la formulation des concepts . Il est consid\u00E9r\u00E9 comme la forme moderne de la logique sto\u00EFcienne."@fr .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/abstract>	"La l\u00F3gica proposicional, tambi\u00E9n llamada l\u00F3gica de enunciados, l\u00F3gica de orden cero o c\u00E1lculo proposicional, es un sistema formal cuyos elementos m\u00E1s simples representan proposiciones o enunciados, y cuyas constantes l\u00F3gicas, llamadas conectivas l\u00F3gicas, representan operaciones sobre proposiciones, capaces de formar otras proposiciones de mayor complejidad.\u200B Las l\u00F3gicas proposicionales carecen de cuantificadores o variables de individuo, pero tienen variables proposicionales (es decir, que se pueden interpretar como proposiciones con un valor de verdad definido), de ah\u00ED el nombre proposicional. Los sistemas de l\u00F3gica proposicional incluyen adem\u00E1s conectivas l\u00F3gicas, por lo que dentro de este tipo de l\u00F3gica se puede analizar la inferencia l\u00F3gica de proposiciones a partir de proposiciones, pero sin tener en cuenta la estructura interna de las proposiciones m\u00E1s simples.\u200B Como las l\u00F3gicas proposicionales no tienen cuantificadores o variables de individuo, cualquier secuencia de signos que constituya una f\u00F3rmula bien formada admite una valoraci\u00F3n en la proposici\u00F3n es verdadera o falsa dependiendo del valor de verdad asignado a las proposiciones que la compongan. Esto implica que cualquier f\u00F3rmula bien formada define una funci\u00F3n proposicional. Por tanto, cualquier sistema l\u00F3gico basado en la l\u00F3gica proposicional es decidible y en un n\u00FAmero finito de pasos se puede determinar la verdad o falsedad sem\u00E1ntica de una proposici\u00F3n. Esto hace que la l\u00F3gica proposicional sea completa y con una sem\u00E1ntica muy sencilla."@es .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/abstract>	"Em l\u00F3gica e matem\u00E1tica, uma l\u00F3gica proposicional (ou c\u00E1lculo sentencial) \u00E9 um sistema formal no qual as f\u00F3rmulas representam proposi\u00E7\u00F5es que podem ser formadas pela combina\u00E7\u00E3o de proposi\u00E7\u00F5es at\u00F4micas usando conectivos l\u00F3gicos e um sistema de regras de deriva\u00E7\u00E3o, que permite que certas f\u00F3rmulas sejam estabelecidas como teoremas do sistema formal. Em termos gerais, um c\u00E1lculo \u00E9 frequentemente apresentado como um sistema formal que consiste em um conjunto de express\u00F5es sint\u00E1ticas (f\u00F3rmulas bem formadas, ou fbfs), um subconjunto distinto dessas express\u00F5es, e um conjunto de regras formais que define uma rela\u00E7\u00E3o bin\u00E1ria espec\u00EDfica, que se pretende interpretar como a no\u00E7\u00E3o de equival\u00EAncia l\u00F3gica, no espa\u00E7o das express\u00F5es. Quando o sistema formal tem o prop\u00F3sito de ser um sistema l\u00F3gico, as express\u00F5es devem ser interpretadas como asser\u00E7\u00F5es matem\u00E1ticas, e as regras, conhecidas como regras de infer\u00EAncia, normalmente s\u00E3o preservadoras da verdade. Nessa configura\u00E7\u00E3o, as regras (que podem incluir axiomas) podem ent\u00E3o ser usadas para derivar \"inferir\" f\u00F3rmulas representando asser\u00E7\u00F5es verdadeiras. O conjunto de axiomas pode ser vazio, um conjunto finito n\u00E3o vazio, um conjunto finito enumer\u00E1vel, ou pode ser dado por axiomas esquem\u00E1ticos. Uma gram\u00E1tica formal define recursivamente as express\u00F5es e f\u00F3rmulas bem formadas (fbfs) da linguagem. Al\u00E9m disso, pode se apresentar uma sem\u00E2ntica para definir verdade e valora\u00E7\u00F5es (ou interpreta\u00E7\u00F5es). A linguagem de um c\u00E1lculo proposicional consiste em: 1. \n* um conjunto de s\u00EDmbolos primitivos, definidos como f\u00F3rmulas at\u00F4micas, proposi\u00E7\u00F5es at\u00F4micas, ou vari\u00E1veis, e 2. \n* um conjunto de operadores, interpretados como operadores l\u00F3gicos ou conectivos l\u00F3gicos. Uma f\u00F3rmula bem formada (fbf) \u00E9 qualquer f\u00F3rmula at\u00F4mica ou qualquer f\u00F3rmula que pode ser constru\u00EDda a partir de f\u00F3rmulas at\u00F4micas, usando conectivos de acordo com as regras da gram\u00E1tica. O que segue define um c\u00E1lculo proposicional padr\u00E3o. Existem muitas formula\u00E7\u00F5es diferentes as quais s\u00E3o todas mais ou menos equivalentes mas que diferem nos detalhes: 1. \n* de sua linguagem, que \u00E9 a cole\u00E7\u00E3o particular de s\u00EDmbolos primitivos e operadores, 2. \n* do conjunto de axiomas, ou f\u00F3rmulas distinguidas, e 3. \n* do conjunto de regras de infer\u00EAncia."@pt .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/abstract>	"\uBA85\uC81C \uB17C\uB9AC(\u547D\u984C\u8AD6\u7406, \uC601\uC5B4: propositional logic)\uB294 \uB0B4\uBD80 \uAD6C\uC870\uAC00 \uC5C6\uB294 \uBA85\uC81C\uC5D0 \uB17C\uB9AC\uD569\uC774\uB098 \uBD80\uC815 \uB530\uC704\uC758 \uB17C\uB9AC \uC5F0\uC0B0\uC744 \uAC00\uD558\uC5EC \uAD6C\uC131\uD55C \uBA85\uC81C\uB4E4\uC744 \uB2E4\uB8E8\uB294 \uB17C\uB9AC \uCCB4\uACC4\uC774\uB2E4.:30, Chapter 3"@ko .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/abstract>	"Le calcul des propositions ou calcul propositionnel, (ou encore logique des propositions) fait partie de la logique math\u00E9matique. Il a pour objet l'\u00E9tude des relations logiques entre \u00AB propositions \u00BB et d\u00E9finit les lois formelles selon lesquelles les propositions complexes sont form\u00E9es en assemblant des propositions simples au moyen des connecteurs logiques et celles-ci sont encha\u00EEn\u00E9es pour produire des raisonnements valides. Il est un des syst\u00E8mes formels, piliers de la logique math\u00E9matique dont il aide \u00E0 la formulation des concepts . Il est consid\u00E9r\u00E9 comme la forme moderne de la logique sto\u00EFcienne."@fr .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/abstract>	"Rachunek zda\u0144 \u2013 dzia\u0142 logiki matematycznej badaj\u0105cy zwi\u0105zki mi\u0119dzy zmiennymi zdaniowymi (zdaniami) lub funkcjami zdaniowymi, utworzonymi za pomoc\u0105 funktor\u00F3w zdaniotw\u00F3rczych (sp\u00F3jnik\u00F3w zdaniowych) ze zda\u0144 lub prostszych funkcji zdaniowych. Rachunek zda\u0144 okre\u015Bla sposoby stosowania funktor\u00F3w zdaniotw\u00F3rczych w poprawnym wnioskowaniu."@pl .
<http://dbpedia.org/resource/Propositional_calculus>	<http://www.w3.org/2000/01/rdf-schema#comment>	"La logica proposizionale (o enunciativa) \u00E8 un linguaggio formale con una semplice struttura sintattica, basata fondamentalmente su proposizioni elementari (atomi) e su connettivi logici di tipo vero-funzionale, che restituiscono il valore di verit\u00E0 di una proposizione in base al valore di verit\u00E0 delle proposizioni connesse (solitamente noti come AND, OR, NOT...). La semantica della logica proposizionale definisce il significato dei simboli e di qualsiasi proposizione che rispetti le regole sintattiche del linguaggio, basandosi sui valori di verit\u00E0 associati agli atomi. Data una interpretazione (o modello) di una proposizione (in generale di un insieme di proposizioni), e cio\u00E8 una associazione tra le proposizioni elementari e le realt\u00E0 rappresentate, possiamo generare un insieme infinito di"@it .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/abstract>	"La l\u00F2gica proposicional \u00E9s una branca de la l\u00F2gica cl\u00E0ssica que estudia les proposicions o sent\u00E8ncies l\u00F2giques, les seves possibles avaluacions de veritat i, en el cas ideal, el seu nivell absolut de veritat. Les seves constants l\u00F2giques, anomenades connectives l\u00F2giques, representen operacions sobre proposicions, capaces de formar altres proposicions de complexitat superior. Les l\u00F2giques proposicionals manquen de quantificadors o de variables d'individu, per\u00F2 tenen (\u00E9s a dir, que es poden interpretar com proposicions amb un valor de veritat definit), \u00E9s per aix\u00F2 que es diuen proposicionals. Els sistemes de l\u00F2gica proposicional inclouen a m\u00E9s connectives l\u00F2giques, i per aix\u00F2 dins d'aquest tipus de l\u00F2gica es pot analitzar la infer\u00E8ncia l\u00F2gica de proposicions a partir de proposicions, per\u00F2 sense tenir en compte l'estructura interna de les proposicions m\u00E9s simples. Com que les l\u00F2giques proposicionals no tenen quantificadors o variables d'individu, qualsevol seq\u00FC\u00E8ncia de signes que constitueixi una f\u00F3rmula ben formada admet una valoraci\u00F3 sobre si la proposici\u00F3 \u00E9s verdadera o falsa depenent del valor de veritat assignat a les proposicions que la componen. Aix\u00F2 implica que qualsevol f\u00F3rmula ben formada defineix una funci\u00F3 proposicional. Per tant, qualsevol sistema l\u00F2gic basat en la l\u00F2gica proposicoinal \u00E9s decible i en un nombre finit de passos es pot determinar la veritat o falsedat sem\u00E0ntica d'una proposici\u00F3. Aix\u00F2 fa que la l\u00F2gica proposicional sigui i amb una sem\u00E0ntica molt senzilla. A difer\u00E8ncia de la l\u00F2gica de primer ordre, la l\u00F2gica proposicional no s'ocupa d'objectes no l\u00F2gics, predicats sobre ells o quantificadors. Tanmateix, tota la maquin\u00E0ria de la l\u00F2gica proposicional s'inclou a la l\u00F2gica de primer ordre i a les l\u00F2giques d'ordre superior. En aquest sentit, la l\u00F2gica proposicional \u00E9s el fonament de la l\u00F2gica de primer ordre i de la l\u00F2gica d'ordre superior."@ca .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://www.w3.org/2000/01/rdf-schema#comment>	"Logika proposizionala, proposizioak eta horiek lotzen dituzten lokailuak osagaitzat hartzen dituen bat da. Logika proposizionalean \"hizkuntza\" edo proposizio konplexuak, proposizioak beraien artean lokailuen bitartez lotuz osatzen da. Premisa izeneko proposizio multzo batetik logikaz erator daitekeen ondoriozko proposiziora heltzea du helburu logika proposizionalak. Logika-sistema guztiak bezalaxe, logika proposizionalak ez du aztertzen proposizio bat errealitatean egiazkoa edo faltsua den, beste proposizioetatik deduzitzeko baliatu den prozesu logikoa edo argumentua zuzena den baizik. Logika proposizionala XIX. mendearen amaieran asmatu zuen Charles Sanders Peirce filosofoak eta XX. mendearen hasieran Ludwig Wittgenstein filosofoak osatu zuen, liburuan."@eu .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://www.w3.org/2000/01/rdf-schema#comment>	"\uBA85\uC81C \uB17C\uB9AC(\u547D\u984C\u8AD6\u7406, \uC601\uC5B4: propositional logic)\uB294 \uB0B4\uBD80 \uAD6C\uC870\uAC00 \uC5C6\uB294 \uBA85\uC81C\uC5D0 \uB17C\uB9AC\uD569\uC774\uB098 \uBD80\uC815 \uB530\uC704\uC758 \uB17C\uB9AC \uC5F0\uC0B0\uC744 \uAC00\uD558\uC5EC \uAD6C\uC131\uD55C \uBA85\uC81C\uB4E4\uC744 \uB2E4\uB8E8\uB294 \uB17C\uB9AC \uCCB4\uACC4\uC774\uB2E4.:30, Chapter 3"@ko .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://www.w3.org/2000/01/rdf-schema#comment>	"Die Aussagenlogik ist ein Teilgebiet der Logik, das sich mit Aussagen und deren Verkn\u00FCpfung durch Junktoren befasst, ausgehend von strukturlosen Elementaraussagen (Atomen), denen ein Wahrheitswert zugeordnet wird. In der klassischen Aussagenlogik wird jeder Aussage ein Element einer Booleschen Algebra als Wahrheitswert zugeordnet. Der Wahrheitswert einer zusammengesetzten Aussage l\u00E4sst sich ohne zus\u00E4tzliche Informationen mittels der Operationen der Booleschen Algebra aus den Wahrheitswerten ihrer Teilaussagen bestimmen."@de .
<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Category:Classical_logic> .
<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/abstract>	"De propositielogica is een tak van logica die zich bezighoudt met het redeneren met proposities. Proposities zijn uitspraken of beweringen die ofwel waar, ofwel onwaar zijn. Voorbeelden hiervan zijn De Winkler Prins is een encyclopedie en Wicky heeft een noormannenhelm op. In de propositielogica kunnen uitspraken alleen waar of onwaar zijn, dit in tegenstelling tot meerwaardige logica's waarbij uitspraken ook andere waarden kunnen hebben. In vergelijking met andere types van logica is de propositielogica eenvoudig van opbouw (structuur, grammatica) maar beperkt in uitdrukkingsmogelijkheid."@nl .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://www.w3.org/2000/01/rdf-schema#comment>	"\u5728\u908F\u8F2F\u548C\u6578\u5B78\u88E1\uFF0C\u547D\u984C\u6F14\u7B97\uFF08\u6216\u7A31\u53E5\u5B50\u6F14\u7B97\uFF09\u662F\u4E00\u500B\u5F62\u5F0F\u7CFB\u7D71\uFF0C\u6709\u8457\u53EF\u4EE5\u7531\u4EE5\u908F\u8F2F\u904B\u7B97\u7B26\u7D50\u5408\u539F\u5B50\u547D\u984C\u4F86\u69CB\u6210\u4EE3\u8868\u300C\u547D\u984C\u300D\u7684\u516C\u5F0F\uFF0C\u4EE5\u53CA\u5141\u8A31\u67D0\u4E9B\u516C\u5F0F\u5EFA\u69CB\u6210\u300C\u5B9A\u7406\u300D\u7684\u4E00\u5957\u5F62\u5F0F\u300C\u8B49\u660E\u898F\u5247\u300D\u3002"@zh .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/abstract>	"\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0648\u0627\u0644\u0645\u0646\u0637\u0642\u060C \u062D\u0633\u0627\u0628 \u0627\u0644\u0642\u0636\u0627\u064A\u0627 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: propositional calculus)\u200F \u0647\u0648 \u0646\u0638\u0627\u0645 \u064A\u062A\u0645 \u0641\u064A\u0647 \u062A\u0645\u062B\u064A\u0644 \u0627\u0644\u0642\u0636\u0627\u064A\u0627 \u0628\u0631\u0628\u0637 \u0642\u0636\u0627\u064A\u0627 \u0630\u0631\u064A\u0629 \u0628\u0648\u0627\u0633\u0637\u0629 \u0631\u0648\u0627\u0628\u0637 \u0645\u0646\u0637\u0642\u064A\u0629\u060C \u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0646\u0638\u0627\u0645 \u0644\u0644\u0627\u0633\u062A\u062F\u0644\u0627\u0644 \u0648\u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u062A\u062A\u0645 \u0628\u0648\u0627\u0633\u0637\u062A\u0647 \u0628\u0631\u0647\u0646\u0629 \u0646\u0638\u0631\u064A\u0627\u062A \u0645\u0646\u0637\u0642\u064A\u0629."@ar .
<http://dbpedia.org/resource/Propositional_calculus>	<http://www.w3.org/2000/01/rdf-schema#comment>	"\u03A0\u03C1\u03BF\u03C4\u03B1\u03C3\u03B9\u03B1\u03BA\u03CC\u03C2 \u03BB\u03BF\u03B3\u03B9\u03C3\u03BC\u03CC\u03C2 (\u03AE \u03B1\u03BB\u03BB\u03B9\u03CE\u03C2 \u03C0\u03C1\u03BF\u03C4\u03B1\u03C3\u03B9\u03B1\u03BA\u03AE \u03BB\u03BF\u03B3\u03B9\u03BA\u03AE) \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BF \u03BA\u03BB\u03AC\u03B4\u03BF\u03C2 \u03C4\u03B7\u03C2 \u03BC\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03AE\u03C2 \u03BB\u03BF\u03B3\u03B9\u03BA\u03AE\u03C2 \u03BF \u03BF\u03C0\u03BF\u03AF\u03BF\u03C2 \u03BC\u03B5\u03BB\u03B5\u03C4\u03AC \u03C4\u03B9\u03C2 \u03BB\u03BF\u03B3\u03B9\u03BA\u03AD\u03C2 \u03C0\u03C1\u03BF\u03C4\u03AC\u03C3\u03B5\u03B9\u03C2 (\u03B1\u03BD \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B1\u03BB\u03B7\u03B8\u03B5\u03AF\u03C2 \u03AE \u03C8\u03B5\u03C5\u03B4\u03B5\u03AF\u03C2) \u03C0\u03BF\u03C5 \u03C3\u03C7\u03B7\u03BC\u03B1\u03C4\u03AF\u03B6\u03BF\u03BD\u03C4\u03B1\u03B9 \u03B1\u03C0\u03CC \u03AC\u03BB\u03BB\u03B5\u03C2 \u03C0\u03C1\u03BF\u03C4\u03AC\u03C3\u03B5\u03B9\u03C2 \u03BC\u03B5 \u03C4\u03B7 \u03C7\u03C1\u03AE\u03C3\u03B7 \u03C4\u03C9\u03BD , \u03BA\u03B1\u03B9 \u03C4\u03BF \u03C0\u03CE\u03C2 \u03B7 \u03B1\u03BB\u03B7\u03B8\u03BF\u03C4\u03B9\u03BC\u03AE \u03C4\u03C9\u03BD \u03C0\u03C1\u03CE\u03C4\u03C9\u03BD \u03B5\u03BE\u03B1\u03C1\u03C4\u03AC\u03C4\u03B1\u03B9 \u03B1\u03C0\u03CC \u03B5\u03BA\u03B5\u03AF\u03BD\u03B7 \u03C4\u03C9\u03BD \u03C4\u03B5\u03BB\u03B5\u03C5\u03C4\u03B1\u03AF\u03C9\u03BD. \u039F\u03B9 \u03BB\u03BF\u03B3\u03B9\u03BA\u03BF\u03AF \u03C3\u03CD\u03BD\u03B4\u03B5\u03C3\u03BC\u03BF\u03B9 \u03B2\u03C1\u03AF\u03C3\u03BA\u03BF\u03BD\u03C4\u03B1\u03B9 \u03B5\u03C0\u03AF\u03C3\u03B7\u03C2 \u03BA\u03B1\u03B9 \u03C3\u03C4\u03B9\u03C2 \u03C6\u03C5\u03C3\u03B9\u03BA\u03AD\u03C2 \u03B3\u03BB\u03CE\u03C3\u03C3\u03B5\u03C2. \u03A3\u03C4\u03B7\u03BD \u03B5\u03BB\u03BB\u03B7\u03BD\u03B9\u03BA\u03AE \u03B3\u03BB\u03CE\u03C3\u03C3\u03B1, \u03B3\u03B9\u03B1 \u03C0\u03B1\u03C1\u03AC\u03B4\u03B5\u03B9\u03B3\u03BC\u03B1, \u03AD\u03C7\u03BF\u03C5\u03BC\u03B5 \u03C4\u03BF\u03C5\u03C2 \u03BB\u03BF\u03B3\u03B9\u03BA\u03BF\u03CD\u03C2 \u03C3\u03C5\u03BD\u03B4\u03AD\u03C3\u03BC\u03BF\u03C5\u03C2 \u00AB\u03BA\u03B1\u03B9\u00BB, \u00AB\u03AE\u00BB (\u03B4\u03B9\u03AC\u03B6\u03B5\u03C5\u03BE\u03B7), \u00AB\u03CC\u03C7\u03B9\u00BB \u03BA\u03B1\u03B9 \u00AB\u03B1\u03BD\u00BB (\u03B1\u03BB\u03BB\u03AC \u03BC\u03CC\u03BD\u03BF \u03CC\u03C4\u03B1\u03BD \u03C7\u03C1\u03B7\u03C3\u03B9\u03BC\u03BF\u03C0\u03BF\u03B9\u03B5\u03AF\u03C4\u03B1\u03B9 \u03BC\u03B5 \u03C4\u03B7\u03BD \u03AD\u03BD\u03BD\u03BF\u03B9\u03B1 \u03C4\u03B7\u03C2 \u03BB\u03BF\u03B3\u03B9\u03BA\u03AE\u03C2 \u03C3\u03C5\u03BD\u03B5\u03C0\u03B1\u03B3\u03C9\u03B3\u03AE\u03C2). \u03A0\u03C1\u03BF\u03BA\u03B5\u03AF\u03BC\u03B5\u03BD\u03B7 1: \u0391\u03BD \u03B2\u03C1\u03AD\u03C7\u03B5\u03B9, \u03C4\u03CC\u03C4\u03B5 \u03AD\u03C7\u03B5\u03B9 \u03C3\u03C5\u03BD\u03BD\u03B5\u03C6\u03B9\u03AC \u03A0\u03C1\u03BF\u03BA\u03B5\u03AF\u03BC\u03B5\u03BD\u03B7 2: \u0392\u03C1\u03AD\u03C7\u03B5\u03B9."@el .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://www.w3.org/2000/01/rdf-schema#comment>	"\u0427\u0438\u0301\u0441\u043B\u0435\u043D\u043D\u044F \u0432\u0438\u0441\u043B\u043E\u0301\u0432\u043B\u0435\u043D\u044C (\u043B\u043E\u0433\u0456\u043A\u0430 \u0432\u0438\u0441\u043B\u043E\u0432\u043B\u0435\u043D\u044C, \u043F\u0440\u043E\u043F\u043E\u0437\u0438\u0446\u0456\u0439\u043D\u0430 \u043B\u043E\u0433\u0456\u043A\u0430, \u0430\u043D\u0433\u043B. propositional calculus) \u2014 \u0444\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u0430 \u0441\u0438\u0441\u0442\u0435\u043C\u0430 \u0432 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u043D\u0456\u0439 \u043B\u043E\u0433\u0456\u0446\u0456, \u0432 \u044F\u043A\u0456\u0439 \u0444\u043E\u0440\u043C\u0443\u043B\u0438, \u0449\u043E \u0432\u0456\u0434\u043F\u043E\u0432\u0456\u0434\u0430\u044E\u0442\u044C \u0432\u0438\u0441\u043B\u043E\u0432\u043B\u0435\u043D\u043D\u044F\u043C, \u043C\u043E\u0436\u0443\u0442\u044C \u0443\u0442\u0432\u043E\u0440\u044E\u0432\u0430\u0442\u0438\u0441\u044C \u0448\u043B\u044F\u0445\u043E\u043C \u0437'\u0454\u0434\u043D\u0430\u043D\u043D\u044F \u043F\u0440\u043E\u0441\u0442\u0438\u0445 \u0432\u0438\u0441\u043B\u043E\u0432\u043B\u0435\u043D\u044C \u0456\u0437 \u0434\u043E\u043F\u043E\u043C\u043E\u0433\u043E\u044E \u043B\u043E\u0433\u0456\u0447\u043D\u0438\u0445 \u043E\u043F\u0435\u0440\u0430\u0446\u0456\u0439, \u0442\u0430 \u0441\u0438\u0441\u0442\u0435\u043C\u0430 \u043F\u0440\u0430\u0432\u0438\u043B \u0432\u0438\u0432\u043E\u0434\u0443, \u044F\u043A\u0456 \u0434\u043E\u0437\u0432\u043E\u043B\u044F\u044E\u0442\u044C \u0432\u0438\u0437\u043D\u0430\u0447\u0430\u0442\u0438 \u043F\u0435\u0432\u043D\u0456 \u0444\u043E\u0440\u043C\u0443\u043B\u0438 \u044F\u043A \u00AB\u0442\u0435\u043E\u0440\u0435\u043C\u0438\u00BB \u0444\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u043E\u0457 \u0441\u0438\u0441\u0442\u0435\u043C\u0438."@uk .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://www.w3.org/2000/01/rdf-schema#comment>	"La l\u00F3gica proposicional, tambi\u00E9n llamada l\u00F3gica de enunciados, l\u00F3gica de orden cero o c\u00E1lculo proposicional, es un sistema formal cuyos elementos m\u00E1s simples representan proposiciones o enunciados, y cuyas constantes l\u00F3gicas, llamadas conectivas l\u00F3gicas, representan operaciones sobre proposiciones, capaces de formar otras proposiciones de mayor complejidad.\u200B"@es .
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<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Truth_table> .
<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Truth_value> .
<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/abstract>	"\u0427\u0438\u0301\u0441\u043B\u0435\u043D\u043D\u044F \u0432\u0438\u0441\u043B\u043E\u0301\u0432\u043B\u0435\u043D\u044C (\u043B\u043E\u0433\u0456\u043A\u0430 \u0432\u0438\u0441\u043B\u043E\u0432\u043B\u0435\u043D\u044C, \u043F\u0440\u043E\u043F\u043E\u0437\u0438\u0446\u0456\u0439\u043D\u0430 \u043B\u043E\u0433\u0456\u043A\u0430, \u0430\u043D\u0433\u043B. propositional calculus) \u2014 \u0444\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u0430 \u0441\u0438\u0441\u0442\u0435\u043C\u0430 \u0432 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u043D\u0456\u0439 \u043B\u043E\u0433\u0456\u0446\u0456, \u0432 \u044F\u043A\u0456\u0439 \u0444\u043E\u0440\u043C\u0443\u043B\u0438, \u0449\u043E \u0432\u0456\u0434\u043F\u043E\u0432\u0456\u0434\u0430\u044E\u0442\u044C \u0432\u0438\u0441\u043B\u043E\u0432\u043B\u0435\u043D\u043D\u044F\u043C, \u043C\u043E\u0436\u0443\u0442\u044C \u0443\u0442\u0432\u043E\u0440\u044E\u0432\u0430\u0442\u0438\u0441\u044C \u0448\u043B\u044F\u0445\u043E\u043C \u0437'\u0454\u0434\u043D\u0430\u043D\u043D\u044F \u043F\u0440\u043E\u0441\u0442\u0438\u0445 \u0432\u0438\u0441\u043B\u043E\u0432\u043B\u0435\u043D\u044C \u0456\u0437 \u0434\u043E\u043F\u043E\u043C\u043E\u0433\u043E\u044E \u043B\u043E\u0433\u0456\u0447\u043D\u0438\u0445 \u043E\u043F\u0435\u0440\u0430\u0446\u0456\u0439, \u0442\u0430 \u0441\u0438\u0441\u0442\u0435\u043C\u0430 \u043F\u0440\u0430\u0432\u0438\u043B \u0432\u0438\u0432\u043E\u0434\u0443, \u044F\u043A\u0456 \u0434\u043E\u0437\u0432\u043E\u043B\u044F\u044E\u0442\u044C \u0432\u0438\u0437\u043D\u0430\u0447\u0430\u0442\u0438 \u043F\u0435\u0432\u043D\u0456 \u0444\u043E\u0440\u043C\u0443\u043B\u0438 \u044F\u043A \u00AB\u0442\u0435\u043E\u0440\u0435\u043C\u0438\u00BB \u0444\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u043E\u0457 \u0441\u0438\u0441\u0442\u0435\u043C\u0438."@uk .
<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Category:Boolean_algebra> .
<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Exclusive_disjunction> .
<http://dbpedia.org/resource/Propositional_calculus>	<http://www.w3.org/2000/01/rdf-schema#label>	"\u041B\u043E\u0433\u0438\u043A\u0430 \u0432\u044B\u0441\u043A\u0430\u0437\u044B\u0432\u0430\u043D\u0438\u0439"@ru .
<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Evert_Willem_Beth> .
<http://dbpedia.org/resource/Propositional_calculus>	<http://www.w3.org/2000/01/rdf-schema#label>	"Logica proposizionale"@it .
<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Term_logic> .
<http://dbpedia.org/resource/Propositional_calculus>	<http://purl.org/dc/terms/subject>	<http://dbpedia.org/resource/Category:Boolean_algebra> .
<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Logical_system> .
<http://dbpedia.org/resource/Propositional_calculus>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/If_and_only_if> .