@prefix rdf: . @prefix dbpedia: . @prefix ns2: . dbpedia:Logical_biconditional rdf:type ns2:BinaryOperations . @prefix owl: . dbpedia:Logical_biconditional owl:sameAs . @prefix foaf: . @prefix ns5: . dbpedia:Logical_biconditional foaf:page ns5:Logical_biconditional . @prefix rdfs: . dbpedia:Logical_biconditional rdfs:label "Bisubjunksjon"@no , "Bikonditional"@de , "Logical biconditional"@en . @prefix dbpprop: . dbpedia:Logical_biconditional dbpprop:abstract "Bisubjunksjon (ogs\u00E5 ekvijunksjon, ekvivalens eller biimplikasjon) er en sannhetsfunksjon i setningslogikken (latin bis = \u00ABto ganger\u00BB, sub = \u00ABunder\u00BB, aequus = \u00ABlik\u00BB, junctio = implicatio = \u00ABforbindelse\u00BB, valere = \u00AB\u00E5 gjelde\u00BB). Bisubjunksjonen av to utsagn er sann hvis og bare hvis begge eller ingen av disse utsagnene er sanne. Den symbolske skrivem\u00E5ten for bisubjunksjonen av to utsagn A og B er <math>\\mathbf A \\leftrightarrow \\mathbf B</math> og kan uttales som f\u00F8lger: \u00ABhvis og bare hvis A, s\u00E5 B,\u00BB \u00ABom og bare om A, s\u00E5 B,\u00BB \u00ABav A f\u00F8lger B og vice versa,\u00BB \u00ABA er tilstrekkelig og n\u00F8dvendig for B. \u00BB I noen programmeringsspr\u00E5k eller andre sammenhenger der s\u00E6rtegn ikke kan brukes, skrives ogs\u00E5 \u00AB\u00BB eller likhetstegn (\u00AB=\u00BB) istedenfor \u00AB\u2194\u00BB. \u00ABX\u00BB er avledet av det engelske uttrykket exclusive nor (i og med at bisubjunksjonen er negasjonen av en \u00ABeksklusiv eller\u00BB). Ekvivalens brukes til tider synonymt med bisubjunksjon, men begrepet er formelt sett kun forbeholdt bisubjunksjoner som er sanne. Symbolet for ekvivalens er \u00AB<math>\\Leftrightarrow</math>\u00BB eller \u00AB\u2261\u00BB mot bisubjunksjonens \u00AB<math>\\leftrightarrow</math>\u00BB og \u00AB=\u00BB. Av og til omskrives ogs\u00E5 A \u2194 B som \u00ABhviss A, s\u00E5 B\u00BB (til dels \u00ABomm A, s\u00E5 B\u00BB). Skrivem\u00E5ten \u00ABhviss\u00BB f\u00F8lger det engelske forbildet iff (for if and only if), men b\u00F8r brukes med forsiktighet, siden det lett kan forveksles med \u00ABhvis\u00BB, som har en annen beydning: Forskjellen mellom biimplikasjonen (\u00ABhviss\u00BB) og implikasjonen (\u00ABhvis\u00BB) er at den sistnevnte ogs\u00E5 er sann hvis bare konklusjonen er sann, men ikke premissen. I motsetning til implikasjonen er derfor biimplikasjonen kommutativ: \u00ABhvis og bare hvis A, s\u00E5 B\u00BB er ekvivalent med \u00ABhvis og bare hvis B, s\u00E5 A\u00BB, eller symbolsk: <math>(\\mathbf A \\leftrightarrow \\mathbf{B}) \\Leftrightarrow (\\mathbf B \\leftrightarrow \\mathbf{A})</math>. Legg merke til at \u00AB<math>\\leftrightarrow</math>\u00BB og \u00AB<math>\\Leftrightarrow</math>\u00BB nettopp ble brukt til \u00E5 uttrykke ulike ting: Den sistnevnte symbolet betegnet en sann ekvivalens mellom to utsagn. De to enkeltutsagnene kan derimot godt v\u00E6re falske, derfor brukes \u00AB\u2194\u00BB i disse. Den eksklusive disjunksjonen kan uttrykkes gjennom andre sannhetsfunksjoner: som \u00ABhvis A, s\u00E5 B, og hvis B, s\u00E5 A\u00BB, <math>(\\mathbf A \\leftrightarrow \\mathbf{B}) \\Leftrightarrow (\\land)</math>; som negasjon av en eksklusiv disjunksjon, <math>(\\mathbf A \\leftrightarrow \\mathbf{B}) \\Leftrightarrow \\neg (\\mathbf A</math> <math>\\mathbf{B})</math>."@no , "Als Bikonditional, Bisubjunktion oder materiale \u00C4quivalenz, manchmal (aber mehrdeutig) einfach nur \u00C4quivalenz bezeichnet man eine zusammengesetzte Aussage, die genau dann wahr ist, wenn ihre beiden Teilaussagen denselben Wahrheitswert haben, also entweder beide wahr oder beide falsch sind; die entsprechend definierte Wahrheitswertfunktion; das sprachliche Zeichen, mit dem diese beiden Teilaussagen zusammengesetzt werden."@de , "In logic and mathematics, logical biconditional (sometimes also known as the material biconditional) is a logical operator connecting two statements to assert, p if and only if q where p is a hypothesis (or antecedent) and q is a conclusion (or consequent). The operator is denoted using a doubleheaded arrow \"\u2194\", an equality sign \"=\", an equivalence sign \"\u2261\", or EQV. It is logically equivalent to (p \u2192 q) \u2227 (q \u2192 p), or the XNOR boolean operator. It is equivalent to \"(not p or q) and (not q or p)\". It is also logically equivalent to \"(not p and not q) or (p and q)\". The hypothesis is sometimes also called \"sufficient condition\" while the conclusion may be called \"necessary condition\". The only difference from material conditional is the case when the hypothesis is false but the conclusion is true. In that case, in the conditional, the result is true, yet in the biconditional the result is false. In the conceptual interpretation, a = b means \"All a 's are b 's and all b 's are a 's\"; in other words, the sets a and b coincide: they are identical. This does not mean that the concepts have the same meaning. Examples: \"triangle\" and \"trilateral\", \"equiangular triangle\" and \"equilateral triangle\". The antecedent is the subject and the consequent is the predicate of a universal affirmative proposition. In the propositional interpretation, a \u21D4 b means that a implies b and b implies a; in other words, that the propositions are equivalent, that is to say, either true or false at the same time. This does not mean that they have the same meaning. Example: \"The triangle ABC has two equal sides\", and \"The triangle ABC has two equal angles\". The antecedent is the premise or the cause and the consequent is the consequence. When an implication is translated by a hypothetical (or conditional) judgment the antecedent is called the hypothesis (or the condition) and the consequent is called the thesis. A common way of demonstrating a biconditional is to use its equivalence to the conjunction of two converse conditionals, demonstrating these separately. When both members of the biconditional are propositions, it can be separated into two conditionals, of which one is called a theorem and the other its reciprocal. Thus whenever a theorem and its reciprocal are true we have a biconditional. A simple theorem gives rise to an implication whose antecedent is the hypothesis and whose consequent is the thesis of the theorem. It is often said that the hypothesis is the sufficient condition of the thesis, and the thesis the necessary condition of the hypothesis; that is to say, it is sufficient that the hypothesis be true for the thesis to be true; while it is necessary that the thesis be true for the hypothesis to be true also. When a theorem and its reciprocal are true we say that its hypothesis is the necessary and sufficient condition of the thesis; that is to say, that it is at the same time both cause and consequence."@en ; rdfs:comment "Bisubjunksjon (ogs\u00E5 ekvijunksjon, ekvivalens eller biimplikasjon) er en sannhetsfunksjon i setningslogikken (latin bis = \u00ABto ganger\u00BB, sub = \u00ABunder\u00BB, aequus = \u00ABlik\u00BB, junctio = implicatio = \u00ABforbindelse\u00BB, valere = \u00AB\u00E5 gjelde\u00BB). Bisubjunksjonen av to utsagn er sann hvis og bare hvis begge eller ingen av disse utsagnene er sanne."@no , "In logic and mathematics, logical biconditional (sometimes also known as the material biconditional) is a logical operator connecting two statements to assert, p if and only if q where p is a hypothesis (or antecedent) and q is a conclusion (or consequent). The operator is denoted using a doubleheaded arrow \"\u2194\", an equality sign \"=\", an equivalence sign \"\u2261\", or EQV. It is logically equivalent to (p \u2192 q) \u2227 (q \u2192 p), or the XNOR boolean operator."@en , "Als Bikonditional, Bisubjunktion oder materiale \u00C4quivalenz, manchmal (aber mehrdeutig) einfach nur \u00C4quivalenz bezeichnet man eine zusammengesetzte Aussage, die genau dann wahr ist, wenn ihre beiden Teilaussagen denselben Wahrheitswert haben, also entweder beide wahr oder beide falsch sind; die entsprechend definierte Wahrheitswertfunktion; das sprachliche Zeichen, mit dem diese beiden Teilaussagen zusammengesetzt werden."@de . @prefix skos: . @prefix ns9: . dbpedia:Logical_biconditional skos:subject ns9:Propositional_logic , ns9:Logic , ns9:Binary_operations . @prefix ns10: . dbpedia:Logical_biconditional dbpprop:wikiPageUsesTemplate ns10:portal , ns10:planetmath ; dbpprop:id 484 ; dbpprop:title "Biconditional"@en ; dbpprop:portalProperty "Brain.png"@en , "Thinking"@en . @prefix ns11: . dbpedia:Logical_biconditional dbpprop:hasPhotoCollection ns11:Logical_biconditional . dbpedia:Biconditional dbpprop:redirect dbpedia:Logical_biconditional . dbpedia:Biconditionality dbpprop:redirect dbpedia:Logical_biconditional . dbpedia:Biconditionals dbpprop:redirect dbpedia:Logical_biconditional . dbpedia:EQV dbpprop:redirect dbpedia:Logical_biconditional . @prefix yago: . yago:Logical_biconditional owl:sameAs dbpedia:Logical_biconditional .