@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .

psr: a skos:ConceptScheme .
psr:-W62W44BV-T
  skos:definition """En logique classique, deux propositions <i>P</i> et <i>Q</i> sont dites logiquement équivalentes ou simplement équivalentes quand il est possible de déduire <i>Q</i> à partir de <i>P</i> et de déduire <i>P</i> à partir de <i>Q</i>. En calcul des propositions, cela revient à dire que <i>P</i> et <i>Q</i> ont même valeur de vérité : <i>P</i> et <i>Q</i> sont soit toutes les deux vraies, soit toutes les deux fausses. L'équivalence logique s'exprime souvent sous la forme si et seulement si, dans des cadres comme l'enseignement ou la métamathématique pour parler des propriétés de la logique elle-même, et non du connecteur logique qui lie deux propositions. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/%C3%89quivalence_logique">https://fr.wikipedia.org/wiki/%C3%89quivalence_logique</a>)"""@fr, """In logic and mathematics, statements <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\\\\displaystyle p}">
    <semantics>
      <mrow class="MJX-TeXAtom-ORD">
        <mstyle displaystyle="true" scriptlevel="0">
          <mi>p</mi>
        </mstyle>
      </mrow>
      <annotation encoding="application/x-tex">{\\\\displaystyle p}</annotation>
    </semantics>
  </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="p"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\\\\displaystyle q}">
    <semantics>
      <mrow class="MJX-TeXAtom-ORD">
        <mstyle displaystyle="true" scriptlevel="0">
          <mi>q</mi>
        </mstyle>
      </mrow>
      <annotation encoding="application/x-tex">{\\\\displaystyle q}</annotation>
    </semantics>
  </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06809d64fa7c817ffc7e323f85997f783dbdf71d" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.07ex; height:2.009ex;" alt="q"></span> are said to be <b>logically equivalent</b> if they have the same truth value in every model. The logical equivalence of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\\\\displaystyle p}">
    <semantics>
      <mrow class="MJX-TeXAtom-ORD">
        <mstyle displaystyle="true" scriptlevel="0">
          <mi>p</mi>
        </mstyle>
      </mrow>
      <annotation encoding="application/x-tex">{\\\\displaystyle p}</annotation>
    </semantics>
  </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="p"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\\\\displaystyle q}">
    <semantics>
      <mrow class="MJX-TeXAtom-ORD">
        <mstyle displaystyle="true" scriptlevel="0">
          <mi>q</mi>
        </mstyle>
      </mrow>
      <annotation encoding="application/x-tex">{\\\\displaystyle q}</annotation>
    </semantics>
  </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06809d64fa7c817ffc7e323f85997f783dbdf71d" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.07ex; height:2.009ex;" alt="q"></span> is sometimes expressed as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\\\\displaystyle p\\\\equiv q}">
    <semantics>
      <mrow class="MJX-TeXAtom-ORD">
        <mstyle displaystyle="true" scriptlevel="0">
          <mi>p</mi>
          <mo>≡<!-- ≡ --></mo>
          <mi>q</mi>
        </mstyle>
      </mrow>
      <annotation encoding="application/x-tex">{\\\\displaystyle p\\\\equiv q}</annotation>
    </semantics>
  </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cf1b853ede16891d0e5cdef8c65cac3495f576b" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:5.427ex; height:2.009ex;" alt="p \\\\equiv q"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\\\\displaystyle p::q}">
    <semantics>
      <mrow class="MJX-TeXAtom-ORD">
        <mstyle displaystyle="true" scriptlevel="0">
          <mi>p</mi>
          <mo>::</mo>
          <mi>q</mi>
        </mstyle>
      </mrow>
      <annotation encoding="application/x-tex">{\\\\displaystyle p::q}</annotation>
    </semantics>
  </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b91ade8154521851c00ad3328d0b3f2044c9d3b7" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:4.912ex; height:2.009ex;" alt="{\\\\displaystyle p::q}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\\\\displaystyle {\\	extsf {E}}pq}">
    <semantics>
      <mrow class="MJX-TeXAtom-ORD">
        <mstyle displaystyle="true" scriptlevel="0">
          <mrow class="MJX-TeXAtom-ORD">
            <mrow class="MJX-TeXAtom-ORD">
              <mtext mathvariant="sans-serif">E</mtext>
            </mrow>
          </mrow>
          <mi>p</mi>
          <mi>q</mi>
        </mstyle>
      </mrow>
      <annotation encoding="application/x-tex">{\\\\displaystyle {\\	extsf {E}}pq}</annotation>
    </semantics>
  </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86464cec35246af84dda8b58cc7e2d4f7389d1a5" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.627ex; height:2.509ex;" alt="{\\\\displaystyle {\\	extsf {E}}pq}"></span>, or <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\\\\displaystyle p\\\\iff q}">
    <semantics>
      <mrow class="MJX-TeXAtom-ORD">
        <mstyle displaystyle="true" scriptlevel="0">
          <mi>p</mi>
          <mspace width="thickmathspace" />
          <mo stretchy="false">⟺<!-- ⟺ --></mo>
          <mspace width="thickmathspace" />
          <mi>q</mi>
        </mstyle>
      </mrow>
      <annotation encoding="application/x-tex">{\\\\displaystyle p\\\\iff q}</annotation>
    </semantics>
  </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae76771560843760a9249bc0468954f43b8c3721" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:9.226ex; height:2.176ex;" alt="{\\\\displaystyle p\\\\iff q}"></span>, depending on the notation being used.
  However, these symbols are also used for material equivalence, so proper interpretation would depend on the context. Logical equivalence is different from material equivalence, although the two concepts are intrinsically related.
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Logical_equivalence">https://en.wikipedia.org/wiki/Logical_equivalence</a>)"""@en ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:broader psr:-NRJSM1FG-4 ;
  skos:prefLabel "logical equivalence"@en, "équivalence logique"@fr ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/%C3%89quivalence_logique>, <https://en.wikipedia.org/wiki/Logical_equivalence> .

psr:-NRJSM1FG-4
  skos:prefLabel "logique mathématique"@fr, "mathematical logic"@en ;
  a skos:Concept ;
  skos:narrower psr:-W62W44BV-T .