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              <h2 class="title" style="clear: both"><a id="section-bridi-connection"></a>14.4. <a id="c14s4"></a>Logical connection of bridi</h2>
            </div>
          </div>
        </div>
        <p><a id="idm22952489283856" class="indexterm"></a><a id="idm22952489282720" class="indexterm"></a> Now we are ready to express 
      <a class="xref" href="chapter-connectives.html#example-random-id-mJ6y" title="Example 14.1. ">Example 14.1</a> in Lojban! The kind of logical connective which is placed between two Lojban bridi to connect them logically is an ijek:</p>
        <div class="interlinear-gloss-example example">
          <a id="example-random-id-h2hN"></a>
          <p class="title">
            <strong>Example 14.3. 
          <a id="c14e4d1"></a>
        </strong>
          </p>
          <div class="interlinear-gloss-example example-contents">
            <div class="informaltable">
              <table class="interlinear-gloss">
                <colgroup></colgroup>
                <tr class="jbo">
                  <td>la</td>
                  <td>djan.</td>
                  <td>nanmu</td>
                  <td>.ija</td>
                  <td>la</td>
                  <td>djeimyz.</td>
                  <td>ninmu</td>
                </tr>
                <tr class="gloss">
                  <td>That-named</td>
                  <td>John</td>
                  <td>is-a-man</td>
                  <td>or</td>
                  <td>that-named</td>
                  <td>James</td>
                  <td>is-a-woman.</td>
                </tr>
              </table>
            </div>
          </div>
        </div>
        <br class="interlinear-gloss-example example-break" />
        <p class="indent">Here we have two separate Lojban bridi, 
      <span xml:lang="jbo" class="foreignphrase" lang="jbo"><em xml:lang="jbo" class="foreignphrase" lang="jbo"><a id="idm22952489270816" class="indexterm"></a>la djan. nanmu</em></span> and 
      <span xml:lang="jbo" class="foreignphrase" lang="jbo"><em xml:lang="jbo" class="foreignphrase" lang="jbo"><a id="idm22952489268864" class="indexterm"></a>la djeimyz. ninmu</em></span>. These bridi are connected by 
      <span xml:lang="jbo" class="foreignphrase" lang="jbo"><em xml:lang="jbo" class="foreignphrase" lang="jbo"><a id="idm22952489267216" class="indexterm"></a><a class="glossterm" href="go01.html#valsi-i"><em class="glossterm">.i</em></a></em></span><span xml:lang="jbo" class="foreignphrase" lang="jbo"><em xml:lang="jbo" class="foreignphrase" lang="jbo"><a id="idm22952489265024" class="indexterm"></a><a class="glossterm" href="go01.html#valsi-ja"><em class="glossterm">ja</em></a></em></span>, the ijek for the truth function 
      <span class="logical-vowel">A</span>. The 
      <span xml:lang="jbo" class="foreignphrase" lang="jbo"><em xml:lang="jbo" class="foreignphrase" lang="jbo"><a id="idm22952489261936" class="indexterm"></a><a class="glossterm" href="go01.html#valsi-i"><em class="glossterm">i</em></a></em></span> portion of the ijek tells us that we are dealing with separate sentences here. Similarly, we can now say:</p>
        <div class="interlinear-gloss-example example">
          <a id="example-random-id-qGiu"></a>
          <p class="title">
            <strong>Example 14.4. 
          <a id="c14e4d2"></a>
        </strong>
          </p>
          <div class="interlinear-gloss-example example-contents">
            <div class="informaltable">
              <table class="interlinear-gloss">
                <colgroup></colgroup>
                <tr class="jbo">
                  <td>la</td>
                  <td>djan.</td>
                  <td>nanmu</td>
                  <td>.ije</td>
                  <td>la</td>
                  <td>djeimyz.</td>
                  <td>ninmu</td>
                </tr>
                <tr class="gloss">
                  <td>That-named</td>
                  <td>John</td>
                  <td>is-a-man</td>
                  <td>and</td>
                  <td>that-named</td>
                  <td>James</td>
                  <td>is-a-woman.</td>
                </tr>
              </table>
            </div>
          </div>
        </div>
        <br class="interlinear-gloss-example example-break" />
        <div class="interlinear-gloss-example example">
          <a id="example-random-id-qGIu"></a>
          <p class="title">
            <strong>Example 14.5. 
          <a id="c14e4d3"></a>
        </strong>
          </p>
          <div class="interlinear-gloss-example example-contents">
            <div class="informaltable">
              <table class="interlinear-gloss">
                <colgroup></colgroup>
                <tr class="jbo">
                  <td>la</td>
                  <td>djan.</td>
                  <td>nanmu</td>
                  <td>.ijo</td>
                  <td>la</td>
                  <td>djeimyz.</td>
                  <td>ninmu</td>
                </tr>
                <tr class="gloss">
                  <td>That-named</td>
                  <td>John</td>
                  <td>is-a-man</td>
                  <td>if-and-only-if</td>
                  <td>that-named</td>
                  <td>James</td>
                  <td>is-a-woman.</td>
                </tr>
              </table>
            </div>
          </div>
        </div>
        <br class="interlinear-gloss-example example-break" />
        <div class="interlinear-gloss-example example">
          <a id="example-random-id-qgJC"></a>
          <p class="title">
            <strong>Example 14.6. 
          <a id="c14e4d4"></a>
        </strong>
          </p>
          <div class="interlinear-gloss-example example-contents">
            <div class="informaltable">
              <table class="interlinear-gloss">
                <colgroup></colgroup>
                <tr class="jbo">
                  <td>la</td>
                  <td>djan.</td>
                  <td>nanmu</td>
                  <td>.iju</td>
                  <td>la</td>
                  <td>djeimyz.</td>
                  <td>ninmu</td>
                </tr>
                <tr class="gloss">
                  <td>That-named</td>
                  <td>John</td>
                  <td>is-a-man</td>
                  <td>whether-or-not</td>
                  <td>that-named</td>
                  <td>James</td>
                  <td>is-a-woman.</td>
                </tr>
              </table>
            </div>
          </div>
        </div>
        <br class="interlinear-gloss-example example-break" />
        <p class="indent"><a id="idm22952489234288" class="indexterm"></a> To obtain the other truth tables listed in 
      
      <a class="xref" href="section-four-basics.html" title="14.2. The Four basic vowels">Section 14.2</a>, we need to know how to negate the two bridi which represent the component sentences. We could negate them directly by inserting 
      <span xml:lang="jbo" class="foreignphrase" lang="jbo"><em xml:lang="jbo" class="foreignphrase" lang="jbo"><a id="idm22952489232048" class="indexterm"></a><a class="glossterm" href="go01.html#valsi-na"><em class="glossterm">na</em></a></em></span> before the selbri, but Lojban also allows us to place the negation within the connective itself.</p>
        <p><a id="idm22952489229600" class="indexterm"></a> To negate the first or left-hand bridi, prefix 
      <span xml:lang="jbo" class="foreignphrase" lang="jbo"><em xml:lang="jbo" class="foreignphrase" lang="jbo"><a id="idm22952489228288" class="indexterm"></a><a class="glossterm" href="go01.html#valsi-na"><em class="glossterm">na</em></a></em></span> to the JA cmavo but after the 
      <span xml:lang="jbo" class="foreignphrase" lang="jbo"><em xml:lang="jbo" class="foreignphrase" lang="jbo"><a id="idm22952489225920" class="indexterm"></a><a class="glossterm" href="go01.html#valsi-i"><em class="glossterm">i</em></a></em></span>. To negate the second or right-hand bridi, suffix 
      <span xml:lang="jbo" class="foreignphrase" lang="jbo"><em xml:lang="jbo" class="foreignphrase" lang="jbo"><a id="idm22952489223328" class="indexterm"></a>-nai</em></span> to the JA cmavo. In either case, the negating word is placed on the side of the connective that is closest to the bridi being negated.</p>
        <p>So to express the truth table FTTF, which requires 
      
      <span class="logical-vowel">O</span> with either of the two bridi negated (not both), we can say either:</p>
        <div class="interlinear-gloss-example example">
          <a id="example-random-id-qgKB"></a>
          <p class="title">
            <strong>Example 14.7. 
          <a id="c14e4d5"></a>
        </strong>
          </p>
          <div class="interlinear-gloss-example example-contents">
            <div class="informaltable">
              <table class="interlinear-gloss">
                <colgroup></colgroup>
                <tr class="jbo">
                  <td>la</td>
                  <td>djan.</td>
                  <td>nanmu</td>
                  <td>.inajo</td>
                  <td>la</td>
                  <td>djeimyz.</td>
                  <td>ninmu</td>
                </tr>
                <tr class="gloss">
                  <td>That-named</td>
                  <td>John</td>
                  <td>is-not-a-man</td>
                  <td>if-and-only-if</td>
                  <td>that-named</td>
                  <td>James</td>
                  <td>is-a-woman.</td>
                </tr>
              </table>
            </div>
          </div>
        </div>
        <br class="interlinear-gloss-example example-break" />
        <div class="interlinear-gloss-example example">
          <a id="example-random-id-qgLH"></a>
          <p class="title">
            <strong>Example 14.8. 
          <a id="c14e4d6"></a>
        </strong>
          </p>
          <div class="interlinear-gloss-example example-contents">
            <div class="informaltable">
              <table class="interlinear-gloss">
                <colgroup></colgroup>
                <tr class="jbo">
                  <td>la</td>
                  <td>djan.</td>
                  <td>nanmu</td>
                  <td>.ijonai</td>
                  <td>la</td>
                  <td>djeimyz.</td>
                  <td>ninmu</td>
                </tr>
                <tr class="gloss">
                  <td>That-named</td>
                  <td>John</td>
                  <td>is-a-man</td>
                  <td>if-and-only-if</td>
                  <td>that-named</td>
                  <td>James</td>
                  <td>is-not-a-woman.</td>
                </tr>
              </table>
            </div>
          </div>
        </div>
        <br class="interlinear-gloss-example example-break" />
        <p class="indent">The meaning of both 
      <a class="xref" href="section-bridi-connection.html#example-random-id-qgKB" title="Example 14.7. ">Example 14.7</a> and 
      <a class="xref" href="section-bridi-connection.html#example-random-id-qgLH" title="Example 14.8. ">Example 14.8</a> is the same as that of:</p>
        <div class="example">
          <a id="example-random-id-1Kp9"></a>
          <p class="title">
            <strong>Example 14.9. 
          <a id="c14e4d7"></a>
        </strong>
          </p>
          <div class="example-contents">
            <p>John is a man or James is a woman, but not both.</p>
          </div>
        </div>
        <br class="example-break" />
        <p class="indent">Here is another example:</p>
        <div class="interlinear-gloss-example example">
          <a id="example-random-id-FXSC"></a>
          <p class="title">
            <strong>Example 14.10. 
          <a id="c14e4d8"></a>
        </strong>
          </p>
          <div class="interlinear-gloss-example example-contents">
            <div class="informaltable">
              <table class="interlinear-gloss">
                <colgroup></colgroup>
                <tr class="jbo">
                  <td>la</td>
                  <td>djan.</td>
                  <td>nanmu</td>
                  <td>.ijanai</td>
                  <td>la</td>
                  <td>djeimyz.</td>
                  <td>ninmu</td>
                </tr>
                <tr class="gloss">
                  <td>That-named</td>
                  <td>John</td>
                  <td>is-a-man</td>
                  <td>or</td>
                  <td>that-named</td>
                  <td>James</td>
                  <td>is-not-a-woman.</td>
                </tr>
              </table>
            </div>
            <div class="informaltable">
              <table class="interlinear-gloss">
                <tr class="para">
                  <td colspan="12321">
                    <p class="natlang">John is a man if James is a woman.</p>
                  </td>
                </tr>
              </table>
            </div>
          </div>
        </div>
        <br class="interlinear-gloss-example example-break" />
        <p class="indent"><a id="idm22952489187568" class="indexterm"></a><a id="idm22952489186400" class="indexterm"></a> How's that again? Are those two English sentences in 
      <a class="xref" href="section-bridi-connection.html#example-random-id-FXSC" title="Example 14.10. ">Example 14.10</a> really equivalent? In English, no. The Lojban TTFT truth function can be glossed 
      <span class="quote">“<span class="quote">A if B</span>”</span>, but the 
      <span class="quote">“<span class="quote">if</span>”</span> does not quite have its English sense. 
      <a class="xref" href="section-bridi-connection.html#example-random-id-FXSC" title="Example 14.10. ">Example 14.10</a> is true so long as John is a man, even if James is not a woman; likewise, it is true just because James is not a woman, regardless of John's gender. This kind of 
      <span class="quote">“<span class="quote">if-then</span>”</span> is technically known as a 
      <span class="quote">“<span class="quote">material conditional</span>”</span>.</p>
        <p>Since James is not a woman (by our assertions in 
      <a class="xref" href="chapter-connectives.html#section-connectives-introduction" title="14.1. Logical connection and truth tables">Section 14.1</a>), the English sentence 
      <span class="quote">“<span class="quote">John is a man if James is a woman</span>”</span> seems to be neither true nor false, since it assumes something which is not true. It turns out to be most convenient to treat this 
      <span class="quote">“<span class="quote">if</span>”</span> as TTFT, which on investigation means that 
      <a class="xref" href="section-bridi-connection.html#example-random-id-FXSC" title="Example 14.10. ">Example 14.10</a> is true. 
      <a class="xref" href="section-bridi-connection.html#example-random-id-EdY5" title="Example 14.11. ">Example 14.11</a>, however, is equally true:</p>
        <div class="interlinear-gloss-example example">
          <a id="example-random-id-EdY5"></a>
          <p class="title">
            <strong>Example 14.11. 
          <a id="c14e4d9"></a>
        </strong>
          </p>
          <div class="interlinear-gloss-example example-contents">
            <div class="informaltable">
              <table class="interlinear-gloss">
                <colgroup></colgroup>
                <tr class="jbo">
                  <td>la</td>
                  <td>djan.</td>
                  <td>ninmu</td>
                  <td>.ijanai</td>
                  <td>la</td>
                  <td>djeimyz.</td>
                  <td>ninmu</td>
                </tr>
                <tr class="gloss">
                  <td>That-named</td>
                  <td>John</td>
                  <td>is-a-woman</td>
                  <td>if</td>
                  <td>that-named</td>
                  <td>James</td>
                  <td>is-a-woman.</td>
                </tr>
              </table>
            </div>
          </div>
        </div>
        <br class="interlinear-gloss-example example-break" />
        <p class="indent"><a id="idm22952489169952" class="indexterm"></a><a id="idm22952489168816" class="indexterm"></a> This can be thought of as a principle of consistency, and may be paraphrased as follows: 
      
      <span class="quote">“<span class="quote">If a false statement is true, any statement follows from it.</span>”</span> All uses of English 
      
      <span class="quote">“<span class="quote">if</span>”</span> must be considered very carefully when translating into Lojban to see if they really fit this Lojban mold.</p>
        <p><a id="idm22952489166016" class="indexterm"></a><a id="idm22952489164864" class="indexterm"></a><a class="xref" href="section-bridi-connection.html#example-random-id-9CCS" title="Example 14.12. ">Example 14.12</a>, which uses the TFTT truth function, is subject to the same rules: the stated gloss of TFTT as 
      <span class="quote">“<span class="quote">only if</span>”</span> works naturally only when the right-hand bridi is false; if it is true, the left-hand bridi may be either true or false. The last gloss of 
      <a class="xref" href="section-bridi-connection.html#example-random-id-9CCS" title="Example 14.12. ">Example 14.12</a> illustrates the use of 
      <span class="quote">“<span class="quote">if ... then</span>”</span> as a more natural substitute for 
      
      <span class="quote">“<span class="quote">only if</span>”</span>.</p>
        <div class="interlinear-gloss-example example">
          <a id="example-random-id-9CCS"></a>
          <p class="title">
            <strong>Example 14.12. 
          <a id="c14e4d10"></a>
        </strong>
          </p>
          <div class="interlinear-gloss-example example-contents">
            <div class="informaltable">
              <table class="interlinear-gloss">
                <colgroup></colgroup>
                <tr class="jbo">
                  <td>la</td>
                  <td>djan.</td>
                  <td>nanmu</td>
                  <td>.inaja</td>
                  <td>la</td>
                  <td>djeimyz.</td>
                  <td>ninmu</td>
                </tr>
                <tr class="gloss">
                  <td>That-named</td>
                  <td>John</td>
                  <td>is-not-a-man</td>
                  <td>or</td>
                  <td>that-named</td>
                  <td>James</td>
                  <td>is-a-woman.</td>
                </tr>
              </table>
            </div>
            <div class="informaltable">
              <table class="interlinear-gloss">
                <tr class="para">
                  <td colspan="12321">
                    <p class="natlang">John is a man only if James is a woman.</p>
                  </td>
                </tr>
                <tr class="para">
                  <td colspan="12321">
                    <p class="natlang">If John is a man, then James is a woman.</p>
                  </td>
                </tr>
              </table>
            </div>
          </div>
        </div>
        <br class="interlinear-gloss-example example-break" />
        <p class="indent"><a id="idm22952489148048" class="indexterm"></a> The following example illustrates the use of 
      <span xml:lang="jbo" class="foreignphrase" lang="jbo"><em xml:lang="jbo" class="foreignphrase" lang="jbo"><a id="idm22952489146416" class="indexterm"></a><a class="glossterm" href="go01.html#valsi-se"><em class="glossterm">se</em></a></em></span> to, in effect, exchange the two sentences. The normal use of 
      <span xml:lang="jbo" class="foreignphrase" lang="jbo"><em xml:lang="jbo" class="foreignphrase" lang="jbo"><a id="idm22952489144096" class="indexterm"></a><a class="glossterm" href="go01.html#valsi-se"><em class="glossterm">se</em></a></em></span> is to (in effect) transpose places of a bridi, as explained in 
      <a class="xref" href="section-place-conversion.html" title="5.11. Conversion of simple selbri">Section 5.11</a>.</p>
        <div class="interlinear-gloss-example example">
          <a id="example-random-id-z43X"></a>
          <p class="title">
            <strong>Example 14.13. 
          <a id="c14e4d11"></a>
        </strong>
          </p>
          <div class="interlinear-gloss-example example-contents">
            <div class="informaltable">
              <table class="interlinear-gloss">
                <colgroup></colgroup>
                <tr class="jbo">
                  <td>la</td>
                  <td>djan.</td>
                  <td>nanmu</td>
                  <td>.iseju</td>
                  <td>la</td>
                  <td>djeimyz.</td>
                  <td>ninmu</td>
                </tr>
              </table>
            </div>
            <div class="informaltable">
              <table class="interlinear-gloss">
                <tr class="para">
                  <td colspan="12321">
                    <p class="natlang">Whether or not John is a man, James is a woman.</p>
                  </td>
                </tr>
              </table>
            </div>
          </div>
        </div>
        <br class="interlinear-gloss-example example-break" />
        <p class="indent"><a id="idm22952489132432" class="indexterm"></a><a id="idm22952489131584" class="indexterm"></a><a id="idm22952489130480" class="indexterm"></a> If both 
      <span xml:lang="jbo" class="foreignphrase" lang="jbo"><em xml:lang="jbo" class="foreignphrase" lang="jbo"><a id="idm22952489128896" class="indexterm"></a><a class="glossterm" href="go01.html#valsi-na"><em class="glossterm">na</em></a></em></span> and 
      <span xml:lang="jbo" class="foreignphrase" lang="jbo"><em xml:lang="jbo" class="foreignphrase" lang="jbo"><a id="idm22952489126544" class="indexterm"></a><a class="glossterm" href="go01.html#valsi-se"><em class="glossterm">se</em></a></em></span> are present, which is legal but never necessary, 
      <span xml:lang="jbo" class="foreignphrase" lang="jbo"><em xml:lang="jbo" class="foreignphrase" lang="jbo"><a id="idm22952489124160" class="indexterm"></a><a class="glossterm" href="go01.html#valsi-na"><em class="glossterm">na</em></a></em></span> would come before 
      <span xml:lang="jbo" class="foreignphrase" lang="jbo"><em xml:lang="jbo" class="foreignphrase" lang="jbo"><a id="idm22952489121792" class="indexterm"></a><a class="glossterm" href="go01.html#valsi-se"><em class="glossterm">se</em></a></em></span>.</p>
        <p><a id="idm22952489119552" class="indexterm"></a><a id="idm22952489118704" class="indexterm"></a><a id="idm22952489117856" class="indexterm"></a> The full syntax of ijeks, therefore, is:</p>
        <div class="blockquote">
          <blockquote class="blockquote">
            <p class="grammar-template">
        .i [na] [se] JA [nai]
      </p>
          </blockquote>
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        <p>where the cmavo in brackets are optional.</p>
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            <th colspan="3" align="center">Chapter 14. If Wishes Were Horses: The Lojban Connective System</th>
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