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Issue with 5 First-order_logic #26
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There is http://www.w3.org/TR/MathML3/chapter4.html#contm.forall we should ensure that the generated MathML is according to this spec. |
See also http://dlmf.nist.gov/LaTeXML/manual/customization/customization.latexml.html#SS1.SSS0.Px1 for details on the macro creation. |
tree looks good! macro \forallscope not used, delete? |
@philsMINT the tree does not look good. There is no \times in the formulae. |
where do we need \times? the tree seems now to be branched logically correctly (even without using my macro \forallscope - should I delete it?) |
@philsMINT I don't understand your question. The MathML, we currently visualize has times in it which is incorrect. <math xmlns="http://www.w3.org/1998/Math/MathML"
xmlns:xlink="http://www.w3.org/1999/xlink"
alttext="\forall x\,\forall y\,P(x,y)\Leftrightarrow\forall y\,\forall x\,P(x,y)"
class="ltx_Math"
display="inline"
id="p1.1.m1.1">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">
<mrow id="p1.1.m1.1.26.1" xref="p1.1.m1.1.26.1.cmml">
<mo id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">∀</mo>
<mrow id="p1.1.m1.1.26.1.1" xref="p1.1.m1.1.26.1.1.cmml">
<mpadded id="p1.1.m1.1.2" width="+1.7pt" xref="p1.1.m1.1.2.cmml">
<mi id="p1.1.m1.1.2a" xref="p1.1.m1.1.2.cmml">x</mi>
</mpadded>
<mo id="p1.1.m1.1.26.1.1.1" xref="p1.1.m1.1.26.1.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.26.1.1.2" xref="p1.1.m1.1.26.1.1.2.cmml">
<mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">∀</mo>
<mrow id="p1.1.m1.1.26.1.1.2.1" xref="p1.1.m1.1.26.1.1.2.1.cmml">
<mpadded id="p1.1.m1.1.5" width="+1.7pt" xref="p1.1.m1.1.5.cmml">
<mi id="p1.1.m1.1.5a" xref="p1.1.m1.1.5.cmml">y</mi>
</mpadded>
<mo id="p1.1.m1.1.26.1.1.2.1.1" xref="p1.1.m1.1.26.1.1.2.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.26.1.1.2.1.2.2" xref="p1.1.m1.1.26.1.1.2.1.2.1.cmml">
<mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">P</mi>
<mo id="p1.1.m1.1.26.1.1.2.1.2.2a" xref="p1.1.m1.1.26.1.1.2.1.2.1.cmml"></mo>
<mrow id="p1.1.m1.1.26.1.1.2.1.2.2.1" xref="p1.1.m1.1.26.1.1.2.1.2.1.cmml">
<mo id="p1.1.m1.1.8"
stretchy="false"
xref="p1.1.m1.1.26.1.1.2.1.2.1.cmml">(</mo>
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">x</mi>
<mo id="p1.1.m1.1.10" xref="p1.1.m1.1.26.1.1.2.1.2.1.cmml">,</mo>
<mi id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">y</mi>
<mo id="p1.1.m1.1.12"
stretchy="false"
xref="p1.1.m1.1.26.1.1.2.1.2.1.cmml">)</mo>
</mrow>
</mrow>
</mrow>
</mrow>
</mrow>
</mrow>
<mo id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">⇔</mo>
<mrow id="p1.1.m1.1.26.2" xref="p1.1.m1.1.26.2.cmml">
<mo id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">∀</mo>
<mrow id="p1.1.m1.1.26.2.1" xref="p1.1.m1.1.26.2.1.cmml">
<mpadded id="p1.1.m1.1.15" width="+1.7pt" xref="p1.1.m1.1.15.cmml">
<mi id="p1.1.m1.1.15a" xref="p1.1.m1.1.15.cmml">y</mi>
</mpadded>
<mo id="p1.1.m1.1.26.2.1.1" xref="p1.1.m1.1.26.2.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.26.2.1.2" xref="p1.1.m1.1.26.2.1.2.cmml">
<mo id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">∀</mo>
<mrow id="p1.1.m1.1.26.2.1.2.1" xref="p1.1.m1.1.26.2.1.2.1.cmml">
<mpadded id="p1.1.m1.1.18" width="+1.7pt" xref="p1.1.m1.1.18.cmml">
<mi id="p1.1.m1.1.18a" xref="p1.1.m1.1.18.cmml">x</mi>
</mpadded>
<mo id="p1.1.m1.1.26.2.1.2.1.1" xref="p1.1.m1.1.26.2.1.2.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.26.2.1.2.1.2.2" xref="p1.1.m1.1.26.2.1.2.1.2.1.cmml">
<mi id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">P</mi>
<mo id="p1.1.m1.1.26.2.1.2.1.2.2a" xref="p1.1.m1.1.26.2.1.2.1.2.1.cmml"></mo>
<mrow id="p1.1.m1.1.26.2.1.2.1.2.2.1" xref="p1.1.m1.1.26.2.1.2.1.2.1.cmml">
<mo id="p1.1.m1.1.21"
stretchy="false"
xref="p1.1.m1.1.26.2.1.2.1.2.1.cmml">(</mo>
<mi id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">x</mi>
<mo id="p1.1.m1.1.23" xref="p1.1.m1.1.26.2.1.2.1.2.1.cmml">,</mo>
<mi id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">y</mi>
<mo id="p1.1.m1.1.25"
stretchy="false"
xref="p1.1.m1.1.26.2.1.2.1.2.1.cmml">)</mo>
</mrow>
</mrow>
</mrow>
</mrow>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26">
<ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">⇔</ci>
<apply id="p1.1.m1.1.26.1.cmml" xref="p1.1.m1.1.26.1">
<csymbol cd="latexml" id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">for-all</csymbol>
<apply id="p1.1.m1.1.26.1.1.cmml" xref="p1.1.m1.1.26.1.1">
<times id="p1.1.m1.1.26.1.1.1.cmml" xref="p1.1.m1.1.26.1.1.1"/>
<ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">𝑥</ci>
<apply id="p1.1.m1.1.26.1.1.2.cmml" xref="p1.1.m1.1.26.1.1.2">
<csymbol cd="latexml" id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">for-all</csymbol>
<apply id="p1.1.m1.1.26.1.1.2.1.cmml" xref="p1.1.m1.1.26.1.1.2.1">
<times id="p1.1.m1.1.26.1.1.2.1.1.cmml" xref="p1.1.m1.1.26.1.1.2.1.1"/>
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">𝑦</ci>
<apply id="p1.1.m1.1.26.1.1.2.1.2.1.cmml" xref="p1.1.m1.1.26.1.1.2.1.2.2">
<csymbol cd="wikidata" id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">Q1144319</csymbol>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">𝑥</ci>
<ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">𝑦</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.26.2.cmml" xref="p1.1.m1.1.26.2">
<csymbol cd="latexml" id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">for-all</csymbol>
<apply id="p1.1.m1.1.26.2.1.cmml" xref="p1.1.m1.1.26.2.1">
<times id="p1.1.m1.1.26.2.1.1.cmml" xref="p1.1.m1.1.26.2.1.1"/>
<ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">𝑦</ci>
<apply id="p1.1.m1.1.26.2.1.2.cmml" xref="p1.1.m1.1.26.2.1.2">
<csymbol cd="latexml" id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">for-all</csymbol>
<apply id="p1.1.m1.1.26.2.1.2.1.cmml" xref="p1.1.m1.1.26.2.1.2.1">
<times id="p1.1.m1.1.26.2.1.2.1.1.cmml" xref="p1.1.m1.1.26.2.1.2.1.1"/>
<ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">𝑥</ci>
<apply id="p1.1.m1.1.26.2.1.2.1.2.1.cmml" xref="p1.1.m1.1.26.2.1.2.1.2.2">
<csymbol cd="wikidata" id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">Q1144319</csymbol>
<ci id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">𝑥</ci>
<ci id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">𝑦</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">\forall x\,\forall y\,P(x,y)\Leftrightarrow\forall y\,\forall x\,P(x,y)</annotation>
</semantics>
</math> |
what about the scope of \forall quantors? position vertically instead of horizontally?
Link to First-order_logic, qID 5
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