| ... | ... | @@ -43,14 +43,13 @@ Semantically enriched MathML: |
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```html
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<math>
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<mrow semantic-type="infixop" semantic-role="addition" id="5" semantic-content="1,3" semantic-children="0,2,4">
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<mi semantic-type="identifier" semantic-role="latinletter" id="0" semantic-parent="0">a</mi>
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<mo semantic-type="operator" semantic-role="addition" id="1" semantic-operator="infixop,+" semantic-parent="1">+</mo>
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<mi semantic-type="identifier" semantic-role="latinletter" id="2" semantic-parent="2">b</mi>
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<mo semantic-type="operator" semantic-role="addition" id="3" semantic-operator="infixop,+" semantic-parent="3">+</mo>
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<mi semantic-type="identifier" semantic-role="latinletter" id="4" semantic-parent="4">c</mi>
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<mi semantic-type="identifier" semantic-role="latinletter" id="0" semantic-parent="5">a</mi>
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<mo semantic-type="operator" semantic-role="addition" id="1" semantic-operator="infixop,+" semantic-parent="5">+</mo>
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<mi semantic-type="identifier" semantic-role="latinletter" id="2" semantic-parent="5">b</mi>
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<mo semantic-type="operator" semantic-role="addition" id="3" semantic-operator="infixop,+" semantic-parent="5">+</mo>
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<mi semantic-type="identifier" semantic-role="latinletter" id="4" semantic-parent="5">c</mi>
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</mrow>
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</math>
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```
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## Operation and Relation
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| ... | ... | @@ -70,12 +69,12 @@ Semantically enriched MathML: |
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```html
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<math>
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<mrow semantic-type="relseq" semantic-role="equality" id="6" semantic-content="1" semantic-children="0,5">
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<mn semantic-type="number" semantic-role="integer" id="0" semantic-parent="0">5</mn>
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<mo semantic-type="relation" semantic-role="equality" id="1" semantic-operator="relseq,=" semantic-parent="1">=</mo>
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<mrow semantic-type="infixop" semantic-role="addition" id="5" semantic-content="3" semantic-children="2,4" semantic-parent="5">
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<mn semantic-type="number" semantic-role="integer" id="2" semantic-parent="2">3</mn>
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<mo semantic-type="operator" semantic-role="addition" id="3" semantic-operator="infixop,+" semantic-parent="3">+</mo>
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<mn semantic-type="number" semantic-role="integer" id="4" semantic-parent="4">2</mn>
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<mn semantic-type="number" semantic-role="integer" id="0" semantic-parent="6">5</mn>
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<mo semantic-type="relation" semantic-role="equality" id="1" semantic-operator="relseq,=" semantic-parent="6">=</mo>
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<mrow semantic-type="infixop" semantic-role="addition" id="5" semantic-content="3" semantic-children="2,4" semantic-parent="6">
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<mn semantic-type="number" semantic-role="integer" id="2" semantic-parent="5">3</mn>
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<mo semantic-type="operator" semantic-role="addition" id="3" semantic-operator="infixop,+" semantic-parent="5">+</mo>
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<mn semantic-type="number" semantic-role="integer" id="4" semantic-parent="5">2</mn>
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</mrow>
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</mrow>
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</math>
|
| ... | ... | @@ -98,12 +97,12 @@ Enriched MathML: |
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```html
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<math>
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<mrow semantic-type="relseq" semantic-role="equality" id="6" semantic-content="1" semantic-children="0,5">
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<mi semantic-type="number" semantic-role="integer" id="0" semantic-parent="0">5</mi>
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<mo semantic-type="relation" semantic-role="equality" id="1" semantic-operator="relseq,=" semantic-parent="1">=</mo>
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<mrow semantic-type="infixop" semantic-role="addition" id="5" semantic-content="3" semantic-children="2,4" semantic-parent="5">
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<mi semantic-type="number" semantic-role="integer" id="2" semantic-parent="2">3</mi>
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<mo semantic-type="operator" semantic-role="addition" id="3" semantic-operator="infixop,+" semantic-parent="3">+</mo>
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<mi semantic-type="number" semantic-role="integer" id="4" semantic-parent="4">2</mi>
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<mi semantic-type="number" semantic-role="integer" id="0" semantic-parent="6">5</mi>
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<mo semantic-type="relation" semantic-role="equality" id="1" semantic-operator="relseq,=" semantic-parent="6">=</mo>
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|
<mrow semantic-type="infixop" semantic-role="addition" id="5" semantic-content="3" semantic-children="2,4" semantic-parent="6">
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<mi semantic-type="number" semantic-role="integer" id="2" semantic-parent="5">3</mi>
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<mo semantic-type="operator" semantic-role="addition" id="3" semantic-operator="infixop,+" semantic-parent="5">+</mo>
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<mi semantic-type="number" semantic-role="integer" id="4" semantic-parent="5">2</mi>
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</mrow>
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</mrow>
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</math>
|
| ... | ... | @@ -129,20 +128,19 @@ Semantically enriched MathML: |
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```html
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<math>
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<mrow semantic-type="infixop" semantic-role="addition" id="9" semantic-content="5" semantic-children="8,6">
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<mrow semantic-type="infixop" semantic-role="subtraction" id="8" semantic-content="3" semantic-children="7,4" semantic-parent="8">
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<mrow semantic-type="infixop" semantic-role="addition" id="7" semantic-content="1" semantic-children="0,2" semantic-parent="7">
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<mi semantic-type="identifier" semantic-role="latinletter" id="0" semantic-parent="0">a</mi>
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|
<mo semantic-type="operator" semantic-role="addition" id="1" semantic-operator="infixop,+" semantic-parent="1">+</mo>
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|
<mi semantic-type="identifier" semantic-role="latinletter" id="2" semantic-parent="2">b</mi>
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<mrow semantic-type="infixop" semantic-role="subtraction" id="8" semantic-content="3" semantic-children="7,4" semantic-parent="9">
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<mrow semantic-type="infixop" semantic-role="addition" id="7" semantic-content="1" semantic-children="0,2" semantic-parent="8">
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<mi semantic-type="identifier" semantic-role="latinletter" id="0" semantic-parent="7">a</mi>
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<mo semantic-type="operator" semantic-role="addition" id="1" semantic-operator="infixop,+" semantic-parent="7">+</mo>
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<mi semantic-type="identifier" semantic-role="latinletter" id="2" semantic-parent="7">b</mi>
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</mrow>
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<mo semantic-type="operator" semantic-role="subtraction" id="3" semantic-operator="infixop,-" semantic-parent="3">-</mo>
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<mi semantic-type="identifier" semantic-role="latinletter" id="4" semantic-parent="4">c</mi>
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<mo semantic-type="operator" semantic-role="subtraction" id="3" semantic-operator="infixop,-" semantic-parent="8">-</mo>
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<mi semantic-type="identifier" semantic-role="latinletter" id="4" semantic-parent="8">c</mi>
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</mrow>
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<mo semantic-type="operator" semantic-role="addition" id="5" semantic-operator="infixop,+" semantic-parent="5">+</mo>
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<mi semantic-type="identifier" semantic-role="latinletter" id="6" semantic-parent="6">d</mi>
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<mo semantic-type="operator" semantic-role="addition" id="5" semantic-operator="infixop,+" semantic-parent="9">+</mo>
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<mi semantic-type="identifier" semantic-role="latinletter" id="6" semantic-parent="9">d</mi>
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</mrow>
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</math>
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```
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|
| ... | ... | @@ -168,26 +166,25 @@ Semantically enriched MathML: |
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|
|
```html
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<math>
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<mrow semantic-type="infixop" semantic-role="addition" id="10" semantic-content="1,6" semantic-children="0,13,14">
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<mi semantic-type="identifier" semantic-role="latinletter" id="0" semantic-parent="0">a</mi>
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<mo semantic-type="operator" semantic-role="addition" id="1" semantic-operator="infixop,+" semantic-parent="1">+</mo>
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<mrow semantic-type="infixop" semantic-role="multiplication" id="13" semantic-content="3" semantic-children="2,12" semantic-parent="13">
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<mi semantic-type="identifier" semantic-role="latinletter" id="2" semantic-parent="2">b</mi>
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<mo semantic-type="operator" semantic-role="multiplication" id="3" semantic-operator="infixop,∘" semantic-parent="3">∘</mo>
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<mrow semantic-type="infixop" semantic-role="implicit" id="12" semantic-content="11" semantic-children="4,5" semantic-parent="12">
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<mi semantic-type="identifier" semantic-role="latinletter" id="4" semantic-parent="4">c</mi>
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<mrow semantic-type="operator" semantic-role="multiplication" id="11" semantic-children="" semantic-operator="infixop," semantic-parent="11"/>
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<mi semantic-type="identifier" semantic-role="latinletter" id="5" semantic-parent="5">d</mi>
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<mi semantic-type="identifier" semantic-role="latinletter" id="0" semantic-parent="10">a</mi>
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<mo semantic-type="operator" semantic-role="addition" id="1" semantic-operator="infixop,+" semantic-parent="10">+</mo>
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<mrow semantic-type="infixop" semantic-role="multiplication" id="13" semantic-content="3" semantic-children="2,12" semantic-parent="10">
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<mi semantic-type="identifier" semantic-role="latinletter" id="2" semantic-parent="13">b</mi>
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<mo semantic-type="operator" semantic-role="multiplication" id="3" semantic-operator="infixop,∘" semantic-parent="13">∘</mo>
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<mrow semantic-type="infixop" semantic-role="implicit" id="12" semantic-content="11" semantic-children="4,5" semantic-parent="13">
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<mi semantic-type="identifier" semantic-role="latinletter" id="4" semantic-parent="12">c</mi>
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<mrow semantic-type="operator" semantic-role="multiplication" id="11" semantic-children="" semantic-operator="infixop," semantic-parent="12"/>
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<mi semantic-type="identifier" semantic-role="latinletter" id="5" semantic-parent="12">d</mi>
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</mrow>
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</mrow>
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|
<mo semantic-type="operator" semantic-role="addition" id="6" semantic-operator="infixop,+" semantic-parent="6">+</mo>
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<mrow semantic-type="infixop" semantic-role="multiplication" id="14" semantic-content="8" semantic-children="7,9" semantic-parent="14">
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<mi semantic-type="identifier" semantic-role="latinletter" id="7" semantic-parent="7">e</mi>
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<mo semantic-type="operator" semantic-role="multiplication" id="8" semantic-operator="infixop,∘" semantic-parent="8">∘</mo>
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<mi semantic-type="identifier" semantic-role="latinletter" id="9" semantic-parent="9">f</mi>
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<mo semantic-type="operator" semantic-role="addition" id="6" semantic-operator="infixop,+" semantic-parent="10">+</mo>
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|
<mrow semantic-type="infixop" semantic-role="multiplication" id="14" semantic-content="8" semantic-children="7,9" semantic-parent="10">
|
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|
<mi semantic-type="identifier" semantic-role="latinletter" id="7" semantic-parent="14">e</mi>
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<mo semantic-type="operator" semantic-role="multiplication" id="8" semantic-operator="infixop,∘" semantic-parent="14">∘</mo>
|
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|
<mi semantic-type="identifier" semantic-role="latinletter" id="9" semantic-parent="14">f</mi>
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|
</mrow>
|
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|
</mrow>
|
|
|
|
</math>
|
|
|
|
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|
|
|
```
|
|
|
|
|
|
|
|
The latter contains an implicit operation, resulting in an empty mrow. The question is: What should we do with elements that are introduced by the semantic interpretation but not part of the original MathML. All these are invisible characters: invisible times, invisible comma, function application.
|
| ... | ... | @@ -226,9 +223,9 @@ Semantically enriched MathML: |
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|
|
```html
|
|
|
|
<math>
|
|
|
|
<mrow semantic-type="infixop" semantic-role="implicit" id="3" semantic-content="2" semantic-children="0,1">
|
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|
|
<mi semantic-type="identifier" semantic-role="latinletter" id="0" semantic-parent="0">a</mi>
|
|
|
|
<mrow semantic-type="operator" semantic-role="multiplication" id="2" semantic-children="" semantic-operator="infixop," semantic-parent="2"/>
|
|
|
|
<mi semantic-type="identifier" semantic-role="latinletter" id="1" semantic-parent="1">b</mi>
|
|
|
|
<mi semantic-type="identifier" semantic-role="latinletter" id="0" semantic-parent="3">a</mi>
|
|
|
|
<mrow semantic-type="operator" semantic-role="multiplication" id="2" semantic-children="" semantic-operator="infixop," semantic-parent="3"/>
|
|
|
|
<mi semantic-type="identifier" semantic-role="latinletter" id="1" semantic-parent="3">b</mi>
|
|
|
|
</mrow>
|
|
|
|
</math>
|
|
|
|
|
| ... | ... | @@ -245,9 +242,9 @@ Original MathML: |
|
|
|
Semantically enriched MathML:
|
|
|
|
<math>
|
|
|
|
<mrow semantic-type="infixop" semantic-role="implicit" id="3" semantic-content="2" semantic-children="0,1">
|
|
|
|
<mi semantic-type="identifier" semantic-role="latinletter" id="0" semantic-parent="0">a</mi>
|
|
|
|
<mrow semantic-type="operator" semantic-role="multiplication" id="2" semantic-children="" semantic-operator="infixop," semantic-parent="2"/>
|
|
|
|
<mi semantic-type="identifier" semantic-role="latinletter" id="1" semantic-parent="1">b</mi>
|
|
|
|
<mi semantic-type="identifier" semantic-role="latinletter" id="0" semantic-parent="3">a</mi>
|
|
|
|
<mrow semantic-type="operator" semantic-role="multiplication" id="2" semantic-children="" semantic-operator="infixop," semantic-parent="3"/>
|
|
|
|
<mi semantic-type="identifier" semantic-role="latinletter" id="1" semantic-parent="3">b</mi>
|
|
|
|
</mrow>
|
|
|
|
</math>
|
|
|
|
|
| ... | ... | @@ -272,22 +269,22 @@ Original MathML: |
|
|
|
Semantically enriched MathML:
|
|
|
|
<math>
|
|
|
|
<mrow semantic-type="infixop" semantic-role="addition" id="10" semantic-content="1,6" semantic-children="0,13,14">
|
|
|
|
<mi semantic-type="identifier" semantic-role="latinletter" id="0" semantic-parent="0">a</mi>
|
|
|
|
<mo semantic-type="operator" semantic-role="addition" id="1" semantic-operator="infixop,+" semantic-parent="1">+</mo>
|
|
|
|
<mrow semantic-type="infixop" semantic-role="multiplication" id="13" semantic-content="3" semantic-children="2,12" semantic-parent="13">
|
|
|
|
<mi semantic-type="identifier" semantic-role="latinletter" id="2" semantic-parent="2">b</mi>
|
|
|
|
<mo semantic-type="operator" semantic-role="multiplication" id="3" semantic-operator="infixop,∘" semantic-parent="3">∘</mo>
|
|
|
|
<mrow semantic-type="infixop" semantic-role="implicit" id="12" semantic-content="11" semantic-children="4,5" semantic-parent="12">
|
|
|
|
<mi semantic-type="identifier" semantic-role="latinletter" id="4" semantic-parent="4">c</mi>
|
|
|
|
<mrow semantic-type="operator" semantic-role="multiplication" id="11" semantic-children="" semantic-operator="infixop," semantic-parent="11"/>
|
|
|
|
<mi semantic-type="identifier" semantic-role="latinletter" id="5" semantic-parent="5">d</mi>
|
|
|
|
<mi semantic-type="identifier" semantic-role="latinletter" id="0" semantic-parent="10">a</mi>
|
|
|
|
<mo semantic-type="operator" semantic-role="addition" id="1" semantic-operator="infixop,+" semantic-parent="10">+</mo>
|
|
|
|
<mrow semantic-type="infixop" semantic-role="multiplication" id="13" semantic-content="3" semantic-children="2,12" semantic-parent="10">
|
|
|
|
<mi semantic-type="identifier" semantic-role="latinletter" id="2" semantic-parent="13">b</mi>
|
|
|
|
<mo semantic-type="operator" semantic-role="multiplication" id="3" semantic-operator="infixop,∘" semantic-parent="13">∘</mo>
|
|
|
|
<mrow semantic-type="infixop" semantic-role="implicit" id="12" semantic-content="11" semantic-children="4,5" semantic-parent="13">
|
|
|
|
<mi semantic-type="identifier" semantic-role="latinletter" id="4" semantic-parent="12">c</mi>
|
|
|
|
<mrow semantic-type="operator" semantic-role="multiplication" id="11" semantic-children="" semantic-operator="infixop," semantic-parent="12"/>
|
|
|
|
<mi semantic-type="identifier" semantic-role="latinletter" id="5" semantic-parent="12">d</mi>
|
|
|
|
</mrow>
|
|
|
|
</mrow>
|
|
|
|
<mo semantic-type="operator" semantic-role="addition" id="6" semantic-operator="infixop,+" semantic-parent="6">+</mo>
|
|
|
|
<mrow semantic-type="infixop" semantic-role="multiplication" id="14" semantic-content="8" semantic-children="7,9" semantic-parent="14">
|
|
|
|
<mi semantic-type="identifier" semantic-role="latinletter" id="7" semantic-parent="7">e</mi>
|
|
|
|
<mo semantic-type="operator" semantic-role="multiplication" id="8" semantic-operator="infixop,∘" semantic-parent="8">∘</mo>
|
|
|
|
<mi semantic-type="identifier" semantic-role="latinletter" id="9" semantic-parent="9">f</mi>
|
|
|
|
<mo semantic-type="operator" semantic-role="addition" id="6" semantic-operator="infixop,+" semantic-parent="10">+</mo>
|
|
|
|
<mrow semantic-type="infixop" semantic-role="multiplication" id="14" semantic-content="8" semantic-children="7,9" semantic-parent="10">
|
|
|
|
<mi semantic-type="identifier" semantic-role="latinletter" id="7" semantic-parent="14">e</mi>
|
|
|
|
<mo semantic-type="operator" semantic-role="multiplication" id="8" semantic-operator="infixop,∘" semantic-parent="14">∘</mo>
|
|
|
|
<mi semantic-type="identifier" semantic-role="latinletter" id="9" semantic-parent="14">f</mi>
|
|
|
|
</mrow>
|
|
|
|
</mrow>
|
|
|
|
</math> |
|
|
\ No newline at end of file |
