P5: Directrices para la codificación y el intercambio de textos electrónicos

19.1 Graphs and DigraphsTEI: Graphs and Digraphs¶

Before proceeding, some additional terminology may be helpful. We define a path in a graph as a sequence of nodes n1, ..., nk such that there is an arc from each ni to ni+1 in the sequence. A cyclic path, or cycle is a path leading from a particular node back to itself. A graph that contains at least one cycle is said to be cyclic; otherwise it is acyclic. We say, finally, that a graph is connected if there is a path from some node to every other node in the graph; any graph that is not connected is said to be disconnected.

Here is an example of an undirected, cyclic disconnected graph, in which the nodes are annotated with three-letter codes for airports, and the arcs connecting the nodes are represented by horizontal and vertical lines, with 90 degree bends used simply to avoid having to draw diagonal lines.

The first child element of graph may be a label to record a label for the graph; similarly, the label child of each node element records the labels of that node. The order and size attributes on the graph element record the number of nodes and number of arcs in the graph respectively; these values are optional (since they can be computed from the rest of the graph), but if they are supplied, they must be consistent with the rest of the encoding. They can thus be used to help check that the graph has been encoded and transmitted correctly. The degree attribute on the node elements record the number of arcs that are incident with that node. It is optional (because redundant), but can be used to help in validity checking: if a value is given, it must be consistent with the rest of the information in the graph. Finally, the from and to attributes on the arc elements provide pointers to the nodes connected by those arcs. Since the graph is undirected, no directionality is implied by the use of the from and to attributes; the values of these attributes could be interchanged in each arc without changing the graph.

Although in many cases the arc element is redundant (since arcs can be described using the adjacency attributes of their adjacent nodes), it has nevertheless been included in this module, in order to allow the convenient specification of identifiers, display or rendition information, and labels for each arc (using the attributes xml:id, rend, and a child label element).

Next, let us modify the preceding graph by adding directionality to the arcs. Specifically, we now think of the arcs as specifying selected routes from one airport to another, as indicated by the direction of the arrowheads in the following diagram.

• » 19.1.2 Family Trees
• Principal | Índice

19.1.1 Transition NetworksTEI: Transition Networks¶

For encoding transition networks and other kinds of directed graphs in which distinctions among types of nodes must be made, the type attribute is provided for node elements. In the following example, the initial and final nodes (or states) of the network are distinguished. It can be understood as accepting the set of strings obtained by traversing it from its initial node to its final node, and concatenating the labels.

<graph
  type="network-transition"
  xml:id="SS8"
  order="5"
  size="6">
 <label>(8)</label>
 <node
   xml:id="Q0"
   inDegree="0"
   outDegree="1"
   type="initial"/>
 <node xml:id="Q1" inDegree="2" outDegree="3"/>
 <node xml:id="Q2" inDegree="1" outDegree="1"/>
 <node xml:id="Q3" inDegree="1" outDegree="1"/>
 <node
   xml:id="Q4"
   inDegree="2"
   outDegree="0"
   type="final"/>
 <arc from="#Q0" to="#Q1">
  <label>THE</label>
 </arc>
 <arc from="#Q1" to="#Q1">
  <label>OLD</label>
 </arc>
 <arc from="#Q1" to="#Q2">
  <label>MAN</label>
 </arc>
 <arc from="#Q1" to="#Q3">
  <label>MEN</label>
 </arc>
 <arc from="#Q2" to="#Q4">
  <label>COMES</label>
 </arc>
 <arc from="#Q3" to="#Q4">
  <label>COME</label>
 </arc>
</graph>

A finite state transducer has two labels on each arc, and can be thought of as representing a mapping from one sequence of labels to the other. The following example represents a transducer for translating the English strings accepted by the network in the preceding example into French. The nodes have been annotated with numbers, for convenience.

<graph type="transducer" order="7" size="10">
 <node
   xml:id="T0"
   inDegree="0"
   outDegree="3"
   type="initial">
  <label>0</label>
 </node>
 <node xml:id="T1" inDegree="2" outDegree="1">
  <label>1</label>
 </node>
 <node xml:id="T2" inDegree="2" outDegree="2">
  <label>2</label>
 </node>
 <node xml:id="T3" inDegree="2" outDegree="2">
  <label>3</label>
 </node>
 <node xml:id="T4" inDegree="1" outDegree="1">
  <label>4</label>
 </node>
 <node xml:id="T5" inDegree="1" outDegree="1">
  <label>5</label>
 </node>
 <node
   xml:id="T6"
   inDegree="2"
   outDegree="0"
   type="final">
  <label>6</label>
 </node>
 <arc from="#T0" to="#T1">
  <label>THE</label>
  <label>L'</label>
 </arc>
 <arc from="#T0" to="#T2">
  <label>THE</label>
  <label>LE</label>
 </arc>
 <arc from="#T0" to="#T3">
  <label>THE</label>
  <label>LES</label>
 </arc>
 <arc from="#T1" to="#T4">
  <label>MAN</label>
  <label>HOMME</label>
 </arc>
 <arc from="#T2" to="#T1">
  <label>OLD</label>
  <label>VIEIL</label>
 </arc>
 <arc from="#T2" to="#T2">
  <label>OLD</label>
  <label>VIEIL</label>
 </arc>
 <arc from="#T3" to="#T3">
  <label>OLD</label>
  <label>VIEUX</label>
 </arc>
 <arc from="#T3" to="#T5">
  <label>MEN</label>
  <label>HOMMES</label>
 </arc>
 <arc from="#T4" to="#T6">
  <label>COMES</label>
  <label>VIENT</label>
 </arc>
 <arc from="#T5" to="#T6">
  <label>COME</label>
  <label>VIENNENT</label>
 </arc>
</graph>

• « 19.1.1 Transition Networks
• » 19.1.3 Historical Interpretation
• Principal | Índice

19.1.2 Family TreesTEI: Family Trees¶

The next example provides an encoding a portion of a family tree, in which nodes are used to represent individuals and parents of individuals, and arcs are used to represent common parentage and descent links. Let us suppose, further, that information about individuals is contained in feature structures, which are contained in feature-structure libraries elsewhere (see 18.4 Feature and Feature-Value Libraries). We can use the value attribute on node elements to point to those feature structures. In this particular representation of the graph, nodes representing females are framed by ovals, nodes representing males are framed by boxes, and nodes representing parents are framed by diamonds.

<graph type="family_tree" order="13" size="12">
 <node
   xml:id="KATHR"
   value="http://example.com/russell-fs/tei/kr1"
   inDegree="0"
   outDegree="1">
  <label>Katherine</label>
 </node>
 <node
   xml:id="AMBER"
   value="http://example.com/russell-fs/tei/ar1"
   inDegree="0"
   outDegree="1">
  <label>Amberley</label>
 </node>
 <node xml:id="KAR" inDegree="2" outDegree="3">
  <label>K+A</label>
 </node>
 <node
   xml:id="BERTR"
   value="http://example.com/russell-fs/tei/br1"
   inDegree="1"
   outDegree="2">
  <label>Bertrand</label>
 </node>
 <node
   xml:id="PETER"
   value="http://example.com/russell-fs/tei/pr1"
   inDegree="0"
   outDegree="1">
  <label>Peter</label>
 </node>
 <node
   xml:id="DORAR"
   value="http://example.com/russell-fs/tei/dr1"
   inDegree="0"
   outDegree="1">
  <label>Dora</label>
 </node>
 <node xml:id="PBR" inDegree="2" outDegree="1">
  <label>P+B</label>
 </node>
 <node xml:id="DBR" inDegree="2" outDegree="2">
  <label>D+B</label>
 </node>
 <node
   xml:id="FRANR"
   value="http://example.com/russell-fs/tei/fr1"
   inDegree="1"
   outDegree="0">
  <label>Frank</label>
 </node>
 <node
   xml:id="RACHR"
   value="http://example.com/russell-fs/tei/rr1"
   inDegree="1"
   outDegree="0">
  <label>Rachel</label>
 </node>
 <node
   xml:id="CONRR"
   value="http://example.com/russell-fs/tei/cr1"
   inDegree="1"
   outDegree="0">
  <label>Conrad</label>
 </node>
 <node
   xml:id="KATER"
   value="http://example.com/russell-fs/tei/kr2"
   inDegree="1"
   outDegree="0">
  <label>Kate</label>
 </node>
 <node
   xml:id="JOHNR"
   value="http://example.com/russell-fs/tei/jr1"
   inDegree="1"
   outDegree="0">
  <label>John</label>
 </node>
 <arc from="#KATHR" to="#KAR">
  <label>Mo</label>
 </arc>
 <arc from="#AMBER" to="#KAR">
  <label>Fa</label>
 </arc>
 <arc from="#KAR" to="#BERTR">
  <label>So</label>
 </arc>
 <arc from="#KAR" to="#FRANR">
  <label>So</label>
 </arc>
 <arc from="#KAR" to="#RACHR">
  <label>Da</label>
 </arc>
 <arc from="#PETER" to="#PBR">
  <label>Mo</label>
 </arc>
 <arc from="#BERTR" to="#PBR">
  <label>Fa</label>
 </arc>
 <arc from="#PBR" to="#CONRR">
  <label>So</label>
 </arc>
 <arc from="#DORAR" to="#DBR">
  <label>Mo</label>
 </arc>
 <arc from="#BERTR" to="#DBR">
  <label>Fa</label>
 </arc>
 <arc from="#DBR" to="#KATER">
  <label>Da</label>
 </arc>
 <arc from="#DBR" to="#JOHNR">
  <label>So</label>
 </arc>
</graph>

bibliography

19.2 TreesTEI: Trees¶

Here is an example of a tree. It represents the order in which the operators of addition (symbolized by +), exponentiation (symbolized by **) and division (symbolized by /) are applied in evaluating the arithmetic formula ((a**2)+(b**2))/((a+b)**2). In drawing the graph, the root is placed on the far right, and directionality is presumed to be to the left.

<tree
  n="ex1"
  arity="2"
  ord="true"
  order="12">
 <root xml:id="G-DIV1" children="#PLU1 #EXP1">
  <label>/</label>
 </root>
 <iNode xml:id="PLU1" parent="#G-DIV1" children="#EXP2 #EXP3">
  <label>+</label>
 </iNode>
 <iNode xml:id="EXP1" parent="#G-DIV1" children="#PLU2 #NUM2.3">
  <label>**</label>
 </iNode>
 <iNode xml:id="EXP2" parent="#PLU1" children="#VARA1 #NUM2.1">
  <label>**</label>
 </iNode>
 <iNode xml:id="EXP3" parent="#PLU1" children="#VARB1 #NUM2.2">
  <label>**</label>
 </iNode>
 <iNode xml:id="PLU2" parent="#EXP1" children="#VARA2 #VARB2">
  <label>+</label>
 </iNode>
 <leaf xml:id="VARA1" parent="#EXP2">
  <label>a</label>
 </leaf>
 <leaf xml:id="NUM2.1" parent="#EXP2">
  <label>2</label>
 </leaf>
 <leaf xml:id="VARB1" parent="#EXP3">
  <label>b</label>
 </leaf>
 <leaf xml:id="NUM2.2" parent="#EXP3">
  <label>2</label>
 </leaf>
 <leaf xml:id="VARA2" parent="#PLU2">
  <label>a</label>
 </leaf>
 <leaf xml:id="VARB2" parent="#PLU2">
  <label>b</label>
 </leaf>
 <leaf xml:id="NUM2.3" parent="#EXP1">
  <label>2</label>
 </leaf>
</tree>

In this encoding, the arity attribute represents the arity of the tree, which is the greatest value of the outDegree attribute for any of the nodes in the tree. If, as in this case, arity is 2, we say that the tree is a binary tree.

Linguistic phrase structure is very commonly represented by trees. Here is an example of phrase structure represented by an ordered tree with its root at the top, and a possible encoding.

<tree
  n="ex3"
  ord="true"
  arity="2"
  order="8">
 <root xml:id="GD-PP1" children="#GD-P1 #GD-NP1">
  <label>PP</label>
 </root>
 <iNode xml:id="GD-P1" parent="#GD-PP1" children="#GD-WITH1">
  <label>P</label>
 </iNode>
 <leaf xml:id="GD-WITH1" parent="#GD-P1">
  <label>with</label>
 </leaf>
 <iNode xml:id="GD-NP1" parent="#GD-PP1" children="#GD-THE1 #GD-PERI1">
  <label>NP</label>
 </iNode>
 <iNode xml:id="GD-ART1" parent="#GD-NP1" children="#GD-THE1">
  <label>Art</label>
 </iNode>
 <leaf xml:id="GD-THE1" parent="#GD-ART1">
  <label>the</label>
 </leaf>
 <iNode xml:id="GD-N1" parent="#GD-NP1" children="#GD-PERI1">
  <label>N</label>
 </iNode>
 <leaf xml:id="GD-PERI1" parent="#GD-N1">
  <label>periscope</label>
 </leaf>
</tree>

Finally, here is an example of an ordered tree, in which a particular node which ordinarily would precede another is specified as following it. In the drawing, the xxx symbol indicates that the arc from VB to PT crosses the arc from VP to PN.

<tree
  n="ex4"
  arity="2"
  order="8"
  ord="true">
 <leaf xml:id="GD-LOOK1" parent="#GD-VB2">
  <label>look</label>
 </leaf>
 <leaf xml:id="GD-THEM1" parent="#GD-PN1">
  <label>them</label>
 </leaf>
 <leaf xml:id="GD-UP1" parent="#GD-PT1">
  <label>up</label>
 </leaf>
 <iNode xml:id="GD-VB2" parent="#GD-VB1" children="#GD-LOOK1">
  <label>VB</label>
 </iNode>
 <iNode xml:id="GD-PN1" parent="#GD-VP1" children="#GD-THEM1">
  <label>PN</label>
 </iNode>
 <iNode
   xml:id="GD-PT1"
   parent="#GD-VB1"
   children="#GD-UP1"
   follow="#GD-PN1">
  <label>PT</label>
 </iNode>
 <iNode xml:id="GD-VB1" parent="#GD-VP1" children="#GD-VB2 #GD-PT1">
  <label>VB</label>
 </iNode>
 <root xml:id="GD-VP1" children="#GD-VB1 #GD-PN1">
  <label>VP</label>
 </root>
</tree>

19.3 Another Tree NotationTEI: Another Tree Notation¶

Like the root, iNode, and leaf of a tree, the eTree, triangle and eLeaf elements may also have value attributes and label children.

To illustrate the use of the eTree and eLeaf elements, here is an encoding of the second example in section 19.2 Trees, repeated here for convenience.

<eTree n="ex1">
 <label>PP</label>
 <eTree>
  <label>P</label>
  <eLeaf>
   <label>with</label>
  </eLeaf>
 </eTree>
 <eTree>
  <label>NP</label>
  <eTree>
   <label>Art</label>
   <eLeaf>
    <label>the</label>
   </eLeaf>
  </eTree>
  <eTree>
   <label>N</label>
   <eLeaf>
    <label>periscope</label>
   </eLeaf>
  </eTree>
 </eTree>
</eTree>

Next, we provide an encoding, using the triangle element, in which the internal structure of the eTree labeled NP is omitted.

<eTree n="ex2">
 <label>PP</label>
 <eTree>
  <label>P</label>
  <eLeaf>
   <label>with</label>
  </eLeaf>
 </eTree>
 <triangle>
  <label>NP</label>
  <eLeaf>
   <label>the periscope</label>
  </eLeaf>
 </triangle>
</eTree>

Ambiguity involving alternative tree structures associated with the same terminal sequence can be encoded relatively conveniently using a combination of the exclude and copyOf attributes described in sections 16.8 Alternation and 16.6 Identical Elements and Virtual Copies. In the simplest case, an eTree may be part of the content of exactly one of two different eTree elements. To mark it up, the embedded eTree may be fully specified within one of the embedding eTree elements to which it may belong, and a virtual copy, specified by the copyOf attribute, may appear on the other. In addition, each of the embedded elements in question is specified as excluding the other, using the exclude attribute. To illustrate, consider the English phrase see the vessel with the periscope, which may be considered to be structurally ambiguous, depending on whether the phrase with the periscope is a modifier of the phrase the vessel or a modifier of the phrase see the vessel. This ambiguity is indicated in the sketch of the ambiguous tree by means of the dotted-line arcs. The markup using the copyOf and exclude attributes follows the sketch.

<eTree n="ex3">
 <label>VP</label>
 <eTree>
  <label>V</label>
  <eLeaf>
   <label>see</label>
  </eLeaf>
 </eTree>
 <eTree>
  <label>NP</label>
  <eTree>
   <label>Art</label>
   <eLeaf>
    <label>the</label>
   </eLeaf>
  </eTree>
  <eTree>
   <label>N</label>
   <eLeaf>
    <label>vessel</label>
   </eLeaf>
  </eTree>
  <eTree xml:id="GD-PPA" exclude="#GD-PPB">
   <label>PP</label>
   <eTree>
    <label>P</label>
    <eLeaf>
     <label>with</label>
    </eLeaf>
   </eTree>
   <eTree>
    <label>NP</label>
    <eTree>
     <label>Art</label>
     <eLeaf>
      <label>the</label>
     </eLeaf>
    </eTree>
    <eTree>
     <label>N</label>
     <eLeaf>
      <label>periscope</label>
     </eLeaf>
    </eTree>
   </eTree>
  </eTree>
 </eTree>
 <eTree xml:id="GD-PPB" copyOf="#GD-PPA" exclude="#GD-PPA">
  <label>PP</label>
 </eTree>
</eTree>

To indicate that one of the alternatives is selected, one may specify the select attribute on the highest eTree as either #GD-PPA or #GD-PPB; see section 16.8 Alternation.

Depending on the grammar one uses to associate structures with examples like see the man with the periscope, the representations may be more complicated than this. For example, adopting a version of the X-bar theory of phrase structure originated by Jackendoff,⁷⁴ the attachment of a modifier may require the creation of an intermediate node which is not required when the attachment is not made, as shown in the following diagram. A possible encoding of this ambiguous structure immediately follows the diagram.

<eTree n="ex4">
 <label>VP</label>
 <eTree xml:id="VBARA" exclude="#VBARB">
  <label>V'</label>
  <eTree xml:id="VA">
   <label>V</label>
   <eLeaf>
    <label>see</label>
   </eLeaf>
  </eTree>
  <eTree>
   <label>NP</label>
   <eTree xml:id="SPEC1A">
    <label>Spec</label>
    <eLeaf>
     <label>the</label>
    </eLeaf>
   </eTree>
   <eTree>
    <label>N'</label>
    <eTree xml:id="NBAR2A">
     <label>N'</label>
     <eTree>
      <label>N</label>
      <eLeaf>
       <label>vessel</label>
      </eLeaf>
     </eTree>
    </eTree>
    <eTree xml:id="PPA1">
     <label>PP</label>
     <eTree>
      <label>P</label>
      <eLeaf>
       <label>with</label>
      </eLeaf>
     </eTree>
     <eTree>
      <label>NP</label>
      <eTree>
       <label>Spec</label>
       <eLeaf>
        <label>the</label>
       </eLeaf>
      </eTree>
      <eTree>
       <label>N'</label>
       <eTree>
        <label>N</label>
        <eLeaf>
         <label>periscope</label>
        </eLeaf>
       </eTree>
      </eTree>
     </eTree>
    </eTree>
   </eTree>
  </eTree>
 </eTree>
 <eTree xml:id="VBARB" exclude="#VBARA">
  <label>V'</label>
  <eTree>
   <label>V'</label>
   <eTree xml:id="VB" copyOf="#VA">
    <label>V</label>
   </eTree>
   <eTree>
    <label>NP</label>
    <eTree xml:id="SPEC1B" copyOf="#SPEC1A">
     <label>Spec</label>
    </eTree>
    <eTree xml:id="NBAR2B" copyOf="#NBAR2A">
     <label>N'</label>
    </eTree>
   </eTree>
  </eTree>
  <eTree xml:id="PPB" copyOf="#PPA1">
   <label>PP</label>
  </eTree>
 </eTree>
</eTree>

A derivation in a generative grammar is often thought of as a set of trees. To encode such a derivation, one may use the forest element, in which the trees may be marked up using the tree, the eTree, or the triangle element. The type attribute may be used to specify what kind of derivation it is. Here is an example of a two-tree forest, involving application of the ‘wh-movement’ transformation in the derivation of what you do (as in this is what you do) from the underlying you do what.⁷⁵

<forest n="ex5" type="derivation-syntactic">
 <eTree n="Stage 1" xml:id="S1SBAR">
  <label>S'</label>
  <eTree xml:id="S1COMP">
   <label>COMP</label>
   <eLeaf xml:id="S1E">
    <label>e</label>
   </eLeaf>
  </eTree>
  <eTree xml:id="S1S">
   <label>S</label>
   <eTree xml:id="S1NP1">
    <label>NP</label>
    <eLeaf>
     <label>you</label>
    </eLeaf>
   </eTree>
   <eTree xml:id="S1VP">
    <label>VP</label>
    <eTree xml:id="S1V">
     <label>V</label>
     <eLeaf>
      <label>do</label>
     </eLeaf>
    </eTree>
    <eTree xml:id="S1NP2">
     <label>NP</label>
     <eLeaf xml:id="S1WH">
      <label>what</label>
     </eLeaf>
    </eTree>
   </eTree>
  </eTree>
 </eTree>
 <eTree n="Stage 2" xml:id="S2SBAR" corresp="#S1SBAR">
  <label>S'</label>
  <eTree xml:id="S2COMP" corresp="#S1COMP">
   <label>COMP</label>
   <eTree copyOf="#S1NP2" corresp="#S1E">
    <label>NP</label>
   </eTree>
  </eTree>
  <eTree xml:id="S2S" corresp="#S1S">
   <label>S</label>
   <eTree xml:id="S2NP1" copyOf="#S1NP1">
    <label>NP</label>
   </eTree>
   <eTree xml:id="S2VP" corresp="#S1VP">
    <label>VP</label>
    <eTree xml:id="S2V" copyOf="#S1V">
     <label>V</label>
    </eTree>
    <eTree xml:id="S2NP2" corresp="#S1NP2">
     <label>NP</label>
     <eLeaf corresp="#S1WH">
      <label>t</label>
     </eLeaf>
    </eTree>
   </eTree>
  </eTree>
 </eTree>
</forest>

In this markup, we have used copyOf attributes to provide virtual copies of elements in the tree representing the second stage of the derivation that also occur in the first stage, and the corresp attribute (see section 16.4 Correspondence and Alignment) to link those elements in the second stage with corresponding elements in the first stage that are not copies of them.

If a group of forests (e.g. a full grammatical derivation including syntactic, semantic, and phonological subderivations) is to be articulated, the grouping element forestGrp may be used.