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<Paper uid="C86-1115">
  <Title>A Concept of Derivation for LFG</Title>
  <Section position="3" start_page="488" end_page="488" type="intro">
    <SectionTitle>
4. The monostratal derivation concept
</SectionTitle>
    <Paragraph position="0"> One obtains the monostratal version quite naturally if for all triples &lt;w,d,g&gt; of a derivation and a rule's right side in the string version the arguments of g are attached as additional labelled edges to the start nodes of the subDAGs of d to which they are assigned qua g. Thus one obtains for the start triple, the derived triple s i.1 and the rule r the following structures: 6)</Paragraph>
    <Paragraph position="2"> If &lt;w,d,g&gt; is a triple of the string version then a DAG s= N{d'eDAGId-C;d'^ V&lt;i,w i &gt;~w VpePATH(g(&lt;i,w i &gt;)=dp-&gt;d'p(i)=~ )} is the corresponding entity in the monostratal version. These entities are augmented partial f-structures. They have additional terminal edges. These edges are labelled with integers and lead to elements of the vocabulary. The labels of such edges which are attached to different nodes have distinct labels. All such edges represent a string over V.</Paragraph>
    <Paragraph position="3"> If FSp is the (undefined) set of partial f-structures then the new structures are elements of the set FSe FSo=(s~DAG\] ~ deFSp ~weV*3 g~\[w-&gt;T(d)\](s=l'q{d'eDAGld -rod' &amp;quot;, V&lt;i,w i &gt;ewVpaPATH(g(&lt;i,w i &gt;)=dp-&gt;d'p(i)=wi)))} The string of such a structure s (S(s)) is simply the set of all these additional edges.</Paragraph>
    <Paragraph position="4"> DEF Vs eFSe(S(s )={&lt;i,x&gt;e//VxVl~ P ~PATH(sp(i)=x)} The derivation concept is defined as follows: DEF A derivation is a sequence s 0...s n where</Paragraph>
    <Paragraph position="6"> As in this version the occurrences are attached as edges to the start nodes of those subDAGs, to which they are assigned in the string version, an adequate concept of direct derivability can be inferred from the definition of the preceding section.</Paragraph>
    <Paragraph position="7"> One properly re-indexes the DAG s i . 1 and the DAG, which is introduced by the rule (d,dr), according to the definition of g'.</Paragraph>
    <Paragraph position="8"> The derived DAG is constructed by the elimination of the edge to be replaced, and the unification of d r with that subDAG of d, to which the replaced edge was attached. A successful unification in the string version can't fail here because the labels of the additional edges of d (after elimination of the edge to be replaced) and d r are pairwise different.</Paragraph>
    <Paragraph position="9"> In the example the result of the application of T on &lt;3,VP&gt; of s i . 1 is defined as follows:  grant no. 1013207 O.</Paragraph>
    <Paragraph position="10"> 1) \[2\] suggests, that atomic feature values are not represented as labelled nodes. Thus in the following illustrations only edges labelled with complex valued features (gran~ticat functions) lead to nodes; edges labelled with atomic valued features (morphological features) point at the atomic values.</Paragraph>
    <Paragraph position="11"> 2) In this version (cf. \[3\]) tong distance dependencies are handled on f-structure level. For that purpose regular expressions over the set of nuclear functions (governable functions plus ADd, XADJ) are allowed to occur in the equations. These rules can be interpreted ns schemata. A rule which is an instance of a schema is then annotated with an expression that is eten~nt of the set, denoted by the regular expression. 3) This integration is necessary because f-structures are control structures of the filter eomt:~nent ii. and the new structures are expanded f-structures. It is also possible to simulate the postponed filter components iii. end iv. in an adequate way during the derivation. This can't be discussed here for tack of space.</Paragraph>
    <Paragraph position="12"> 4) This example is derivable with the grannmr of \[1\]. The annotations are attached to the nodes in order to make d and f reconstructable, l represent nodes as sequences ef integers in the usual way (start node 1; ij is the j-th daughter of the node i). For reasons of clarity f is specified only for the terminal nodes.</Paragraph>
    <Paragraph position="13"> 5) If d is a DAG and p a path (a sequence of attributes), then dp is an abbreviation of a term (descriptor) denoting a sub0AG of d. The actual structure of such s term depel~ds on the chosen metatheoreticat reconstruetion of DAGs (partial functions vs. graphs) (cf. eg. \[4\]). 6) Note that the VCORP substructure comprises a discontinous structure whose corresponding symbols do not form a proper subs\[ring in w.</Paragraph>
  </Section>
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