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<Paper uid="E89-1009">
  <Title>Inference in DATR</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
2 Syntax
</SectionTitle>
    <Paragraph position="0"> The syntax of DATR, especially the use of valueterminated attribute trees to encode information, derives from OATR (Shieber 1986). The language consists of strings of symbols drawn from the set SYM - {:, &amp;quot;,., -, --, &lt;, &gt;, (,)} and the sets ATOM and NODE, all of which are disjoint.</Paragraph>
    <Paragraph position="1"> A string is in OATR, (with respect to given sets ATOM of \[atom\]s and NODE of \[node\]s) iff it is a \[sentence\] as defined by the following set of rules:</Paragraph>
    <Paragraph position="3"> There are two kinds of sentence, those containing '==' and those containing '='. Both kinds have on their left-hand side a node:path specification, where a path is a sequence of atoms enclosed in &lt;...&gt;. Pragmatically, the '==' sentences are intended for defining the network, whilst the '=' statements express the values at individual nodes. Put another way, the former provide the database definition language whilst the latter provide the query language: the useful premises will standardly all be '---' statements, whilst the interesting theorems will standardly all be '=' statements (though the language itself also allows the former to be derived as theorems and the latter to be used as premises).</Paragraph>
    <Paragraph position="4"> In view of this distinction, we shall sometimes refer to '---' sentences as definitional and '=' sentences as extensional. Throughout the exampies in this paper, we shall use bold for nodes and roman for atoms. Bold italic and italic will be used for corresponding meta-notational variables. Variables such as N, P, L, G and V will be assumed to be typed (as nodes, paths, lvalues, gvalues and values respectively). We shall sometimes refer to atoms occurring in paths as attributes.</Paragraph>
    <Paragraph position="5"> The right-hand sides of extensional sentences are values, that is, simple atoms or lists of atoms/nested lists enclosed in (...). Lists are provided to allow the components of complex values to be specified independently (inherited from different places, for example). As an example, the following sentences might be derivable from a lexical entry for English 'be': Be:&lt;pres tense sing one&gt; = am.</Paragraph>
    <Paragraph position="6"> Be:&lt;pres participle&gt; = (concat be ing).</Paragraph>
    <Paragraph position="7"> Likewise, the following for German 'Buch': Bach: &lt;sing&gt; = Buch.</Paragraph>
    <Paragraph position="8"> Bach: &lt;plat&gt; = (concat (umlaut Buch) er).</Paragraph>
    <Paragraph position="9"> Values are the principal 'results' of a I)ATR description: the most typical operation is to determine the value associated (by an extensional sentence) with some node/path pair.</Paragraph>
    <Paragraph position="10"> The right-hand sides of definitional sentences are lvalues, which can be simple atoms, inheritance descriptors (quoted or unquoted), or lists of lvalues. An atom is primitive, an inheritance descriptor specifies where the required value can be inherited from, and lists allow arbitrary structures to be built as values. Inheritance descriptors come in several forms with two dimensions of variation. The unquoted/quoted distinction specifies whether the inheritance context is local (the most recent context employed) or global (the initial context employed). Once the context is established, the descriptor specifies a new node, a new lpath, or both to be used to determine the inherited value. For example, the following sentences might be found in a description of a lexicon for English:  EN MOR: &lt; &gt; == VERB.</Paragraph>
    <Paragraph position="11"> m EN MOR: &lt;past participle&gt; == (concat &amp;quot;&lt;root&gt;&amp;quot; en). Take: &lt; &gt; == EN MOR.</Paragraph>
    <Paragraph position="12"> Take: &lt;root&gt; ~ take.</Paragraph>
    <Paragraph position="13">  Finally an lpath is a path made up of lvalues, that is, elements which themselves may need evaluation, as in this example: Adjective: &lt;form&gt; --= &lt;&amp;quot;&lt;gen&gt;&amp;quot; &amp;quot;&lt;num&gt;&amp;quot; &amp;quot;&lt;case&gt;&amp;quot;&gt;. We adopt the following abbreviation convention for sets of sentences about a single node:</Paragraph>
    <Paragraph position="15"> Thus the 'take' example given above could appear, in abbreviated form, as follows:</Paragraph>
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