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<Paper uid="W04-0312">
  <Title>Incremental Parsing, or Incremental Grammar?</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
2 Background
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    <Paragraph position="0"> Dynamic Syntax (DS) (Kempson et al., 2001) is a parsing-directed grammar formalism in which a decorated tree structure representing a semantic interpretation for a string is incrementally projected following the left-right sequence of the words. Importantly, this tree is not a model of syntactic structure, but is strictly semantic, being a representation of the predicate-argument structure of the sentence. In DS, grammaticality is de ned as parsability (the successful incremental construction of a tree-structure logical form, using all the information given by the words in sequence): there is no central use-neutral grammar of the kind assumed by most approaches to parsing and/or generation. The logical forms are lambda terms of the epsilon calculus (see (Meyer-Viol, 1995) for a recent development), so quanti cation is expressed through terms of type e whose complexity is re ected in evaluation procedures that apply to propositional formulae once constructed, and not in the tree itself. With all quanti cation expressed as type e terms, the standard grounds for mismatch between syntactic and semantic analysis for all NPs is removed; and, indeed, all syntactic distributions are explained in terms of this incremental and monotonic growth of partial representations of content. Hence the claim that the model itself constitutes a NL grammar formalism.</Paragraph>
    <Paragraph position="1"> Parsing (Kempson et al., 2001) de nes parsing as a process of building labelled semantic trees in a strictly left-to-right, word-by-word incremental fashion by using computational actions and lexical actions de ned (for some natural language) using the modal tree logic LOFT (Blackburn and Meyer-Viol, 1994). These actions are de ned as transition functions between intermediate states, which monotonically extend tree structures and node decorations.</Paragraph>
    <Paragraph position="2"> Words are speci ed in the lexicon to have associated lexical actions: the (possibly partial) semantic trees are monotonically extended by applying these actions as each word is consumed from the input string. Partial trees may be underspeci ed: tree node relations may be only partially speci ed; node decorations may be dened in terms of unful lled requirements and metavariables; and trees may lack a full set of scope constraints. Anaphora resolution is a familiar case of update: pronouns are de ned to project metavariables that are substituted from context as part of the construction process. Relative to the same tree-growth dynamics, long-distance dependency e ects are characterised through restricted licensing of partial trees with relation between nodes introduced with merely a constraint on some xed extension (following D-Tree grammar formalisms (Marcus, 1987)), an underspeci cation that gets resolved within the left-to-right construction process.3 Quantifying terms are also built up using determiner and noun to yield a partially speci ed term e.g.</Paragraph>
    <Paragraph position="4"> statement. These scope statements, of the form x &lt; y ('the term binding x is to be evaluated as taking scope over the term binding y'), are added to a locally dominating type-t-requiring node. Generally, they are added to an accumulating set following the serial order of processing in determining the scope dependency, but inde nites (freer in scope potential) are assigned a metavariable as rst argument, allow3In this, the system is also like LFG, modelling long-distance dependency in the same terms as functional uncertainty (Kaplan and Zaenen, 1989), di ering from that concept in the dynamics of update internal to the construction of a single tree.</Paragraph>
    <Paragraph position="5">  ing selection from any term already added, including temporally-sorted variables associated with tense/modality speci cations. The general mechanism is the incremental analogue of quanti er storage; and once a propositional formula of type t has been derived at a node with some collection of scope statements, these are jointly evaluated to yield fully expanded terms that re ect all relative dependencies within the restrictor of the terms themselves. For example, parsing A man coughed yields the pair Si &lt; x,</Paragraph>
    <Paragraph position="7"> tion), then evaluated as Man0(a) ^ Cough0(a) where a = ( ; x; Man0(x) ^ Cough0(x)).4 Once all requirements are satis ed and all partiality and underspeci cation is resolved, trees are complete, parsing is successful and the input string is said to be grammatical. Central to the formalism is the incremental and monotonic growth of labelled partial trees: the parser state at any point contains all the partial trees which have been produced by the portion of the string so far consumed and which remain candidates for completion.5  names correspond directly to scopeless names in the log-Generation (Otsuka and Purver, 2003; Purver and Otsuka, 2003) (hereafter O&amp;P) give an initial method of context-independent tactical generation based on the same incremental parsing process, in which an output string is produced according to an input semantic tree, the goal tree. The generator incrementally produces a set of corresponding output strings and their associated partial trees (again, on a left-to-right, word-by-word basis) by following standard parsing routines and using the goal tree as a subsumption check.</Paragraph>
    <Paragraph position="8"> At each stage, partial strings and trees are tentatively extended using some word/action pair from the lexicon; only those candidates which produce trees which subsume the goal tree are kept, and the process succeeds when a complete tree identical to the goal tree is produced. Generation and parsing thus use the same tree representations and tree-building actions throughout.</Paragraph>
  </Section>
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