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<Paper uid="W04-0312">
  <Title>Incremental Parsing, or Incremental Grammar?</Title>
  <Section position="4" start_page="0" end_page="0" type="metho">
    <SectionTitle>
3 Contextual Model
</SectionTitle>
    <Paragraph position="0"> The current proposed model (and its implementation) is based on these earlier de nitions but modi es them in several ways, most significantly by the addition of a model of context: ical language that decorate the tree.</Paragraph>
    <Paragraph position="1"> while they assume some notion of context they give no formal model or implementation.6 The contextual model we now assume is made up not only of the semantic trees built by the DS parsing process, but also the sequences of words and associated lexical actions that have been used to build them. It is the presence of (and associations between) all three, together with the fact that this context is equally available to both parsing and generation processes, that allow our straightforward model of dialogue phenomena.7 For the purposes of the current implementation, we make a simplifying assumption that the length of context is nite and limited to the result of some immediately previous parse (although information that is independently available can be represented in the DS tree format, so that, in reality, larger and only partially ordered contexts are no doubt possible): context at any point is therefore made up of the trees and word/action sequences obtained in parsing the previous sentence and the current (incomplete) sentence.</Paragraph>
    <Paragraph position="2"> Parsing in Context A parser state is therefore de ned to be a set of triples hT; W; Ai, where T is a (possibly partial) semantic tree,8 W the sequence of words and A the sequence of lexical and computational actions that have been used in building it. This set will initially contain only a single triple hTa;;;;i (where Ta is the basic axiom taken as the starting point of the parser, and the word and action sequences are empty), but will expand as words are consumed from the input string and the corresponding actions produce multiple possible partial trees. At any point in the parsing process, the context for a particular partial tree T in 6There are other departures in the treatment of linked structures (for relatives and other modi ers) and quanti cation, and more relevantly to improve the incrementality of the generation process: we do not adopt the proposal of O&amp;P to speed up generation by use of a restricted multiset of lexical entries selected on the basis of goal tree features, which prevents strictly incremental generation and excludes modi cation of the goal tree.</Paragraph>
    <Paragraph position="3"> 7In building n-tuples of trees corresponding to predicate-argument structures, the system is similar to LTAG formalisms (Joshi and Kulick, 1997). However, unlike LTAG systems (see e.g. (Stone and Doran, 1997)), both parsing and generation are not head-driven, but fully (word-by-word) incremental. This has the advantage of allowing fully incremental models for all languages, matching psycholinguistic observations (Ferreira, 1996).</Paragraph>
    <Paragraph position="4">  part of the tree.</Paragraph>
    <Paragraph position="5"> this set can then be taken to consist of: (a) a similar triple hT0; W0; A0i given by the previous sentence, where T0 is its semantic tree representation, W0 and A0 the sequences of words and actions that were used in building it; and (b) the triple hT; W; Ai itself. Once parsing is complete, the nal parser state, a set of triples, will form the new starting context for the next sentence. In the simple case where the sentence is unambiguous (or all ambiguity has been removed) this set will again have been reduced to a single triple hT1; W1; A1i, corresponding to the nal interpretation of the string T1 with its sequence of words W1 and actions A1, and this replaces hT0; W0; A0i as the new context; in the presence of persistent ambiguity there will simply be more than one triple in the new context.9 Generation in Context A generator state is now de ned as a pair (Tg; X) of a goal tree Tg and a set X of pairs (S; P), where S is a candidate partial string and P is the associated parser state (a set of hT; W; Ai triples). Initially, the set X will usually contain only one pair, of an empty candidate string and the standard initial parser state, (;;fhTa;;;;ig). However, as both parsing and generation processes are strictly incremental, they can in theory start from any state. The context for any partial tree T is de ned exactly as for parsing: the previous sentence triple hT0; W0; A0i; and the current triple hT; W; Ai. Generation and parsing are thus very closely coupled, with the central part of both processes being a parser state: a set of tree/word-sequence/action-sequence triples.</Paragraph>
    <Paragraph position="6"> Essential to this correspondence is the lack of construction of higher-level hypotheses about the state of the interlocutor. All transitions are de ned over the context for the individual (parser or generator). In principle, contexts could be extended to include high-level hypotheses, but these are not essential and are not implemented in our model (see (Millikan, 2004) for justi cation of this stance).</Paragraph>
  </Section>
  <Section position="5" start_page="0" end_page="0" type="metho">
    <SectionTitle>
4 Shared Utterances
</SectionTitle>
    <Paragraph position="0"> One primary evidence for this close coupling and sharing of structures and context is the ease with which shared utterances can be expressed.</Paragraph>
    <Paragraph position="1"> O&amp;P suggest an analysis of shared utterances,  9The current implementation of the formalism does not include any disambiguation mechanism. We simply assume that selection of some (minimal) context and attendant removal of any remaining ambiguity is possible by inference.</Paragraph>
    <Paragraph position="3"> and this can now be formalised given the current model. As the parsing and generation processes are both fully incremental, they can start from any state (not just the basic axiom state hTa;;;;i). As they share the same lexical entries, the same context and the same semantic tree representations, a model of the switch of roles now becomes relatively straightforward.</Paragraph>
    <Paragraph position="4"> Transition from Hearer to Speaker Normally, the generation process begins with the initial generator state as de ned above: (Tg;f(;; P0)g), where P0 is the standard initial \empty&amp;quot; parser state fhTa;;;;ig. As long as a suitable goal tree Tg is available to guide generation, the only change required to generate a continuation from a heard partial string is to replace P0 with the parser state (a set of triples hT; W; Ai) as produced from that partial string: we call this the transition state Pt. The initial hearer A therefore parses as usual until transition,10 then given a suitable goal tree Tg, forms a transition generator state Gt = (Tg;f(;; Pt)g), from which generation can begin directly { see gure 2.11 Note that the context does not change between processes.</Paragraph>
    <Paragraph position="5"> For generation to begin from this transition state, the new goal tree Tg must be subsumed by at least one of the partial trees in Pt (i.e.</Paragraph>
    <Paragraph position="6"> the proposition to be expressed must be subsumed by the incomplete proposition that has been built so far by the parser). Constructing 10We have little to say about exactly when transitions occur. Presumably speaker pauses and the availability to the hearer of a possible goal tree both play a part. 11Figure 2 contains several simpli cations to aid readability, both to tree structure details and by showing parser/generator states as single triples/pairs rather than sets thereof.</Paragraph>
    <Paragraph position="7"> Tg prior to the generation task will often be a complex process involving inference and/or abduction over context and world/domain knowledge { Poesio and Rieser (2003) give some idea as to how this inference might be possible { for now, we make the simplifying assumption that a suitable propositional structure is available.</Paragraph>
    <Paragraph position="8"> Transition from Speaker to Hearer At transition, the initial speaker B's generator state G0t contains the pair (St; P0t), where St is the partial string output so far, and P 0t is the corresponding parser state, the transition state as far as B is concerned.12 In order for B to interpret A's continuation, B need only use P 0t as the initial parser state which is extended as the string produced by A is consumed.</Paragraph>
    <Paragraph position="9"> As there will usually be multiple possible partial trees at the transition point, A may continue in a way that does not correspond to B's initial intentions { i.e. in a way that does not match B's initial goal tree. For B to be able to understand such continuations, the generation process must preserve all possible partial parse trees (just as the parsing process does), whether they subsume the goal tree or not, as long as at least one tree in the current state does subsume the goal tree. A generator state must therefore rule out only pairs (S; P) for which P contains no trees which subsume the goal tree, rather than thinning the set P directly via the subsumption check as proposed by O&amp;P.</Paragraph>
    <Paragraph position="10"> It is the incrementality of the underlying grammar formalism that allows this simple switch: the parsing process can begin directly 12Of course, if both A and B share the same lexical entries and communication is perfect, Pt = P0t, but we do not have to assume that this is the case.</Paragraph>
    <Paragraph position="11"> from a state produced by an incomplete generation process, and vice versa, as their intermediate representations are necessarily the same.</Paragraph>
  </Section>
  <Section position="6" start_page="0" end_page="0" type="metho">
    <SectionTitle>
5 Cross-Speaker Ellipsis
</SectionTitle>
    <Paragraph position="0"> This inherent close coupling of the two incremental processes, together with the inclusion of tree-building actions in the model of context, also allows a simple analysis of many cross-speaker elliptical phenomena.</Paragraph>
    <Paragraph position="1"> Fragments Bare fragments (3) may be analysed as taking a previous structure from context as a starting point for parsing (or generation). WH-expressions are analysed as particular forms of metavariables, so parsing a wh-question yields a type-complete but open formula, which the term presented by a subsequent fragment can update:  (3) A: What did you eat for breakfast?B: Porridge.  Parsing the fragment involves constructing an un xed node, and merging it with the contextually available structure, so characterising the wellformedness/interpretation of fragment answers to questions without any additional mechanisms: the term ( ; x; porridge0(x)) stands in a licensed growth relation from the metavariable WH provided by the lexical actions of what.</Paragraph>
    <Paragraph position="2"> Functional questions (Ginzburg and Sag, 2000) with their fragment answers (4) pose no problem. As the wh-question contains a metavariable, the scope evaluation cannot be completed; completion of structure and evaluation of scope can then be e ected by merging in the term the answer provides, identifying any introduced metavariable in this context (the genitive imposes narrow scope of the introduced epsilon term):  (4) A: Who did every student ignore?B: Their supervisor.</Paragraph>
    <Paragraph position="4"> VP Ellipsis Anaphoric devices such as pronouns and VP ellipsis are analysed as decorating tree nodes with metavariables licensing update from context using either established terms, or, for ellipsis, (lexical) tree-update actions. Strict readings of VP ellipsis result from taking a suitable semantic formula directly from a tree node in context: any node n 2 (T0 [ T) of suitable type (e ! t) with no outstanding requirements.</Paragraph>
    <Paragraph position="5"> Sloppy readings involve re-use of actions: any sequence of actions (a1; a2; : : :; an) 2 (A0 [ A) can be used (given the appropriate elliptical trigger) to extend the current tree T if this provides a formula of type e ! t.13 This latter approach, combined with the representation of quanti ed elements as terms, allows a range of phenomena, including those which are problematic for other (abstraction-based) approaches (for discussion see (Dalrymple et al., 1991)): (5) A: A policeman who arrested Bill read him his rights.</Paragraph>
    <Paragraph position="6"> B: The policeman who arrested Tom did too.</Paragraph>
    <Paragraph position="7"> The actions associated with A's use of read him his rights in (5) include the projection of a metavariable associated with him, and its resolution to the term in context associated with Bill. B's ellipsis allows this action sequence to be re-used, again projecting a metavariable and resolving it, this time (given the new context) to the term provided by parsing Tom. This leads to a copy of Tom within the constructed predicate, and a sloppy reading.</Paragraph>
    <Paragraph position="8"> This analysis also applies to yield parallellism e ects in scoping (Hirschb uhler, 1982; Shieber et al., 1996), allowing narrow scope construal for inde nites in subject position:  (6) A: A nurse interviewed every patient.B: An orderly did too.  Resolution of the underspeci cation in the scope statement associated with an inde nite can be performed at two points: either at the immediate point of processing the lexical actions, or at the later point of compiling the resulting node's interpretation within the emergent tree.14 In (6), narrow scope can be assigned to the subject in A's utterance via this late assignment of scope; at this late point in the 13In its re-use of actions provided by context, this approach to ellipsis is essentially similar to the glue language approach (see (Asudeh and Crouch, 2002) and papers in (Dalrymple, 1999) but, given the lack of independent syntax /semantics vocabularies, the need for an intermediate mapping language is removed.</Paragraph>
    <Paragraph position="9"> 14This pattern parallels expletive pronouns which equally allow a delayed update (Cann, 2003).</Paragraph>
    <Paragraph position="10"> parse process, the term constructed from the object node will have been entered into the set of scope statements, allowing the subject node to be dependent on the following quanti ed expression. The elliptical word did in B's utterance will then license re-use of these late actions, repeating the procedures used in interpreting A's antecedent and so determining scope of the new subject relative to the object.</Paragraph>
    <Paragraph position="11"> Again, these analyses are possible because parsing and generation processes share incrementally built structures and contextual parsing actions, with this being ensured by the incrementality of the grammar formalism itself.</Paragraph>
  </Section>
  <Section position="7" start_page="0" end_page="0" type="metho">
    <SectionTitle>
6 Alignment &amp; Routinization
</SectionTitle>
    <Paragraph position="0"> The parsing and generation processes must both search the lexicon for suitable entries at every step (i.e. when parsing or generating each word). For generation in particular, this is a computationally expensive process in principle: every possible word/action pair must be tested { the current partial tree extended and the result checked for goal tree subsumption. As proposed by O&amp;P (though without formal de nitions or implementation) our model of context now allows a strategy for minimising this e ort: as it includes previously used words and actions, a subset of such actions can be re-used in extending the current tree, avoiding full lexical search altogether. High frequency of elliptical constructions is therefore expected, as ellipsis licenses such re-use; the same can be said for pronouns, as long as they (and their corresponding actions) are assumed to be pre-activated or otherwise readily available from the lexicon.</Paragraph>
    <Paragraph position="1"> As suggested by O&amp;P, this can now lead directly to a model of alignment phenomena, characterisable as follows. For the generator, if there is some action a 2 (A0 [A) suitable for extending the current tree, a can be re-used, generating the word w which occupies the corresponding position in the sequence W0 or W. This results in lexical alignment { repeating w rather than choosing an alternative word from the lexicon. Alignment of syntactic structure (e.g. preserving double-object or full PP forms in the use of a verb such as give rather than shifting to the semantically equivalent form (Branigan et al., 2000)) also follows in virtue of the procedural action-based speci cation of lexical content. A word such as give has two possible lexical actions a0 and a00 despite semantic equivalence of output, corresponding to the two alternative forms. A previous use will cause either a0 or a00 to be present in (A0 [ A); re-use of this action will cause the same form to be repeated.15 A similar de nition holds for the parser: for a word w presented as input, if w 2 (W0[W) then the corresponding action a in the sequence A0 or A can be used without consulting the lexicon.</Paragraph>
    <Paragraph position="2"> Words will therefore be interpreted as having the same sense or reference as before, modelling the semantic alignment described by (Garrod and Anderson, 1987). These characterisations can also be extended to sequences of words { a sub-sequence (a1; a2; : : :; an) 2 (A0 [ A) can be re-used by a generator, producing the corresponding word sequence (w1; w2; : : :; wn) 2 (W0 [ W); and similarly the sub-sequence of words (w1; w2; : : :; wn) 2 (W0 [ W) will cause the parser to use the corresponding action sequence (a1; a2; : : :; an) 2 (A0 [ A). This will result in sequences or phrases being repeatedly associated by both parser and generator with the same sense or reference, leading to what Pickering and Garrod (2004) call routinization (construction and re-use of word sequences with consistent meanings).</Paragraph>
    <Paragraph position="3"> It is notable that these various patterns of alignment, said by Pickering and Garrod (2004) to be alignment across di erent levels, are expressible without invoking distinct levels of syntactic or lexical structure, since context, content and lexical actions are all de ned in terms of the same tree con gurations.</Paragraph>
  </Section>
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