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<Paper uid="P90-1002">
  <Title>I Logical Form = Argument Structure Z Surface Structure -- Intonation Structure = Information Structure I Phdegndegldeggi Pdegrm I</Title>
  <Section position="3" start_page="9" end_page="10" type="metho">
    <SectionTitle>
COMBINATORY GRAMMARS.
</SectionTitle>
    <Paragraph position="0"> Combinatory Categorial Grammar (CCG, \[16\]) is an extension of Categorial Grammar (CG). Elements like verbs are associated with a syntactic &amp;quot;category&amp;quot; which identifies them as functions, and specifies the type and  (6) prefers := (S\NP)/NP : prefer'  The category can be regarded as encoding the semantic type of their translation, which in the notation used here is identified by the expression to the right of the colon. Such functions can combine with arguments of the appropriate type and position by functional application: null  Because the syntactic types are identical to the semantic types, apart form directionality, the derivation also builds a compositional interpretation, (prefer' corduroy') mary', and of course such a &amp;quot;pure&amp;quot; categorial grammar is context free. Coordination might be included in CG via the following rule, allowing constituents of like type to conjoin to yield a single constituent of the same type:  (8) X conj X ::~ X (9) I loath and detest velvet</Paragraph>
    <Paragraph position="2"> (The rest of the derivation is omitted, being the same as in (7).) In order to allow coordination of contiguons strings that do not constitute constituents, CCG generalises the grammar to allow certain operations on functions related to Curry's combinators \[3\]. For example, functions may nondeterministically compose, as well as apply, under the following rule:</Paragraph>
    <Paragraph position="4"> The most important single property of combinatory rules like this is that they have an invariant semantics.</Paragraph>
    <Paragraph position="5"> This one composes the interpretations of the functions that it applies to, as is apparent from the right hand side of the rule. 1 Thus sentences like I suggested, tThe rule uses the notation of the ,~-calculus in the semantics, for clarity. This should not obscure the fact that it is functional composition itself that is the primitive, not the ,~ operator.</Paragraph>
    <Paragraph position="6">  and would prefer, corduroy can be accepted, via the following composition of two verbs (indexed as B, following Curry's nomenclature) to yield a composite of the same category as a transitive verb. Crucially, composition also yields the appropriate interpretation for the composite verb would prefer:  Combinatory grammars also include type-raising rules, which turn arguments into functions over functions-over-such-arguments. These rules allow arguments to compose, and thereby take part in coordinations like I suggested, and Mary prefers, corduroy. They too have an invariant compositional semantics which ensures that the result has an appropriate interpretation. For example, the following rule allows the conjuncts to form as below (again, the remainder of the derivation is omitted):  This apparatus has been applied to a wide variety of coordination phenomena (cf. \[4\], \[15\]).</Paragraph>
  </Section>
  <Section position="4" start_page="10" end_page="11" type="metho">
    <SectionTitle>
INTONATION AND CONTEXT
</SectionTitle>
    <Paragraph position="0"> Examples like the above show that combinatory grammars embody a view of surface structure according to which strings like Mary prefers are constituents. It follows, according to this view, that they must also be possible constituents of non-coordinate sentences like Mary prefers corduroy, as in the following derivation:  (See \[9\], \[18\] and \[19\] for a discussion of the obvious problems for parsing written text that the presence of such &amp;quot;spurious&amp;quot; (i.e. semantically equivalent) derivations engenders, and for some ways they might be overcome.) An entirely unconstrained combinatory grammar would in fact allow any bracketing on a sentence, although the grammars we actually write for configurational languages like English are heavily constrained by local conditions. (An example might be a condition on the composition rule that is tacitly assmned below, forbidding the variable Y in the composition rule to be instantiated as NP, thus excluding constituents like .\[ate the\]v P/N).</Paragraph>
    <Paragraph position="1"> The claim of the present paper is simply that particular surface structures that are induced by the specific combinatory grammar that are postulated to explain coordination in English subsume the intonational structures that are postulated by Pierrehumbert et al. to explain the possible intonation contours for sentences of English. More specifically, the claim is that that in spoken utterance, intonation helps to determine which of the many possible bracketings permitted by the combinatory syntax of English is intended, and that the interpretations of the constituents that arise from these derivations, far from being &amp;quot;spurious&amp;quot;, are related to distinctions of discourse focus among the concepts and open propositions that the speaker has in mind.</Paragraph>
    <Paragraph position="2"> The proof of this claim lies in showing that the rules of combinatory grammar can be made sensitive to intonation contour, which limit their application in spoken discourse. We must also show that the major constituents of intonated utterances like (1)b, under the analyses that are permitted by any given intonation, correspond to the information structure of the context to which the intonation is appropriate, as in (a) in the example (1) with which the paper begins.</Paragraph>
    <Paragraph position="3"> This demonstration will be quite simple, once we have established the following notation for intonation contours. null I shall use a notation which is based on the theory of Pierrehumbert \[10\], as modified in more recent work by Selkirk \[14\], Beckman and Pierrehumbert \[1\], \[11\], and Pierrehumbert and Hirschberg \[12\]. I have tried as far as possible to take my examples and the associated intonational annotations from those authors. The theory proposed below is in principle compatible with any of the standard descriptive accounts of phrasal intonation. However, a crucial feature of Pierrehumberts theory for present purposes is that it distinguishes two subcomponents of the prosodic phrase, the pitch accent and the boundary. 2 The first of these tones or tone-sequences coincides with the perceived major stress or stresses of the prosodic phrase, while the second marks the righthand boundary of the phrase. These two components are essentially invariant, and all other parts of the intonational tune are interlx)lated. Pierrehumberts theory thus captures in a very natural way the intuition that the same tune can be spread over longer or shorter strings, in order to mark the corresponding constituents for the particular distinction of focus and propositional attitude that the melody denotes. It will help the exposition to augment Pierrehumberts notation with explicit prosodic phrase boundaries, using brackets. These do not change her theory in any way: all the information is implicit in the original notation.</Paragraph>
    <Paragraph position="4"> Consider for example the prosody of the sentence Fred ate the beans in the following pair of discourse settings, which are adapted from Jackendoff \[7, pp.</Paragraph>
    <Paragraph position="5"> 260\]:</Paragraph>
    <Paragraph position="7"> two tunes are reversed: this time the tune with pitch accent T.+H* and boundary LH% is spread across a prosodic phrase Fred ate, while the other tune with pitch accent H* and boundary LL% is carried by the prosodic phrase the beans (again starting with an interpolated or null tone). 4 The meaning that these tunes convey is intuitively very obvious. As Pierrehumbert and Hirschberg point out, the latter tune seems to be used to mark some or all of that part of the sentence expressing information that the speaker believes to be novel to the hearer. In traditional terms, it marks the &amp;quot;comment&amp;quot; - more precisely, what Halliday called the '~rheme'. In contrast, the r.+H* LH% tune seems to be used to mark some or all of that part of the sentence which expresses information which in traditional terms is the &amp;quot;topic&amp;quot; in I-lalliday's terms, the &amp;quot;theme&amp;quot;. 5 For present purposes, a theme can be thought of as conveying what the speaker assumes to be the subject of mutual interest, and this particular tune marks a theme as novel to the conversation as a whole, and as standing in a contrastive relation to the previous one. (If the theme is not novel in this sense, it receives no tone in Pierrehumbert's terms, and may even be left out altogether.) 6 Thus in (16), the L+H* Lrt% phrase including this accent is spread across the phrase Fred  the object of the open proposition ate the beans, because the intonation of the original question indicates that eating beans as opposed to some other comestible is the new topic, s (16) q: I/ell, what about FRED?  In these contexts, the main stressed syllables on both Fred and the beans receive a pitch accent, but a different one. In the former example, (15), there is a prosodic phrase on Fred made up of the pitch accent which Pierrehumbert calls H*, immediately followed by an r. boundary. There is another prosodic phrase having the pitch accent called L+H* on beans, preceded by null or interpolated tone on the words ate the, and immediately followed by a boundary which is written LH%. (I base these annotations on Pierrehumber and Hirschberg's \[12, ex. 33\] discussion of this example.) 3 In the second example (16) above, the 2For the purpose s of this abstract, I am ignoring the distinction between the intonational phrase proper, and what Pierrehumben and her colleagues call the &amp;quot;intermediate&amp;quot; phrase, which differ in respect of boundary tone-sequences.</Paragraph>
    <Paragraph position="8"> 3I continue to gloss over Pierrehumbert's distinction between *'intermediate&amp;quot; and &amp;quot;intonational&amp;quot; phrases.</Paragraph>
  </Section>
  <Section position="5" start_page="11" end_page="14" type="metho">
    <SectionTitle>
COMBINATORY PROSODY
</SectionTitle>
    <Paragraph position="0"> The r,+H* r,H% intonational melody in example (16) belongs to a phrase Fred ate ... which corresponds under the combinatory theory of grammar to a gram- null paper also follows Lyons \[8\] in rejecting Hallidays' claim that the theme must necessarily be sentence-initial.</Paragraph>
    <Paragraph position="1"> ran alternative prosody, in which the contrastive tune is confined to Fred, seems equally coherent, and may be the one intended by Jackendoff. I befieve that this altemative is informationally distinct, and arises from an ambiguity as to whether the topic of this discourse is Fred or What Fred ate. It too is accepted by the rules below.</Paragraph>
    <Paragraph position="2"> SNore that the position of the pitch accent in the phrase has to do with a further dimension of information structure within both theme and theme, which me might identify as &amp;quot;focus': I ignore this dimension here.</Paragraph>
    <Paragraph position="3">  matical constituent, complete with a translation equivalent to the open proposition Az\[(ate' z) fred'\]. The combinatory theory thus offers a way to derive such intonational phrases, using only the independently motivated rules of combinatory grammar, entirely under the control of appropriate intOnation contOurs like L+H* LH%. 9 It is extremely simple tO make the existing combinatory grammar do this. We interpret the two pitch accents as functions over boundaries, of the following types: I0</Paragraph>
    <Paragraph position="5"> - that is, as functions over boundary tOnes into the two major informational types, the Hallidean &amp;quot;theme&amp;quot; and &amp;quot;rheme&amp;quot;. The reader may wonder at this point why we do not replace the category Theme by a functional category, say Utterance/Rheme, corresponding to its semantic type. The answer is that we do not want this category to combine with anything but a complete rheme. In particular, it must not combine with a function into the category Rheme by functional composition. Accordingly we give it a non-functional category, and supply the following special purpose prosodic combinatory rules:  We next define the various boundary tOnes as arguments to these functions, as follows:</Paragraph>
    <Paragraph position="7"> (As usual, we ignore for present purposes the distinction between intermediate- and intonational- phrase boundaries.) Finally, we accomplish the effect of interpolation of other parts of the tune by assigning the following polymorphic category to all elements bearing no tOne specification, which we will represent as the tOne 0:</Paragraph>
    <Paragraph position="9"> bert and Hirschberg's own proposal to compositionally assemble discourse meanings from more primitive elements of meaning carfled by each individual tone) would be to make the boundary tone the function and the pitch accent an argument.</Paragraph>
    <Paragraph position="10">  Syntactic combination can then be made subject to the following simple restriction: (21) The Prosodic Constituent Condition: Combination of two syntactic categories via a syntactic combinatory rule is only allowed if their prosodic categories can also combine.</Paragraph>
    <Paragraph position="11"> (The prosodic and syntactic combinatory rules need not be the same).</Paragraph>
    <Paragraph position="12"> This principle has the sole effect of excluding certain derivations for spoken utterances that would be allowed for the equivalent written sentences. For example, consider the derivations that it permits for example (16) above. The rule of forward composition is allowed tO apply tO the words Fred and ate, because the prosodic categories can combine (by functional  The category x/x of the null tone allows intonational phrasal tunes like T,+H* LH% tune tO spread across any sequence that forms a grammatical constituent according to the combinatory grammar. For example, if the reply to the same question What did Fred eat? is FRED must have eaten the BEANS, then the tune will typically be spread over Fred must have eaten .... as in the following (incomplete) derivation, in which much of the syntactic and semantic detail has been omitted in the interests of brevity:  The division of the utterance into an open proposition constituting the theme and an argument constituting the rheme is appropriate to the context established in (16). Moreover, the theory permits no other derivation for this intonation contour. Of course, repeated application of the composition rule, as in (23), would allow the L+H* LH% contour to spread further, as in (FRED must have eaten)(the BEANS).</Paragraph>
    <Paragraph position="13"> In contrast, the parallel derivation is forbidden by the prosodic constituent condition for the alternative intonation contour on (15). Instead, the following derivation, excluded for the previous example, is now  No other analysis is allowed for (25). Again, the derivation divides the sentence into new and given information consistent with the context given in the example. The effect of the derivation is to annotate the entire predicate as an L+H* LH%. It is emphasised that this does not mean that the tone is spread, but that the whole constituent is marked for the corresponding discourse function -- roughly, as contrastive given, or theme. The finer grain information that it is the object that is contrasted, while the verb is given, resides in the tree itself. Similarly, the fact that boundary sequences are associated with words at the lowest level of the derivation does not mean that they are part of the word, or specified in the lexicon, nor that the word is the entity that they are a boundary of. It is  prosodic phrases that they bound, and these also are defined by the tree.</Paragraph>
    <Paragraph position="14"> All the other possibilities for combining these two contours on this sentence are shown elsewhere \[17\] to yield similarly unique and contextually appropriate interpretations.</Paragraph>
    <Paragraph position="15"> Sentences like the above, including marked theme and rheme expressed as two distinct intonationalAntermediate phrases are by that token unambiguous as to their information structure. However, sentences like the following, which in Pierrehumberts' terms bear a single intonational phrase, are much more ambiguous as to the division that they convey between theme and rheme: (26) I read a book about CORduroy</Paragraph>
    <Paragraph position="17"> Such a sentence is notoriously ambiguous as to the open proposition it presupposes, for it seems equally apropriate as a response to any of the following questions: null  (27) a. What did you read a book about? b. What did you read? c. What did you do?  Such questions could in suitably contrastive contexts give rise to themes marked by the L+H* LH% tune, bracketing the sentence as follows: (28) a. (1 read a book about)(CORduroy) b. (I read)(a book about CORduroy) c. (I)(read a book about CORduroy) It seems that we shall miss a generalisation concerning the relation of intonation to discourse information unless we extend Pierrehumberts theory very slightly, to allow null intermediate phrases, without pitch accents, expressing unmarked themes. Since the boundaries of such intermediate phrases are not explicitly marked, we shall immediately allow all of the above analyses for (26). Such a modification to the theory can be introduced by the following rule, which non-deterministically allows certain constituents bearing the null tone to become a theme: (29) r. r~</Paragraph>
  </Section>
  <Section position="6" start_page="14" end_page="14" type="metho">
    <SectionTitle>
X/X ::~ Theme
</SectionTitle>
    <Paragraph position="0"> The symbol E is a variable ranging over syntactic categories that are (leftward- or rightward- looking) functions into S. al The rule is nondeterministic, so it correctly continues to allow a further analysis of the entire sentence as a single Intonational Phrase conveying the Rheme. Such an utterance is the appropriate response to yet another open-proposition establishing question, What happened?.) With this generalisation, we are in a position to make the following claim: (30) The structures demanded by the theory of intonation and its relation to contextual informarion are the same as the surface syntactic structures permitted by the combinatory grammar.</Paragraph>
    <Paragraph position="1"> A number of corollaries follow, such as the following: (31) Anything which can coordinate can be an intonational constituent, and vice versa.</Paragraph>
  </Section>
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