Structured Discourse Reference to Individuals

The paper argues that discourse reference in natural language involves two equally important components with essentially the same interpretive dynamics, namely reference to values, i.e. (non-singleton) sets of objects, and reference to structure, i.e. the correlation / dependency between such sets, which is introduced and incrementally elaborated upon in discourse. To define and investigate structured discourse reference, a new dynamic system couched in classical (many-sorted) type logic is introduced which extends Compositional DRT (Muskens, 1996) with plural information states, i.e. information states are modeled as sets of variable assignments (following van den Berg, 1996), which can be can be represented as matrices with assignments (sequences) as rows. A plural info state encodes both values (the columns of the matrix store sets of objects) and structure (each row of the matrix encodes a correlation / dependency between the objects stored in it). Given the underlying type logic, compositionality at sub-clausal level follows automatically and standard techniques from Montague semantics (e.g. type shifting) become available. The idea that plural info states are semantically necessary is motivated by relative-clause donkey sentences with multiple instances of anaphora: mixed reading (weak & strong) sentences and sentences exemplifying donkey anaphora to structure. 1. Multiple Donkey Anaphora The main goal of this paper is to argue that discourse reference in natural language involves two equally important components with essentially the same interpretive dynamics, namely reference to values, i.e. (non-singleton) sets of objects (individuals, events, times, propositions etc.), and reference to structure, i.e. the correlation / dependency between such sets that is introduced and incrementally elaborated upon in discourse. The notion of structured discourse reference enables us to provide a precise compositional interpretation procedure for discourses involving complex descriptions of multiple related objects as, for example, the sentences in (1) and (2) below which contain multiple instances of donkey anaphora. Indefinites introduce a discourse referent (dref) u, u'' etc., represented by a superscript, while pronouns are anaphoric to a dref, represented by a subscript. 1. Everyu person who buys au' book on amazon.com and has au'' credit card uses itu'' to pay for itu'. 2. Everyu boy who bought au' Christmas gift for au'' girl in his class asked heru'' deskmate to wrap itu'. Sentence (1) shows that singular donkey anaphora can refer to (non-singleton) sets of individuals (i.e. values), while (2) shows that singular donkey anaphora can refer to a dependency between such sets (i.e. structure). Let us examine them in turn. Sentence (1) is a mixed weak & strong donkey sentence: it asserts that, for every book (strong) that any credit-card owner buys on amazon.com, there is some credit card (weak) that s/he uses to pay for the book. Note in particular that the credit card can vary from book to book, e.g. I can use my MasterCard to buy set theory books and my Visa to buy detective novels; that is, even the weak indefinite au'' credit card can introduce a nonsingleton set. For each buyer, the two sets of objects, i.e. all the purchased books and some of the credit cards, are correlated and the dependency between these sets – left implicit in the restrictor of the quantification – is specified in the nuclear scope: each book is correlated with the credit card that was used to pay for it. The translation of sentence (1) in classical (static) firstorder logic is provided in (3) below. 3. ∀x(pers(x)∧∃y(bk(y)∧buy(x,y))∧∃z(card(z)∧hv(x,z)) → ∀y'(bk(y')∧buy(x,y') → ∃z'(card(z')∧hv(x,z')∧use_to_pay(x,z',y')))) The challenge posed by sentence (1) is to compositionally derive its interpretation while allowing for: (i) the fact that the two donkey indefinites in the restrictor of the quantification receive two distinct readings (strong and weak respectively) and (ii) the fact that the value of the weak indefinite au'' credit card covaries with / is dependent on the value of the strong indefinite au' book although the strong indefinite cannot syntactically scope over the weak one, since both DP's are trapped in their respective VP-conjuncts. Sentence (2) contains two instances of strong donkey anaphora: we are considering every Christmas gift and every girl. The restrictor introduces a dependency between the set of gifts and the set of girls: each gift is correlated with the girl it was bought for. The nuclear scope of the donkey quantification retrieves not only the two sets of objects, but also the structure associated with them, i.e. the dependency between them: each gift was wrapped by the deskmate of the girl that the gift was bought for. Thus, we have here donkey anaphora to structure in addition to donkey anaphora to values. Importantly, the structure associated with the two sets, i.e. the dependency between gifts and girls, is semantically encoded and not pragmatically inferred: the correlation between the two sets is not left vague / underspecified and subsequently made precise based on various extralinguistic factors. To see that the structure is semantically encoded, consider the following situation: suppose that John buys two gifts, one for Mary and the other for Helen; moreover, the two girls are deskmates. Intuitively, sentence (2) is true if John asked Mary to wrap Helen's gift and Helen to wrap Mary's gift and it is false if John