Local Discourse and Reference

Anaphoric Reference

A key concept in reference is that of an anaphor.

anaphora: The explication of a word by words appearing previous to it in the text: Mary died. She was very old. (She is explained by Mary.)
(Macquarie Dictionary)

14.1 Defining Local Discourse Context and Discourse Entities

• Think of local context as including
  • the syntactic and semantic analysis of the preceding sentence
  • a list of objects mentioned in the sentence that could be antecedents for later pronouns and definite noun phrases.

  1a	Jack[i] lost his wallet[j] in his car[k].
  1b	He[i] looked for it[j] for several hours.
  1c	Later he[i] found the wallet[j] under the front seat[k??].

• Jack in 1a is said to be the antecedent for he in 1b.
  That is, the pronoun and antecedent co-refer.

Local Discourse Context and Discourse Entities 2

2a	Jack forgot his wallet.
2b	Sam did too.

• did in 2b has the VP in 2a as antecedent.

• Reference is sometimes intra-sentential:

  5	Jack forgot his wallet, and Sam did too.

Local Discourse Context and Discourse Entities 3

• An important part of the local context is the list of possible antecedents for pronouns, etc., which we will call the discourse entity (DE) list.

• At the start of processing sentence 1c, the DE-list contains:

  Jack his wallet his car

  lost his wallet lost his wallet in his car

  looked for it looked for it for several hours

  Jack lost his wallet in the car He looked for it for several hours

Evoked Discourse Entities

• Sometimes a DE is not explicitly mentioned previously, but rather introduced or evoked (like the front seat in 1c).

• The item referred to may not be identified precisely:

  8a	John bought a car[i] yesterday.
  8b	It[i] was very expensive.

• Neither speaker nor hearer may be able to identify the car (we can't say that it is CAR56 in our knowledge base (KB).)

Evoked Discourse Entities 2

• How can we refer to such an object - in effect a constant whose identity is unknown to us?

• So we must introduce a new constant, like C1, into our (logical) language whenever we meet something like <A c1 CAR1>.

• If we also introduce a constant I1 for the expression <PRO i1 IT1>, then we can capture co-reference by asserting I1 = C1.

Generating Discourse Entities

• Discourse entities are generated for each noun phrase.

• In many cases, there will be constraints on the entities:

  indefinite noun phrases	creates new DE
  proper names	describe some object often already in KB
  definite noun phrases and pronouns	refer to objects previously mentioned or known, often DE in local context
  complex NP like John and Mary	evokes a set consisting of all the conjuncts

Indefinite Noun Phrases within the Scope of Universals

10a	Three boys[i] each bought a pizza[j].
10b	They[i] ate them[j] in the park.

Initial translation of 10a:

  ∃ B : |B| = 3 & {x | Boy(x)} ⊇ B
      ∀ b : b ∈ B .
          ∃ p : Pizza(p) . Buy(b, p)

Discourse entities from 10a:

   B1: |B1| = 3 & {x | Boy(x)} ⊇ B1
   P1: P1 = {x | Pizza(x) & ∃ y ∈ B1 . x = sk4(y)}

Semantic content:

   ∀ b : b ∈ B1. sk4(b) ∈ P1 & Buy1(b, sk4(b))

This is related to the ambiguity issue we considered with the sentence Every man loves a woman in the section on logical form.

14.2 A Simple Model of Anaphora Based on History Lists

• The history list is a list of discourse entities generated by the preceding sentences, with the most recent listed first.

• Some systems retain just the last two or three sentences, while some let the list grow indefinitely.

• The DEs evoked by each sentence are referred to as a local context.

• The algorithm for finding an antecedent for a pronoun proceeds as follows:

Antecedent-Finding Algorithm

1. check the most recent local context for an antecedent that matches all the constraints related to the pronoun.

   Constraints include number, gender, and other grammatical phenomena such as the rules for the use of reflexive pronouns.

   Semantic constraints imposing selectional restrictions may occur too: e.g. in There was cheese on the table. Jack ate it. the word it cannot refer to the table.

2. if no referent is found in the current local context, move down the history list to the next most recent local context and search there.

Definite Descriptions

• Similar techniques will often work with definite descriptions.

  18a	Helen bought a car[i] and a boat yesterday.
  18b	She paid too much for the car[i].

• The phrase the car behaves somewhat like an it with the constraint of being of type car.

Indirect Reference

• Sometimes the antecedent is not something mentioned directly in a preceding context, but nevertheless introduced in one.

  20a	My club held a raffle.
  20b	The winner won a car.

• In 20a/b, the winner is introduced by the raffle.
  

  22a	Jack brought a pencil to class.
  22b	However, he found that the lead was broken.

• In 22a/b the lead is a subpart of the pencil.

Indirect Reference 2

• With 20a/b, one can interpret the winner as

  ∃ w : Win(w, *PRO*)

  where *PRO* is a "pro-form", which can then be looked for in the local context.

Indirect Reference 3

• In 22a/b, it is rather more awkward:

  Interpret the lead as

  ∃ !  l  : Lead(l) & *R* (l, *PRO*)

  where this time the relation *R* and the pro-form *PRO* must be identified.

• The answer should be *R* = SubPartOf, and *PRO* = Pencil1, where Pencil1 is the DE generated from a pencil in 22a).

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Copyright (C) Bill Wilson, 2007, except where another source is acknowledged. Most material is adapted from James Allen's book "Natural Language Understanding".