The term anaphora is used most commonly in theoretical linguistics to denote any case where two nominal expressions are assigned the same referential value or range. Discussion here focuses on noun phrase (NP) anaphora with pronouns (see BINDING THEORY for an explanation of the types of expressions commonly designated "anaphors," e.g., reflexive pronouns).

Pronouns are commonly viewed as variables. Thus, (1b) corresponds to (2), where the predicate contains a free variable. This means that until the pronoun is assigned a value, the predicate is an open property (does not form a set). There are two distinct procedures for pronoun resolution: binding and covaluation. In binding, the variable gets bound by the λ-operator, as in (3a), where the predicate is closed, denoting the set of individuals who think they have the flu, and where the sentence asserts that Lili is in this set.

a. Lucie didn't show up today.
b. Lili thinks she's got the flu.
Lili (λx (x thinks z has got the flu))
a. Binding: Lili (λx (x thinks x has got the flu))
b. Covaluation: Lili (λx (x thinks z has got the flu) & z = Lucie)

In covaluation, the free variable is assigned a value from the DISCOURSE storage, as in (3b). An assumption standard since the 1980s is that, while processing sentences in context, we build an inventory of discourse entities, which can further serve as antecedents of anaphoric expressions (Heim 1982; McCawley 1979; Prince 1981). Suppose (1b) is uttered in the context of (1a). We have stored an entry for Lucie, and when the pronoun she is encountered, it can be assigned this value. In theory-neutral terms, this assignment is represented in (3b), where Lucie is a discourse entry, and the pronoun is covalued with this entry.

The actual resolution of anaphora is governed by discourse strategies. Ariel (1990) argues that pronouns look for the most accessible antecedent, and discourse topics are always the most accessible. For example, (3b) is the most likely anaphora resolution for (1b) in the context of (1a), since Lucie is the discourse topic that will make this minimal context coherent.

Given the two procedures, it turns out that if Lili is identified as the antecedent of the pronoun in (1b), the sentence has, in fact, two anaphora construals. Since Lili is also in the discourse storage, (1b) can have, along with (3a), the covaluation construal (4).

Lili (λx (x thinks z has got the flu) & z = Lili)
Lili thinks she has got the flu, and Max does too.

Though (3a) and (4) are equivalent, it was discovered in the 1970s that there are contexts in which these sentences display a real representational ambiguity (Keenan 1971). For example, assuming that she is Lili, the elliptic second conjunct of (5) can mean either that Max thinks that Lili has the flu, or that Max himself has it. The first is obtained if the elided predicate is construed as in (4), and the second if it is the predicate of (3a).

Let us adopt here the technical definitions in (6). ((6a) differs from the definition used in the syntactic binding theory). In (3a), then, Lucie binds the pronoun; in (4), they are covalued.

a. Binding: α binds β iff α is an argument of a λ-predicate whose operator binds β.
b. Coevaluation: α and β are covalued iff neither binds the other and they are assigned the same value.

Covaluation is not restricted to referential discourse-entities -- a pronoun can be covalued also with a bound variable. Indeed, Heim (1998) showed that covaluation-binding ambiguity can show up also in quantified contexts. In (7a), the variable x (she) binds the pronoun her. But in (7b) her is covalued with x.

Every wife thinks that only she respects her husband.
a. Binding: Every wife (λx (x thinks that [only x (λy (y respects y's husband))]))
b. Covaluation: Every wife (λx (x thinks that [only x (λy (y respects x's husband))]))

In many contexts the two construals will be equivalent, but the presence of only enables their disambiguation here: (7a) entails that every wife thinks that other wives do not respect their husbands, while (7b) entails that every wife thinks other wives do not respect her husband. This is so, because the property attributed only to x in (7a) is respecting one's own husband, while in (7b) it is respecting x's husband.

The binding interpretation of pronouns is restricted by syntactic properties of the derivation (see BINDING THEORY). A question that has been debated is whether there are also syntactic restrictions on their covaluation interpretation. On the factual side, under certain syntactic configurations, covaluation is not allowed. For example, in (9), binding is independently excluded. The NP Lucie is not in a configuration to bind the pronoun (since it is not the argument of a λ-predicate containing the pronoun). Suppose, however, that (9) is uttered in the context of (8), so that Lucie is in the discourse storage. The question is what prevents the covaluation construal in (10) for (9) (# marks an excluded interpretation). It cannot be just the fact that the pronoun precedes the antecedent. For example, in (11), the preceding pronoun can be covalued with Max.

Can we go to the bar without Lucie?
She said we should invite Lucie.
#She (λx x said we should invite Lucie) & she = Lucie)
a. The woman next to him kissed Max.
b. The woman next to him (λx (x kissed Max) & him = Max)

In the 1970s, it was assumed that there is a syntactic restriction blocking such an interpretation (Langacker 1966; Lasnik 1976). Reinhart (1976) formulated it as the requirement that a pronoun cannot be covalued with a full NP it c-commands, which became known as Chomsky's "condition C" (1981). (In (11), the pronoun does not c-command Max.) Another formulation in logical syntax terms was proposed by Keenan (1974): The reference of an argument must be determinable independently of its predicate.

The empirical problem with these restrictions is that, as shown in Evans (1980), there are systematic contexts in which they can be violated. Reinhart (1983) argued that this is possible whenever covaluation is not equivalent to binding.

[Who is the man with the gray hat?] He is Ralph Smith.
a. He (λx (x is Ralph Smith) & he = Ralph Smith)
b. He (λx (x is x) & he = Ralph Smith)
Only he (himself) still thinks that Max is a genius.
a. Only he (λx (x thinks Max is a genius) & he = Max)
b. Only Max (λx (x thinks x is a genius)

In (12), it is not easy to imagine a construal of the truth conditions that would not include covaluation of the pronoun with Ralph Smith. But this covaluation violates condition C, as does (13). In both cases, however, the covaluation reading (a) is clearly distinct from the bound reading (b). (12b) is a tautology, whereas (12a) is not. (13a) attributes a different property only to Max from what (13b) does. Believing oneself to be a genius may be true of many people, but what (13) attributes only to Max is believing Max to be a genius (13a).

The alternative (proposed by Reinhart 1983) is that covaluation is not governed by syntax, but by a discourse strategy that takes into account the options open for the syntax in generating the given derivation. The underlying assumption is that variable binding is a more efficient way to obtain anaphora than covaluation. So whenever the syntactic configuration allows, in principle, variable binding, obtaining an equivalent anaphora-interpretation through covaluation is excluded. Given a structure like (9), variable binding could be derived, with a different placement of Lucie and her, as in Lucie said we should invite her. The result would be equivalent to the covaluation construal (10) (for (9)). Hence, (10) is excluded. In (11a), no placement of he and Max could enable variable binding, so the covaluation in (11b) is the only option for anaphora. When a variable binding alternative exists, but it is not equivalent to covaluation, covaluation is permitted, as in (12)-(13).

A relevant question is why variable binding is more efficient than covaluation. One answer, developed in Levinson (1987), is purely pragmatic and derives this from the Gricean maxims of quantity and manner. The other, developed in Fox (1998), is based on the notion of semantic processing: variable binding is less costly since it enables immediate closure of open properties, while covaluation requires that the property is stored open until we find an antecedent for the variable.

The optimality account for the covaluation restriction entails a much greater computational complexity than the syntactic approach (condition C), since it requires constructing and comparing two interpretations for one derivation. This is among the reasons why covaluation is still a matter of theoretical debate. Nevertheless, evidence that such complexity is indeed involved in computing sentences like (10) comes from the acquisition of anaphora. Many studies (e.g., Wexler and Chien 1991) report that children have much greater difficulties in ruling out illicit covaluation than in violations of the syntactic restrictions on variable binding. Grodzinsky and Reinhart (1993) argue that this is because their working memory is not yet sufficiently developed to carry such complex computation.

See also

Additional links

-- Tanya Reinhart


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