Haug & Dalrymple (2020) @cite{haug-dalrymple-2020} #
Reciprocity: Anaphora, scope, and quantification. Semantics & Pragmatics 13(10): 1--62.
This paper develops the relational analysis of reciprocals, where each other is a pronoun bearing an anaphoric relation (reciprocity R) to its antecedent. The narrow/wide scope ambiguity reduces to the choice of anaphoric relation between the local antecedent and the matrix subject:
- Narrow scope (we-reading): group identity (∪) + reciprocity (R)
- Wide scope (I-reading): binding (=) + reciprocity (R)
- Crossed reading (§3.3): group identity (∪) + group identity (∪), with reciprocity contributed by the DRS distinctness presupposition
The formal semantics of the three anaphoric relations (binding, group
identity, reciprocity) are defined in Theories.Semantics.Reference.Reciprocals
as bindingSem, groupIdentitySem, and reciprocitySem.
Key Contributions Formalized #
- Formal semantics of anaphoric relations (§§2.2--2.4): three relations
over discourse referent functions
S → E - Scope from anaphoric relation (§3): narrow ↔ ∪, wide ↔ =
- Crossed readings (§3.3): both relations are ∪
- Underspecification (§4.2): German sich, Czech se, Cheyenne REFL/RECIP affix (@cite{murray-2008}) — group identity without distinctness permits reflexive, reciprocal, and mixed readings
- Maximize Anaphora (§6): replaces Strongest Meaning Hypothesis of @cite{dalrymple-et-al-1998}; maximize the set of pairs standing in R_u subject to world knowledge consistency
Connection to Cumulativity #
The groupIdentitySem definition — bidirectional existential coverage of
value ranges — is structurally parallel to cumulativeOp in
Theories.Semantics.Lexical.Plural.Cumulativity. Both express that two
pluralities cover the same set of atomic parts. This is not a coincidence:
reciprocity is a species of cumulativity, as @cite{langendoen-1978}
first observed and @cite{haug-dalrymple-2020} §1 reaffirms.
Narrow scope uses group identity between the local antecedent and the matrix subject.
Wide scope uses binding between the local antecedent and the matrix subject.
The narrow-scope antecedent relation denotes groupIdentitySem.
The wide-scope antecedent relation denotes bindingSem.
Both readings use the reciprocity relation for the reciprocal itself,
which denotes reciprocitySem.
Crossed readings arise when both anaphoric relations are group
identity (∪). The subject pronoun bears group identity to the matrix
subject (∪u₂ → ∪u₁), and the reciprocal bears group identity to
the subject pronoun (∪u₃ → ∪u₂). Reciprocity is contributed by
the DRS distinctness presupposition (∂(u₃ ≠ u₂)), not by an
anaphoric reciprocity relation.
Example: "Two girls thought they saw each other" on the crossed reading — girl₁ thought girl₂ saw girl₁ and vice versa.
Equations
- One or more equations did not get rendered due to their size.
Instances For
Crossed readings use neither binding nor reciprocity as an anaphoric relation — both slots are group identity. This distinguishes them from narrow and wide readings.
Both components of the crossed reading denote groupIdentitySem.
Group identity does not imply binding: a Bool counterexample where
id and not have the same range ({true, false}) but differ
pointwise.
Underspecified pronouns (German sich, Czech se, Cheyenne REFL/RECIP
affix) allow any reading consistent with group identity: reflexive
(binding + group identity), reciprocal (reciprocity + group identity),
or mixed (@cite{murray-2008}). The underspecified meaning
underspecifiedSem is exactly groupIdentitySem.
Underspecified pronouns permit reciprocal readings: reciprocity implies underspecification.
Maximize Anaphora replaces the Strongest Meaning Hypothesis of @cite{dalrymple-et-al-1998}. In interpreting a DRS K containing a discourse referent u introduced by a reciprocal with antecedent u', maximize the set of pairs R_u standing in the relation φ(u, u'), subject to the constraint that φ(u, u') holds in K given world knowledge.
Maximize Anaphora is orthogonal to reciprocal scope (§6.3): it constrains the strength of the reciprocal relation (weak vs. strong reciprocity), not the scope (narrow vs. wide). Scope is determined by the anaphoric relation on the antecedent (binding vs. group identity), which is a separate parameter.
Key constraint: on the relational analysis, the reciprocal's scope is determined by the anaphoric relation on its antecedent. There is no independent scope mechanism. Local antecedent properties directly constrain scope, unlike the quantificational analysis where scope is independent (@cite{williams-1991}).
The scope constraint additionally means that the reciprocal never scopes higher than the highest binder of the local antecedent (@cite{williams-1991}, @cite{haug-dalrymple-2020} §3.4). On the relational analysis this falls out automatically: scope is parasitic on the antecedent's anaphoric relation, and binding is limited by c-command. The quantificational analysis must stipulate this constraint separately.