In linguistics, sloppy identity is an interpretive property that is found with verb phrase ellipsis where the identity of the pronoun in an elided VP (verb phrase) is not identical to the antecedent VP.
For example, English allows VPs to be elided, as in example (1). The elided VP can be interpreted in at least two ways, as follows: The "strict" reading: sentence (1) is interpreted as (1a), where the pronoun his denotes the same referent in both the antecedent VP and the elided VP. In (1a), the pronoun his refers to John in both the first and the second clause. This is done by assigning the same index to John and to both the "his" pronouns. This is called the "strict identity" reading because the elided VP is interpreted as being identical to the antecedent VP. The "sloppy" reading: sentence (1) is interpreted as (1b) where the pronoun his refers to John in the first clause, but the pronoun his in the second clause refers to Bob. This is done by assigning a different index to the pronoun his in the two clauses. In the first clause, the pronoun his is co-indexed with John, in the second clause, pronoun his is co-indexed with Bob. This is called the "sloppy identity" reading because the elided VP is not interpreted as identical to the antecedent VP.
1) John scratched his arm and Bob did too. a. Strict reading: Johni scratched hisi arm and Bobj [scratched hisi arm] too. b. Sloppy reading: Johni scratched hisi arm and Bobj [scratched hisj arm] too.
History
The discussion of "sloppy identity" amongst linguists dates back to a paper by John Robert Ross in 1967, in which Ross identified the interpretational ambiguity in the elided Verb Phrase of the previously stated sentence 1) found in the intro. Ross tried, without success, to account for "sloppy" identity using strictly syntactic structural relations, and concluded that his theories predicted too many ambiguities.
A linguist named Lawrence Bouton (1970) was the first to develop a syntactic explanation of VP-Deletion, commonly referred to by contemporary linguists as VP – ellipsis. Bouton's theory of VP-Deletion and Ross' observation of sloppy identity served as an important foundation for linguists to build on.
Many advances followed within the next decade, providing much of the theoretical scaffolding necessary for linguists to address issues of "sloppy identity" up to present day. Most notable of these advances are Lawrence Bouton's VP-Deletion rule (1970), Barbara Partee's "Derived-VP rule" (1975), and Ivan Sag's "Deletion Approach" (1976), based on the Derived-VP rule. Theories beyond Ross's initial discovery have all extended beyond analyses based on observations of structural relations, often using logical form and phonetic form to account of instances of sloppy and strict identity. The deletion (derived VP) approach, in combination with the use of logical form (LF) and phonetic form (PF) components to syntax, is one of the most widely used syntactic analysis of sloppy identity to date.
Analyses
Y model
This model represents the interface level of the phonological system and interpretive system that give us judgements of form and meaning of D-structure. Early theorists seemed to suggest that phonetic form and logical form are two distinct approaches for explaining the derivation of VP ellipsis.
The deletion-at-PF (phonetic form) analysis Scholars like Noam Chomsky (1955),Chomsky, N. (1955) The logical structure of linguistic theory. Manuscript, Harvard University. Ross (1969) and Sag (1976) have suggested the process responsible for VP ellipsis is a syntactic deletion rule applied at the level of PF, this process is named as VP Deletion.
The PF-deletion hypothesis assumes the elided VP is fully syntactically represented but deleted in the phonological component between SPELLOUT and PF. It suggests that VP deletion is the process that generates sloppy identities because co-indexation needs to occur with respect to binding conditions.
Example
2.i) John will eat his apple, and Sam will [VPØ] too. 2.ii) [Johni will eat hisi apple] and [Samj will eat hisj apple].
Looking at example 2.i), VP deletion is why a null VP is derived. Before deletion, as seen in example 2.ii), the sentence would in fact be read as "John will eat his apple, and Sam will eat his apple too." The clauses [John will eat his apple] and [Sam will eat his apple] share an identical VP in the sense they have the same constituent structure, so the second clause can be deleted because it is identical to its antecedent VP.
Now turning to coindexation, this sentence contains two constituents combined by the conjunction "and". The clauses are each independent complete sentence structures, so presumably each pronoun would co-index to its referent in its constituent to comply with binding theories. With this co-indexation, illustrated in example 2. ii), a sloppy reading is produced.
However, when considering cases sensitive to binding theories, the expected strict reading of sentence 3) would violate the Binding Principle A. According to this principle, an anaphor must be bound in its binding domain, meaning it must be bound within the same clause as its referent.
3) John blamed himself and Bill blamed himself
Expected strict reading: 3.i) John i [VP blamed himselfi], and Billj [VP blamed himself i]
Expected sloppy reading: 3.ii) Johni [VP blamed himselfi], and Billj [VP blamed himselfj]
Taking this into consideration, it is observed that strict readings are difficult to be obtained in sentences like this, because if the anaphor himself in the elided VP is co-indexed with 'John' it would violate Binding Theory A because they are in separate clauses. C-command relationships are represented by colour coding in the syntax tree. As depicted in the tree diagram and illustrated in green, 'Johni' c-commands 'himselfi' in the first VP. 'Billj' on the other hand c-commands 'himselfj' in the second VP, colour coded in orange. Due to binding domains, the DPs closest to the anaphors have to be the ones they bind to and co-index with. Therefore, 'Johni' cannot not c-command the 'himselfj' in the second VP, as shown through the difference in colour coding. Consequently, Binding Theory A would be violated if the co-indexation of example 2.i) generates a strict reading. Hence, PF-deletion hypothesis generates sloppy readings because it treats the elided VP as identical structures to the antecedent VP and co-indexation is constrained by locality.
The copying-at-LF (logical form) analysis According to Carnie, the sloppy identity problem can be explained using an LF-copying hypothesis. This hypothesis claims that before SPELLOUT, the elided VP has no structure and exists as an empty or null VP (as opposed to the PF-deletion hypothesis, which asserts that the elided VP has structure throughout the derivation). Only by copying structure from the VP antecedent does it have structure at LF. These copying processes occur covertly from SPELLOUT to LF.
According to LF-copying, the ambiguity found in sloppy identity is due to different orderings of the copying rules for pronouns and verbs. Consider the following derivations of the sloppy reading and the strict reading for sentence (4), using the Covert VP-Copying Rule and the Anaphor-Copying Rule:
4) Calvin will strike himself and Otto will [vp Ø] too.
Sloppy reading
In the sloppy reading, the VP-copying rule applies first, as can be seen in sentence 5). The VP-copying rule copies the VP in the antecedent into the empty VP:
Covert VP-copying rule
5) Calvin will [strike himself] and Otto will [strike himself] too.
Following the VP-copying rule, the anaphor-copying rule applies, as can be seen in sentence 6). The anaphor-copying rule, which is clause-bound, copies NPs into anaphors within the same clause:
Covert anaphor-copying rule
6) Calvin will [strike Calvin] and Otto will [strike Otto] too.
Strict reading
In the strict reading, the application of these rules occur in the opposite order. Therefore, the anaphor-copying rule is applied first. Due to the fact that the empty VP does not contain an anaphor, the NP "Otto" cannot be copied into it. This process can be seen in sentence 7):
Covert anaphor-copying rule
7) Calvin will [strike Calvin] and Otto will [vp Ø] too.
Following the anaphor-copying rule, the VP-copying rule applies and produces the sentence in 8):
Covert VP-copying rule
8) Calvin will [strike Calvin] and Otto will [strike Calvin] too.
The derivation used in this LF copying hypothesis can be found here.
Combination of PF and LF
Building on the work of Bouton (1970) and Ross (1969), Barbara Partee (1975) developed what has come to be one of the most important and influential approaches to explain VP to date, the Derived VP-Rule, which introduces a null operator at the VP level. Shortly thereafter, Ivan A. Sag (1976) developed the Deletion Derived VP approach, and Edwin S. Williams (1977) developed the Interpretive Derived VP Approach. These rules are still used by many today.
Derived VP-rule:
According to Williams (1977), the Derived VP Rule converts VPs in surface structure into properties written in lambda notation. This is a very important rule that has been built on over the years to make sense of sloppy identity. This VP-rule is used by many linguists as a foundation for their ellipsis rules.
Deletion-derived VP approach Source:
Ivan Sag proposed two logical forms, one of which the coreferential pronoun is replaced by a bound variable. This leads to the rule of semantic interpretation that takes pronouns and changes them into bound variables. This rule is abbreviated as Pro→BV, where "Pro" stands for pronoun, and "BV" stands for bound variable.
Simple sentence example
9) [Betsyi loves heri dog]
The strict reading of sentence 9) is that "Betsy loves her own dog". Application of Pro→BV then derives the sentence in 9.i):
9.i) [Betsyi loves herj(or x's) dog]
Where herj is someone else or x's is anyone else's dog
Complex example
10) Betsyi loves heri dog and Sandyj does ∅ too
where ∅ = loves her dog
Strict reading
The strict reading of 10) is "Betsy loves Betsy's dog and Sandy loves Betsy's dog as well", which implies that ∅ is a VP that has been deleted. This is represented in the following sentence:
10.i) Betsyi λx (x loves heri dog) and Sandy λy (y loves heri dog)
The VPs that are being represented by λx and λy are syntactically identical. For this reason the one that is being c-commanded (λy) can be deleted.
This then forms:
10.ii) Betsyi loves heri dog and Sandyj does ∅ too
Sloppy reading
The sloppy reading of this sentence is "Betsy loves Betsy's dog and Sandy loves Sandy's dog". That is, both women love their own dog. This is represented in the following sentence:
10.iii) Betsyi λx (x loves heri dog) and Sandyj λy (y loves herj dog)
Since the embedded clauses are identical, the logic of this form is that the variable x must be bound to the same noun phrase in both cases. Therefore, "Betsy" is in the commanding position that determines the interpretation of the second clause.
The Pro → BV rule that converts pronouns into bound variables can be applied to all the pronouns.
This then allows for the sentence in 10.iii) to be:
10.iv) Betsyi λx (x loves x's dog) & Sandyj λy (y loves y's dog)
Another way the VP can be syntactically identical is, if λx(A) and λy(B) where every instance of x in A has a corresponding instance of y in B. So, like in the example above, for all instances of x there is a corresponding instance of y and therefore they are identical and the VP that is being c-commanded can be deleted.
Step-by-step derivation