Remarks on Rule H

Fox (2000) argues that a single principle, Rule H, can account for (i) Strong Crossover, (ii) the ban on using co-binding to sneak around Condition B, and (iii) the Dahl paradigm. The focus of this paper is Fox’s analysis of the Dahl paradigm. Though elegant and appealing, the analysis faces both conceptual and empirical problems. On the conceptual side, the analysis assumes that a bound pronoun within an elided VP must be bound in a structurally parallel configuration to its counterpart in the antecedent VP. This requirement does not follow from independently-motivated constraints on VP ellipsis. On the empirical side, Roelofsen (2011) has turned up additional ellipsis phenomena that do not pattern as Fox’s analysis predicts. I will argue that a relatively minor modification to Fox’s analysis suffices to solve both the conceptual and empirical problems. Taking inspiration from Kehler & Büring (2008), I increase the domain of application of Rule H to include syntactic structures which underlie Focus Semantic Values, so that Rule H acts as a filter on Focus Semantic Values. The only relevant constraint on VP ellipsis is an independently-motivated Rooth-style contrast constraint.


INTRODUCTION
introduces Rule H, which requires that bound pronouns be bound as locally as possible.Fox exploits Rule H in his analysis of three classes of phenomena: (i) Strong Crossover.
(ii) The ban on using co-binding to "sneak around" Condition B (together with certain exceptional cases).
(iii) The Dahl paradigm (Dahl 1973(Dahl , 1974)), and a number of related restrictions on the interpretation of pronouns in elided VPs.
The focus of this paper is Fox's analysis of class (iii) phenomena in terms of Rule H.This analysis faces two main problems.The first, pointed out by Heim (2008), is that the analysis relies on a form of the Parallelism constraint on VP ellipsis that lacks independent motivation. 1 The second problem, raised by Roelofsen (2011), is that Rule H cannot account for certain quantificational variations on the Dahl paradigm, nor for the apparent availability of co-binding in certain configurations.
I show that Fox's analysis can be tweaked to solve the preceding problems.The key component of my analysis is the hypothesis that Rule H acts as a filter on Focus Semantic Values (FSVs).Given this hypothesis, Parallelism can be replaced by an independently-motivated contrast constraint on VP ellipsis of the type proposed in Rooth (1992).The paper is organized as follows.Section 2 gives some background on Rule H. Section 3 outlines a number of problems relating to the Parallelism constraint on VP ellipsis and introduces my proposed replacement for Parallelism.Section 4 explains how this new constraint on VP ellipsis accounts for the Dahl paradigm.Sections 5-7 extend the analysis to various additional binding and ellipsis phenomena.Section 8 presents a presuppositional reformulation of Rule H designed to deal with certain co-binding structures that are problematic for Fox's analysis.Throughout the text I assume that focus alternatives are derived via syntactic substitution.The Appendix shows how this assumption can be disposed with.
I assume that binding and coreference dependencies are represented along the lines proposed by Heim & Kratzer (1998).Each DP starts out with a freely-assigned index.When a DP moves, a λ-node is adjoined immediately below the landing site and an arbitrary index is chosen for the λ-node and the trace.If the λ-node c-commands and is non-vacuously coindexed with a pronoun, then the pronoun is bound as a variable.A DP must move in order to bind a pronoun as a variable via a λ-node.This movement may be QR, or A-movement from the VP-internal subject position to Spec,TP.

Rule H
A pronoun A can be bound by an antecedent B only if there is no closer potential antecedent C such that it is possible to bind A by C and get the same interpretation.
As is evident from (1), evaluation of Rule H proceeds via the construction of a competitor LF where binding is more local than in the original.The principal effect of Rule H is to block the following configurations: 2 1 For critical commentary on Fox's formulation of Parallelism see e.g.Heim (2008); Roelofsen (2010); Reinhart (2006).The principal objections in the literature relate to Fox's disjunctive definition of Parallelism in terms of separate Referential Parallelism and Structural Parallelism constraints.Fox's analysis of the Dahl paradigm does not in itself require this disjunctive definition, since Structural Parallelism is sufficient to license all of the available readings (on the assumption that each pronoun in the antecedent VP can be interpreted as either a referential or a bound pronoun).However, certain other phenomena, such as the ability of a single antecedent VP to license both strict and sloppy ellipsis (Fiengo & May 1994, 169-171;Fox 2000, 117), suggest that not all instances instances of VP ellipsis satisfy Structural Parallelism.Thus an additional licensing mechanism, in the form of Referential Parallelism, appears to be required.A Rooth-style contrast constraint on VP ellipsis, which is the basis of the present analysis, straightforwardly accounts for the ability of a single antecedent VP to license both strict and sloppy ellipsis.

2
I annotate LFs with links to make it easier to discern patterns of binding dependencies.These links never convey any information that the LFs themselves do not.Dahl (1973;1974) observes that the interpretation of the elided VP in ( 6) is restricted in a surprising way.When both pronouns in the first conjunct are anteceded by John, the pronouns in the elided VP may receive either strict or sloppy readings.However, the second pronoun may receive a sloppy reading only if the first does also: (6) John knows he loves his mother and Bill F does too.

THE DAHL PARADIGM
(

STRONG CROSSOVER
A typical Strong Crossover configuration is shown in ( 11): The co-binding configuration in (11) is blocked by Rule H. Binding t 1 by he 1 yields (12), which has the same interpretation as (11).This example illustrates the point that Rule H applies even if the competing LF is one that could not be the output of a licit syntactic derivation. (

CONDITION B
Assume the following formulation of Condition B: (13) A pronoun cannot be semantically bound 3 by a local c-commanding antecedent.
It is easy to 'sneak around' this formulation of Condition B using co-binding.The co-binding configuration in ( 14) does, however, violate Rule H. Rule H thus makes it possible to retain an attractively simple formulation of Condition B in terms of semantic binding.This contrasts with the rather complex formulation of Condition B proposed in Heim (1998) in light of ( 14) and related data.
If ( 13) is defined in terms of syntactic binding (c-command plus co-indexation) rather than semantic binding, then ( 14) is blocked directly by Condition B. However, more complex examples such as ( 15) can be constructed where the pronoun is not coindexed with its local antecedent (Bach & Partee 1980): Rule H blocks binding of [him 2 ] by the first instance of [he 1 ] (since the second instance of [he 1 ] is a closer potential antecedent).Heim (1998) argues that there are certain exceptional situations in which co-binding can in fact be used to obviate Condition B. In particular, this is possible when co-binding yields an interpretation that could not be derived using transitive binding.If Condition B is defined, as in ( 13), in terms of semantic binding, then Rule H predicts precisely this generalization.Rule H forces transitive binding in preference to co-binding only when both yield the same interpretation. 4

THE PARALLELISM PROBLEM
Fox's disjunctive Parallelism constraint does not follow from independently motivated constraints on VP ellipsis.In particular, constraints on VP ellipsis stemming from the proposals in Rooth (1985;1992) do not enforce a strict structural parallelism requirement on bound pronouns within elided VPs.The licensing constraint that Rooth proposes on VP ellipsis can be formulated as in ( 17), following Heim (1997). 5There are many proposals in the literature regarding exactly how Focus Semantic Values should be defined.I assume the definition in terms of syntactic substitution given in ( 16). (16)

Focus Semantic Value (FSV)
The Focus Semantic Value of a constituent ϕ for an assignment g, written FSV g (ϕ), is the set of ⟦ϕ′⟧ g such that ⟦ϕ′⟧ g is defined and ϕ′ can be obtained from ϕ by replacing all its focused subconstituents with unfocused constituents of the same semantic type. (17)

Rooth-Style Contrast Constraint (RSCC)
For ellipsis of a VP ϕ to be licensed in an utterance context C, there must be a constituent ϕ′ containing ϕ, and an antecedent constituent ψ, such that for all assignments g extending C g , ⟦ψ⟧ g is contained in FSV g (ϕ′).
(C g is the assignment determined by the utterance context C.) The following discourse illustrates the application of ( 16)-( 17). (18) He 1 smokes. b.
The FSV of (18b) has the following members: 4 If Condition B restricts only semantic binding then it can also be sneaked around using coreference.This paper takes no position on how to solve this problem.One possible solution is the addition of a constraint on the use of coreference such as Grodzinsky & Reinhart's (1993) Rule I. Büring (2005) proposes to collapse Rule H and Rule I into a single 'Have Local Binding!' (HLB) constraint.See section 5 for discussion of HLB.See also Heim (1998), Reinhart (2006), Heim (2008), Reuland (2010), Roelofsen (2010) for different perspectives on the correct formulation of Condition B and pertinent economy conditions (if any).

5
The constraint in ( 17) is not the only constraint on VP ellipsis according to Rooth.There is also a matching constraint on the syntactic form and lexical content of the antecedent and elided VPs.Drummond Glossa: a journal of general linguistics DOI: 10.5334/g jgl.333 The assignment C g given by the utterance context includes 1 ↦ John, so RSCC considers only assignments g such that g(1) = John.For any such assignment, ⟦[John] does [ VP smoke]⟧ g is equal to ⟦(18b)⟧ g .As ⟦[John] does [ VP smoke]⟧ g is a member of FSV g (( 18b)), RSCC is satisfied and VP ellipsis in (18b) is licensed.
RSCC must be interpreted in conjunction with Heim's (1997) ban on meaningless coindexing. 6ithout such a constraint, arbitrary choices of indexation that have no effect on interpretation become relevant when RSCC is computed.For example, the ungrammatical instance of VP ellipsis in (20c) is not licensed with respect to α in (20b), but is licensed with respect to α in (20a): (20) a.
No (*Parallelism) The assignment C g given by the utterance context includes 1 ↦ John.Thus, under all assignments that extend C g , the first pronoun in the second conjunct is coreferential with [John] and the second is bound by [Bill F ]. Once [Bill F ] is replaced by its alternative [John], the first and second conjuncts have, for all assignments that extend C g , the same semantic value (the proposition 'John knows John knows John's mother').RSCC is therefore satisfied.This result is empirically significant as (21) does not violate Rule H, and Fox relies on Structural Parallelism to block it.
Why exactly does Fox's analysis of the Dahl paradigm require the Parallelism constraint?The essential reason is the following.It is only in the first conjunct of (7) that there is any possibility of local and non-local binding giving rise to the same interpretation (thereby triggering a violation of Rule H); and yet it is in the second conjunct that non-local binding must be blocked in order to rule out the unattested interpretation (7d).The role of Parallelism is to 'translate' the ban on non-local binding in the first conjunct over to the second conjunct.If there were a means to block non-local binding directly in the second conjunct, then Parallelism would no longer be required.
Given a broadly Roothean theory of focus and ellipsis licensing, it is in fact possible to arrange for all the theoretical action to take place in the second conjunct of ( 7).The precise pattern of binding dependencies in the first conjunct is then irrelevant -except insofar as it affects the proposition expressed.The key idea is to replace Parallelism with RSCC while imposing a further constraint in the definition of Focus Semantic Value.The revised definition of FSV is as follows: (22)

Strict Focus Semantic Value (SFSV)
The SFSV of a constituent ϕ for an assignment g, written SFSV g (ϕ), is the set of ⟦ϕ′⟧ g such that ϕ′ does not violate Rule H for g, and ϕ′ can be obtained from ϕ by replacing its focused subconstituents with constituents of the same semantic type.

THE DAHL PARADIGM REVISITED
The LF in (9), repeated here as ( 24), yields the unattested reading (7d) of the Dahl paradigm.This LF satisfies Rule H but violates Parallelism: (24) , since none of the members of the FSV of the second conjunct then has John's mother as the object of love.Thus, to derive reading (7d), the first pronoun in the second conjunct must refer to John and the second must be bound by [Bill].And as we have just seen, the SFSV of the second conjunct will then lack the member necessary to license ellipsis given RSCC+SFSV.
Readings (7a)-(7c) can all be derived without using non-local binding (either in the original LF or in the LFs used to derive members of the relevant FSVs).Replacing FSV with SFSV therefore makes no difference for these examples.

THE EMBEDDED DAHL PARADIGM
Roelofsen (2011) discusses a variation on the original Dahl paradigm where the referential subject DPs are replaced by pronouns bound by a higher quantifier.The pattern of available and unavailable readings remains abstractly the same, as illustrated in ( 28)-( 29): (28) Every worker says he knows how he broke his tools, and that the boss does too.Similarly, to derive reading (29c) while respecting Parallelism, [every worker] must bind the first and third pronouns in the first conjunct; and to derive reading (29d) while respecting Parallelism, [every worker] must bind the first and second pronouns in the first conjunct.In both cases, a co-binding configuration is created giving rise to a violation of Rule H.
What if we replace Parallelism with RSCC+FSV?This option is explored in Roelofsen (2011).
Roelofsen points out that without further constraints, RSCC+FSV allows all of the readings (29a)-( 29d) to be derived from LFs that comply with Rule H. 7 RSCC+FSV is therefore too lax.Does RSCC+SFSV fare any better?I will now show that it does.The desired result is for the LFs in ( 33)-( 35) to be allowed and for the LF in (36) to be blocked: (33) sloppy-sloppy ] is bound within (40). 9Fortunately, the additional strength of HLB is of no consequence with regard to the phenomena Büring discusses.That is, all of his arguments still go through if Rule H and Rule I are separate constraints -as his exposition initially assumes.

FSVS VS. QUDS
My analysis of the Dahl paradigm is similar in spirit to that of Kehler & Büring (2008).K&B introduce the 'Be Bound or Be Disjoint' constraint in (41).This constraint resembles Rule H insofar as it blocks co-binding and binding across a coreferential expression.
(41) Be Bound Or Be Disjoint (BBOBD) Kehler & Büring (2008) If a pronoun p is free in the c-command domain of a (non-Wh) DP α, p bears a presupposition of disjointness with α (unless α binds p).
K&B's analysis makes reference not only to the structures containing the antecedent and elided VPs, but also to an additional syntactic structure, the 'Question Under Discussion' (QUD).Informally, a QUD for a given discourse is a question that its participants are concerned to ask or answer.As syntactic structures, QUDs are subject to BBOBD.
Consider the discourse in (42).The LF (42b) yields a strict-strict reading of the pronouns in the elided VP.Ellipsis is licensed in (42b) iff there is a BBOBD-respecting QUD to which both (42a) and (42b) are answers.There is in fact such a QUD -( 43 The QUD in ( 45) is 'Who is such that they think John loves their wife?' BBOBD adds the presupposition that [his 1 ] is disjoint in reference from [John].As a result, (44a) is not an appropriate answer to (45).Thus, ( 45) is not a QUD to which both (44a) and (44b) are answers, and ellipsis in (44b) is not licensed.
In the examples K&B consider, it is clear enough what the question under discussion is.However, in cases such as the embedded Dahl paradigm, where the elided VP and its antecedent contain pronouns bound by the same higher quantifier, it is less clear what the QUD responsible for licensing ellipsis should be.In the case of (28), for example, is there a single QUD which receives multiple answers (one for each worker in the domain), or is there a different QUD for each worker?To deal adequately with these examples, a significant amount of technical work would have to be done to clarify the notion of a QUD and explain how exactly the QUD is derived from the context together with the other syntactic structures present.An advantage of the present theory is that it makes reference only to syntactic structure of the sentence itself (modulo substitution of focus alternatives), and relies on concepts from Rooth's theory of focus that have already been thoroughly investigated.

THE DAHL PARADIGM OUTSIDE ELLIPSIS CONTEXTS
A number of analyses of the Dahl paradigm tie it to VP ellipsis.For example, the analysis of Schlenker (2005: 33-37) crucially depends on there being two independent pairs of pronouns, 9 Reinhart and Grodzinsky do not define coreference precisely, but coreference -in the tradition of Reinhart (1983)  My analysis can be extended to the paradigm in (46).The starting point is Rooth's (1992) analysis of adverbial only.Consider reading (46d).This reading requires [his] to be bound by [John F ] and [he] to be interpreted as a referential pronoun.An LF along these lines is shown in ( 47 The property denoted by the matrix VP ('told John that John loves John's mother') is not a member of the SFSV of the matrix VP, since when [John] is taken as the alternative to [John] F , binding of [his] by [John] across a pronoun coreferential with John violates Rule H. Thus, this property is not a member of C when the denotation of ( 47) is computed via application of the denotation of only in (48).The denotation of ( 47) is shown in ( 50): (50) where P = λx e λw .x told John that John loves John's mother in w As P is not a member of C, no member of C can equal P. It follows that ( 50) is true iff there is no property in C which holds of Mary.Rooth's ∼ operator introduces a presupposition:10 (51) ϕ ∼ Γ, evaluated for an assignment g, presupposes that i.
Thus, (47) presupposes that C contains the property 'told John that John loves John's mother' (via ii), but also that C does not contain this property (via i, where ⟦ in this instance is C).The inaccessibility of reading (46d) then follows from (47) having an unsatisfiable presupposition.
The available readings of (52) follow the same pattern as those of (46).If the LF constituency of these examples is as shown in (53a), the analysis in section 7 carries over without modification.If, however, the constituency is as shown in (53b), then that analysis does not carry over.
(52) Only John F said he loves his mother.
Only [John F said he loves his mother].b.
[Only John F ] said he loves his mother.
The unavailable reading corresponding to (46d) can be derived from the following LF: Here, [only [John 1 ] F ] QRs and binds a type e trace.An ordinary two-place denotation for only suffices for interpretation.Roughly, (54) asserts that for every member x of SFSV g ([ On the present analysis the only SFSV computed is the SFSV of [John] F .As a result there is no opportunity for Rule H to winnow the set of alternatives, so that the unattested reading in ( 54) is let through.I return to this issue at the end of the next section.Drummond Glossa: a journal of general linguistics DOI: 10.5334/g jgl.333 (60) .⟦[λ 2 [t 2 said he 1 loves his 2 mother]]⟧ g (x) The presupposition introduced by the ⚬ operator is satisfied iff x ≠ John (i.e.iff [he] does not refer to John).In this way, what was formerly a direct violation of Rule H becomes an instance of presupposition failure.
Let us now consider the interaction of Presuppositional Rule H with focus.If an LF's presuppositions are not satisfied then -depending on the theoretical treatment of presuppositions -its denotation is either undefined, or it denotes some special indeterminate value.In the former case the LF's denotation cannot be included in an FSV.In the latter case, its denotation may be included in an FSV, but will not match any putative antecedent or attested interpretation.Thus, Presuppositional Rule H acts as a filter on FSVs.It is not longer necessary to explicitly filter out Rule-H-violating members of FSVs.
An important question now arises.Following substitution of alternatives for focused phrases, does Presuppositional Rule H apply anew to each LF underlying a member of an FSV?That is, is the value of the variable associated with each ⚬ operator updated following substitution?Or is it left unaltered?This makes no difference in the examples we have seen prior to this section, where any focused constituents always lie outside the lambda phrase of interest.In (61), for example, replacing [Bill] F with another DP does not alter the lambda phrase.But consider (62), the LF required to license ellipsis in the second sentence of (55).Here, [the teacher] F is within the lambda phase.For ellipsis to be licensed in ( 55), the FSV of (62) must contain the denotation of ( 63).The LF in ( 63) is derived from (62) by replacing [no student] F with [every student] and [the teacher] F with [he 1 ].If Presuppositional Rule H applies anew in (63), reassigning v, then then the presupposition of the lambda phrase is derived from the value of v shown in (63b).If, on the other hand, the value of v remains unaltered, as shown in (63a), then the presupposition of the lambda phrase remains the same as in (62).
(61) If v is valued as in (63a), then the presupposition introduced by ⚬ in ( 63) is satisfied for every student x, so that ⟦ (63)⟦ is admitted to the FSV of (62), and ellipsis is licensed in (55) -as desired.
Conversely, if v is valued as in (63b), then the presupposition introduced by ⚬ is not satisfied for any value of x, ⟦(63)⟧ is not admitted to the FSV of ( 62), and ellipsis is not licensed in (55).
A constituent ϕ violates Rule H for an assignment g iff there are A,B,C within ϕ such that A is a pronoun bound by B across the closer potential antecedent C, and and the LF ϕ′ derived by binding A by C is such that ⟦ϕ⟧ g = ⟦ϕ′⟧ g .I will use the abbreviation 'RSCC+FSV' to refer to RSCC when interpreted in relation to the definition of Focus Semantic Value in (16), and 'RSCC+SFSV' to refer to RSCC when interpreted in relation to the definition of Strict Focus Semantic Value in (22).The conjunction of Rule H and RSCC+SFSV allows certain structural mismatches between elided and antecedent VPs that are not permitted by Parallelism.However, the requirement that the members of a constituent's Focus Semantic Value derive from structures that have maximally local binding has the consequence that there are certain configurations where Parallelism is satisfied and yet RSCC+SFSV is violated.
John 1 knows he 1 [λ 2 [t 2 loves his 2 mother]] and Bill F [λ 3 [t 3 does [know he 1 loves his 3 mother]]] too (*Parallelism)RSCC+FSV is satisfied in (24), since[John]can substitute for[Bill]and α is therefore contained in the FSV of β.The conjunction of Rule H with RSCC+FSV thus fails to block the unattested reading (7d).If, however, SFSVs are used instead of FSVs, (24) is ruled out.To see this, note that in order for ellipsis to be licensed in (24), the following proposition n must be a member of the SFSV of β: 4 [t 4 did say he 1 [λ 5 [t 5 loves his 5 mother]] too]] Are there any other LFs that derive reading (7d) and also satisfy Rule H and RSCC+SFSV?The first pronoun in the second conjunct of (24) must refer to John if reading (7d) is to be derived.The second pronoun can therefore pick out Bill either by referring to Bill or by being bound by[Bill](since being bound by the first pronoun would cause it to pick out John instead).Whatever the pattern of binding/coreference in the first conjunct, RSCC is violated if [his] is coreferential with[Bill] [t 1 says he 1 [λ 2 [t 2 knows how he 2 [λ 3 [t 3 broke his 3 tools]]]] and that [TB][λ 4 does [t 4 know how he 4 [λ 5 [t 5 broke his 5 tools]]]] too]]None of the other readings in (29) can be generated without violating at least one of Rule H and Parallelism.To derive the strict-strict reading (29b) while respecting Parallelism, it is necessary to have the first and second pronouns in the first conjunct bound by every worker, but this gives rise to a co-binding configuration that violates Rule H.For example, the LF in (31) is blocked by its competitor (32), which violates Parallelism: [EW] [λ 1 [t 1 says [he 1 [knows how he 1 [λ 2 [t 2 broke his 2 tools]]]] and that [TB] F does [know how he 1 [λ 3 [t 3 broke his 3 tools]]] too]] [EW] [λ 1 [t 1 says he 1 [λ 2 [t 2 [knows how he 2 [λ 3 [t 3 broke his 3 tools]]]]]and that [TB] F does [know how he 1 [λ 4 [t 4 broke his 4 tools]] too]] ) -so ellipsis is licensed.VP think John [λ 4 [t 4 loves his 4 wife] too]] and subsequent work -is a relation between two referential expressions, and hence not a relation that a bound variable can enter into.There may be a Rule I violation in (40) in virtue of [he 1 ] being in a configuration to bind [his 1 ].However, binding [his 1 ] by [he 1 ] would give rise to a co-binding LF that violates Rule H.One could hypothesize that Rule I considers only those alternative LFs that do not violate other economy conditions.Drummond VP told John F that he loves his mother]].a. John is the only x s.t.Mary told x that x loves x's mother.b.John is the only x s.t.Mary told x that John loves John's mother.c. John is the only x s.t.Mary told x that x loves John's mother.d. *John is the only x s.t.Mary told x that John loves x's mother.