2.1. Basics

We begin with some notation. We take any linguistic expression to be a triple of sound, category, and meaning, notated as <[sound], Cat, [[meaning]]> (I use orthography to represent the sound part). I assume a small set of basic categories, we can take these initially to be S, NP, N, PP, CP, although there might be a few others. I also assume that the categories can have features. In fact, as discussed in Chomsky (Reference Chomsky, Jacobs and Rosenbaum1970), GKPS, and others, we can think of the basic categories as themselves being feature bundles. This means that at the bottom of the system is a set of features where category features like S, NP, etc. are just themselves the value of one of the features. But for convenience I will notate the usual category features S, NP, etc. as given above. I also continue to use the terminology of basic categories, ignoring the fact that these are actually feature bundles.

In addition to the basic categories, we will (as is standard in CG) add in a set of function categories. We can define these recursively as follows:

A/_RB is something that can combine with a B to its right to give an expression of category A, and A/_LB takes its argument to the left. The semantics and semantic combinatorics are parallel; each expression of some basic category A has as its extension (I ignore intentions throughout) some member of set a, and each function category of the form A/B denotes as function in bXa. As is standard, we use <b,a> to mean the set of all functions in bXa. Moreover, we take these function categories to literally correspond to functions on actual strings; this is central to this paper. The function corresponding to any category of the form A/B applies to any string which is of that category and gives back a function from strings of category B to strings of category A. Technically, then, the function corresponding to any category A/B is a function in <string, <string, string>>, and which actual function it is depends on the directionality of the slash.Footnote ² Thus, the function corresponding to S/_LNP, for example, applies to a string like [walks], and the result is a function mapping [Lee] to [Lee walks], [Sandy] to [Sandy walks], etc. Incidentally, while there is no primitive category VP (VP is S/_LNP or perhaps in some cases S/_LCP, etc.), I use VP for convenience as an abbreviation. And I will use TV to mean (S/_LNP)/_RNP.

For any category X, we notate the corresponding function as F:X (read that as the function corresponding to the category X), and for every function F we refer to the corresponding category as CAT:F. We then define the relevant functions as follows:

In prose, (a) says that the function corresponding to the category A/_RB is such that when it applies first to a string [x] and then to [y], it yields the string [xy] and the reverse for (b). Given this, we can formalize how the syntactic and semantic combinatorics work by adopting the very general rule schema in (6), where X ranges over R and L:

Note that the directional features on items are largely predictable: All expressions of category S/NP, for example, take their subject NPs to the left. And all transitive verbs (expressions of category (S/NP)/NP take their objects to the right. Therefore, we surely do not want to list the directional features on a case-by-case basis on lexical items. To this end, Jacobson (Reference Jacobson2014) suggests that lexical items are (in general) listed in underspecified form without directional features (although there could be occasional listed exceptions to the general rules), and the directional features are supplied by rules further specifying the items. For present purposes, it suffices to adopt three such rules (there are probably a few others):

These rules apply only when not already marked; they do not override existing features. And (c) will have to apply after the other two rules.Footnote ⁴ (This is the only place in the system where there is any kind of ordering among the rules.)

We assume that and is listed in the lexicon as being of category (X/X)/X – in other words, it takes its arguments one at a time rather than in a flat ternary fashion. For arguments for this, see, among others, Munn (Reference Munn1993), Jacobson (Reference Jacobson2014). The word order rules thus predict that the fully fleshed out category for and is (X/_LX)/_RX. This predicts that and takes its first argument to the right (by the default rule) and second to the left (by the fact that the inner part here is a modifier; something like and chews gum is a VP modifier as it maps a VP like walks to the VP walks and chews gum). Partee and Rooth (Reference Partee, Rooth, Bäuerle, Schwarze and von Stechow1983) proposed that and has a generalized meaning corresponding to the meet operation, which is a binary operator. But since actual English and takes its arguments one at a time, we can take its meaning to be the Curryed version of this meet operation. In most of the cases looked at here, it conjoins things of type <x,t>, so it ends up having a meaning in those cases which is the Curryed version of the intersection operation. (For a case like Lee and Sandy, the two NPs here have to be generalized quantifiers to be conjoinable; see Partee and Rooth (Reference Partee, Rooth, Bäuerle, Schwarze and von Stechow1983) and the remarks below about Lift). Also central to this paper is the behavior of what I call silent and, which I notate as and (as in walks,and talks, and chews gum). The analyses work out effortlessly if indeed this is just a silent version of ordinary and – it has no phonology but its syntax and semantics are the same. Thus, it is listed in the lexicon as (slightly simplified) <[∅], (X/X)/X, Curryed meet>. The directional features on the slashes will be the same as for ordinary and.

But there is one interesting issue raised by and . Since everything said above regarding and is also true for or (except of course with generalized join instead of meet semantics), and since there is also a silent or , the grammar needs a way to ensure that and (or or) be part of a chain where at the bottom there is the corresponding overt item. Thus, we get chains like Lee, Sandy, or Kelly left, but not *Lee, Sandy, Kelly left. (I use or here as it is completely clear that the second cannot mean the same as the first – meaning we cannot just have or all the way. But it is not very good even if interpreted as Lee, Sandy, and Kelly left, although I have found people who marginally accept lists like this on the and reading. I have no account here for that dialect.) And we certainly do not want Lee, Sandy, or Kelly to be interpreted as Lee and Sandy or Kelly. All of this can be accomplished with appropriate feature passing; for details, see Jacobson (Reference Jacobson2025). As such, the category for and given above would be further elaborated, but this will do for present purposes.

2.2. Additional operations: Lift

The results in this paper rely on the adoption of two further operations – both of which have independent motivation and are not adopted just for the material here. The first is a Lift operation. By way of background, it is well known that ordinary NPs like Mitka, the most disobedient husky, etc., have the same distribution as generalized quantifiers like every dog, no cat, etc. To account for this, Montague (Reference Montague, Suppes, Moravcsik and Hintikka1973) assigned them all the same semantic type and syntactic category. Looking only at the semantics here, Montague’s treated both as being of type <<e,t>,t>. Partee and Rooth (Reference Partee, Rooth, Bäuerle, Schwarze and von Stechow1983), however, argued against having them only have the higher type, and proposed that they are born as denoting just individuals (hence type e) but can lift to the <<e,t>,t> type. While Partee and Rooth did not adopt a CG syntax (and hence treated these all as NPs), it is natural here to marry this with the syntax, which means that expressions of category NP can shift to S/(S/NP) (we ignore the directional features momentarily). We will, however, generalize the Partee and Rooth rule to allow expressions of any category to lift. We thus adopt a unary rule (a rule mapping a single triple into another triple) as follows:

Two related notes about (8). First, Lift is a perfectly general operation, totally independent of its role in linguistics. For any member a of a set A and any set of functions F from A to B, we can define the lift of a over such functions to be a function in <<a,b>,b>, such that for any function f in F, Lift(a) takes f as argument and returns f(a). Note that the semantics of the operation in (8) is just the lift of [[α]] over functions in <a,b>. Second, one might wonder why the syntactic output here apparently just happens to preserve word order; the lifted item will combine with some expression with a function category to give just what we would have gotten had that expression taken the original α as argument. (This is ensured by the way the slash directions are given in (8).) But once we take seriously the notion of syntactic function categories as literally being functions in <string, <string,string>>, this follows from the very definition of lift.Footnote ⁵ Moreover, the disjunctive syntactic category in the output means that (8) as given here is really two rules. But this inelegance also disappears once we reformulate this to actually incorporate the lift operation on syntactic categories. To exposit this requires more space, so we refer simply to Jacobson (Reference Jacobson2025) for a formalized version that does incorporate the actual lift operation and collapses the two cases in (8) into one as both just instantiate lift. Here we will adopt (8) with the understanding that is really one general lift rule which, by definition, preserves order.Footnote ⁶

2.3. Function composition (or Geach)

The second operation is function composition, put forth in Steedman (Reference Steedman1987) and in many of his subsequent works. Steedman introduced this as an account of wh-extraction constructions, and indeed it is that very analysis that I will be rejecting later, in favor of something closer to that in GKPS. Nonetheless, the adoption of function composition (or, as discussed below, a Curryed version of function composition) as a combinatory possibility has other welcome consequences.

Steedman proposed that two function expressions can combine by function composition (rather than function expressions always having to first take their arguments) and in particular proposes (among others) the following two rule schemas:

Unlike Steedman, I will assume these are the only two composition rules (modulo the possibility of having infix slashes, see fns. 2 and 6). But, one might ask, why just these two? (Indeed, Steedman actually allows for two others; we return directly.) Why, for example, is there no schema exactly like (9a) but where the phonological part of the output is [βα]? Steedman (Reference Steedman2024) rules this out by his Principle of Consistency: ‘All rules linearize their inputs consistent with the directionality specified in the governing category’. As far as I can tell, this needs a minor reformulation; the principle needs to restrict the output category rather than directly restricting the way in which items are linearized, since the latter is a consequence of the former. But while a suitably reformulated principle might be quite general, it nonetheless would need to be stipulated in the grammar as an additional principle. It also does no work without being supplemented with a definition of governing category (Despite the convergence of terminology, I suspect the definition in Chomsky Reference Chomsky1981 is irrelevant here.). And this alone does not preclude what I will call S-crossing composition (which actually is allowed by Steedman). S-crossing composition would allow a string [α] of category A/_RB to combine with a string [β] of category B/_LC to give a string [αβ] of category A/_LC, and similarly for the reverse. One of the key contributions of this paper is to provide evidence that this does not exist. Note that such a possibility would, for example allow believe (of category VP/_RS) to combine with won the election (of category S/_LNP) to give believe won the election of category VP/_LNP; and that in turn would (given the assumptions here) allow for sentences like Lee Don believes won the election, meaning ‘Lee believes Don won the election’, obviously an unfortunate result. It should be noted that – as mentioned above – Steedman does in fact allow S-crossing composition. He nonetheless successfully rules out the above by the assumption there actually are no expressions of category NP; they all have raised categories. We return to this (Section 5.2), but note that since we are – with Partee and Rooth – assuming that Don is born with category NP, having S-crossing composition would allow for a VP like Don believes won the election, meaning ‘believes Don won the election’. Thus, we rule this out here by the claim that S-crossing composition is not allowed – so the question at hand is why this is not allowed.

Indeed, the important point to note is that ruling out S-crossing composition – and all sorts of other imaginable possibilities – involves no stipulation here. Rather, the set of allowable function compositions follows from the very idea that syntactic categories correspond to functions on strings. Once this is taken seriously, the combinations are just those that are actual function composition; S-crossing composition is not. To show this requires an extra step: What we want to be composing is two functions in <string, string>, but recall that some function corresponding to a category A/B yield a function in <string, string> only after it has taken its first argument (some string). Thus, let F be the function corresponding to some category A/B. For any expression α, F([α]) is a function in <string,string> and let us call that function F’- α. With that definition, we recast the two schemas in (9) into the single schema in (10), where we can see that both the phonological effect of the rule and the resulting category literally are function composition:

As the reader can verify, this schema does not allow for S-crossing composition nor does it allow for many other conceivable possibilities but only for just the two instantiations shown in (9).Footnote ⁷

2.4. Function composition recast as the Geach rule

Function composition is a binary operator: It takes two arguments to yield a third. But, like any binary operator, it can be Curryed to take one argument at a time. The Curryed version of this is found in a lot of CG literature and is known as the Geach rule or Division; I will refer to it here as Geach (but see Humberstone Reference Humberstone2005) and notate that as g. Thus, g takes a function h in <a,b> and returns a function in <<c,a>,<c.b>>, more specifically g(h) = λX_<c,a>[λC_c[h(X(V))]]. This is just the Curryed version of the function composition operation, such that for any functions h (in <a,b>) and f (in <b,c>), g(h)(f) = h o f. Given this, the schema in (10) could instead be replaced by g in such a way as to ensure that what is allowed in (10) is simply recast to happen in two steps (g followed by application).Footnote ⁸ I believe that there are reasons for this (see Jacobson Reference Jacobson2014, Reference Jacobson2025 for some advantages). However, for expository simplicity, we will for the rest of this paper instead adopt direct function composition via the schema in (10); switch to g plus application has no effect on the main points here. By the very definition of g, the only allowable instances are a mapping of an expression of category A/_RB to (A/_RC)/_R(B/_RC) or the left inverse. In particular, there is no mapping of A/_RB to (A/_LC)/_R(B/_LC) or A/_LB to (A/_RC)/_L(B/_RC), which has the same effect as Steedman’s two S-crossing compositions.

5.1. Rightward extraction (RNR) vs. wh-extraction: Some known differences

As noted above, there are well-known differences between rightward extraction (as in e.g. RNR) and wh-extraction, a few of which we review below. (In dealing with rightward extraction, we for the most part restrict discussion to cases of RNR; although, see (15b), which – if it were good – would go under the rubric of Heavy NP Shift. We will say little about the latter here as it requires a more thorough discussion of three-place verbs than space allows here.Footnote ¹⁰) These differences led Oehrle (Reference Oehrle and Halpern1990) – working within a CG framework – to adopt a different account of wh-extraction from the account well known from the works of Steedman. Borrowing heavily from GPSG, he suggested another recursive category A|B (I have modified his notation slightly) where | is not the same as the ordinary CG slash but encodes what we are used to thinking of informally as an extraction gap. (Of course, the notion of an extraction gap is not something that has any real theoretical status in the theory assumed here but is just used here to include a group of constructions that often go under that rubric. The actual role of this in the theory is completely determined by what sorts of items select for something of category A|B.) Note that Jacobson (Reference Jacobson1999) suggests a similar strategy for pronouns, where she uses A^B to denote an expression of category A but with an unbound proform of category B within it; we might see the | and superscript as closely related. Any expression of category A/B, A|B, or A^B has a meaning of type <b,a>. An A/B is something expecting an actual B argument in the syntax, and A^B encodes (in general) that the expression has within it a proform of category B, and A|B encodes a missing B. (This is informal: In GKPS, this is cashed out by having the missing B actually be a silent item of that category – much like a trace. We could adopt this but will not; here, by a missing B, we just mean a case where an item of category A/B (expecting a B in the syntax) maps to one of category A|B and will never find a B in the syntax.)

Following the exposition of SLASH given in Section 1, we posit that the top of wh-extraction construction involves some item which subcategorizes for A|B (usually S|X for X some set of categories). A question word like what asks for S|NP, and for Topicalization, we might suppose that there is a rule (which is not a general rule but is an additional rule stated for English) by which an S|X can map to S/_LX (or perhaps S[TOP]/_LX) for X some set of categories – i.e. just those that can topicalize. For the passing of |, we assume that any item of category A/B can map to (A|C)/(B|C), with the semantics of the Geach rule. This involves adding very little extra to the system that was developed for pronouns in Jacobson (Reference Jacobson1999), whereby A/B can map to A^C/B^C. Finally, for the bottom, we can assume that any item of category A/B can map to A|B (with no meaning change). Note that we have not here made any restriction on the directional feature on the slash, allowing an A/_LB to map to (A|C)/_L(B|C), which in turn allows for a gap to be on a left branch. The reason for this will be clear below, and we revisit this in Section 6.4. (Whatever analysis one gives for and will involve cases of gaps only on the left branch.) Finally, we follow Jacobson (Reference Jacobson2014) in defining the rules recursively. That system allows an (A/B)/C to combine with a B to give A/C and an (A/B)^C to combine with B to give A^C, and we extend this to allow (A/B)|C combine with B to give A|C. (Some of this can be circumvented by the use of Lift, but many derivations are simplified by this recursive definition.)

As to some differences between wh-extraction and RNR, McCawley (Reference McCawley1982) notes that RNR is impervious to most island effects while of course wh-extraction is not, as in (14):

This, however, is not entirely conclusive since – if island effects are about processing rather than a grammatical principle (see Newmeyer Reference Newmeyer2016 for an overview) – the difference could well reduce to what happens when processing the filler comes first (ordinary wh-extraction) vs. processing the filler at the end. But much stronger evidence is found in McCloskey (Reference McCloskey1986), who shows that RNR cases allow preposition stranding in Irish, whereas wh-extraction cases do not.

There is another obvious difference between wh-extraction and RNR (and cases that might look like Heavy NP Shift). The difference in question concerns embedded subject extraction. The basic empirical facts are these: Embedded subject gaps are not allowed in rightward cases but are in wh cases. It is helpful to give a context to give the bad cases every chance of being good:

Since one referee was dubious about the facts, I did what is admittedly only an informal survey but gives at least a preliminary bit of data beyond those that are just one particular referee’s judgments (or just my judgments). There is no claim here to being an experiment in the sense in which that term is often used in much modern work (but see Jacobson Reference Jacobson, Ball and Rabern2018 for the position that that sense is too narrow an interpretation of the experimental method). However, besides going beyond a single informant, the informal survey here has the advantage of carefully controlling for context, something that is sometimes missing in many large-scale informant judgment studies. Thus, I checked the very cases above with the scenario given above with six consultants (all linguists), and all gave the lowest possible rating to (a) and the highest rating to (c). Three did find a slight improvement in (b) (as do I), and I will not give an account of this here but will assume that both (a) and (b) are bad, but I suspect it is the added length and complexity that allow for a more charitable judgment for (b). The claim that Heavy NP Shift is impossible from the subject of a tensed clause is also documented in the literature; see e.g. Postal (Reference Postal1974), Bach (Reference Bach1977).Footnote ¹¹

Note that the ungrammaticality of (15a, b) is not actually surprising in any system using function composition for rightward extraction (including Heavy NP Shift), because no proposed function composition will allow believes to compose with won to give a VP/_RNP. The question then becomes not why rightward extraction is bad, but why leftward extraction as (15c) (or, for that matter, the simpler case of which student Professor Carberry said was terrific is good. Here the answer is that this involves | and not composition, but what happens in a system with mixed composition?

5.2 A digression on Steedman’s explanation

Steedman (Reference Steedman2024) has an interesting analysis of (15c). Since his system allows S-crossing composition, said was terrific can indeed compose, giving the category VP/_LNP. This can then combine by another S-crossing composition with Professor Carberry of category S/_RVP, which yields Professor Carberry said was terrific of category S/_LNP (i.e. an ordinary VP). Similarly for Professor Glazie said was terrible, and the two can conjoin by the ordinary conjunction of likes. And we have seen independently that question phrases like which candidate can take VPs as well as S/_RNPs to give questions, which is what happens here. So, the goodness of leftward extraction in (15c) is quite unremarkable.

But it raises a new question. This analysis makes use of assuming that said was terrific is a VP/_LNP. But then, what keeps this expression from combining with an NP like that candidate to its left, to give Sally said was terrific meaning ‘said that Sally was terrific’? Steedman’s answer is that Sally is not an NP. More generally, with Montague (Reference Montague, Suppes, Moravcsik and Hintikka1973), he assumes that there are no actual expressions of category NP even though NP is one of the primitive categories in the grammar. Similarly, while individuals are presumably in the ontology (since there are functions of type <e,t>), there are no linguistic expressions that denote individuals. Rather, what we may think of as expressions of category NP are actually all type raised, where the raising happens via Case Marking (all NPs need case). NP is a schema over raised categories that includes S/_R(S/_LNP) for subject NPs, (S/_LNP)/_L((S/_LNP)/_RNP) for object NPs, etc. (so none of these denote individuals but have more complex meanings). Moreover – slightly oversimplifying – the allowable categories are just those that are raised over lexical categories, from which it follows that there is no item of category VP/_R(VP/_LNP), because there are no lexical items of category VP/_LNP. There is, then, no way to derive the VP Sally said was terrific with the meaning ‘said that Sally was terrific’.

Aside from the oddity noted in Partee and Rooth (Reference Partee, Rooth, Bäuerle, Schwarze and von Stechow1983) of having individuals in the ontology but no linguistic expressions with those denotations and having NP as a grammatical category but where there are no expressions with this category, this has problems. First, one needs to ensure the directionality of the main slash in each of these raised categories is as it is. That is, subject NPs must be S/_R(S/_LNP) – a completely unexpected category in view of the basic word order generalizations of English, where the last argument that is supplied to give S goes to the left. And object NPs must take the TV to the left – not to the right as is the general default. Steedman (personal communication) suggests that this follows from various principles, such as the Principle of Consistency, all of which taken together ensure that there are no combinatory rules that override the possible orders specified by the lexical categories. But the existence the Principle of Consistency itself does not follow from anything; there is no obvious reason why it should be the case that some combinatory rules introduce new order possibilities. As such, this is a stipulation. (It is reminiscent of early transformational grammar adding a stipulation ensuring that all non-root transformations rules preserve structure; see Emonds (Reference Emonds1976).) Note that it might appear that the view here also has a similar problem if one assumes that e.g. everyone is listed in the lexicon with the unexpected category S/_R(S/_LNP). But Jacobson (Reference Jacobson2014, Reference Jacobson2025) proposes that it can instead simply be listed with category Lift(NP); see those works for detail. Second, an additional category (not given by Steedman’s generalized schema) needs to be posited for the RNR cases, as the object in RNR cases has to be S/_L(S/_RNP). This is a valid category if derived from lifting NPs but not a valid instantiation of Steedman’s schema since there are no lexical items of category S/_RNP.Footnote ¹² The third problem comes from the fact that other categories besides NPs can be subjects. For example, we get CP subjects in That Don lost is surprising. There is reason to believe that CPs might – like NPs – denote individuals in some sense (i.e. what one might take as an individual correlate of a proposition), but there is evidence that they are not the same syntactic category. See e.g. Rosenbaum (Reference Rosenbaum1967) and Grimshaw (Reference Grimshaw and Zaenen1982) for important distributional differences. Hence is suprising is presumably of category S/_LCP (as well as S/_LNP), so again we would expect the two to compose to give believes is surprising of category VP/_LCP. This would allow that Don lost believes is surprising as a VP, and ultimately we should get Lee that Don lost believes is surprising meaning ‘Lee believes (that) that Don lost is surprising’. Extending the explanation for the badness of the parallel case with an NP subject would, I believe, require the view that there are also no CPs that enter into the composition; all CPs are type raised via case marking. But this is highly unlikely, given that we generally do not find case marking on CPs.

5.3 Back to the analysis here: | is not /

If, on the other hand, | and / are different and we take the view of syntactic categories advocated here, it is easy to allow embedded subject extraction in wh constructions but not in RNR while at the same time ruling out the bad cases above. The fact that Professor Carberry said was terrible in (15a, b) cannot be an S/_RNP follows here exactly as in Steedman’s account (no function composition will allow for this). But our explanation for (15c) does not rely on a stage in the derivation in which said was terrible is a VP/_LNP and we can maintain that that student is an ordinary NP. The fact that (15c) is good follows from the conventions passing | which are different from function composition. And the impossibility of e.g. Professor Carberry the butterfly researcher said was terrible (meaning [Carberry said that the butterfly researcher was terrible]) follows because there is no S-crossing composition. We now turn to new evidence for separating out extraction slash from the normal expected argument of the CG slash.

6.1. The so-called Coordinate Structure Constraint and Lakoff chains

One of the initially exciting results in GPSG was the appearance that Coordinate Structure Constraint (CSC) effects followed immediately from the fact that this would involve coordination of unlikes; see Gazdar (Reference Gazdar1979, Reference Gazdar1981). But a closer examination – especially of the way in which the SLASH passing conventions were developed in GKPS combined with their analysis of and – revealed that this was not really so; nothing would stop the passing of SLASH onto just one conjunct.Footnote ¹³ Without going into the details of their actual analysis and solution, we can note that in a CG analyses there is also nothing to predict CSC effects. This holds regardless of whether we are looking at function composition or at the passing of |. The latter is governed by a rule mapping any A/B to (A|C)/(B|C), and this should allow | to occur on just one conjunct, as shown in (16). In (16a) | occurs on the left conjunct only and in (16b) on the right conjunct only. (The case where it is on both is just coordination of likes; thus, the analysis of ATB extraction in GKPS and in earlier works within GPSG carry over directly here.) Note that in (16b), the expression of category (VP/_LVP)|NP combines directly with a VP to its left to give VP|NP by the recursive specification of the rules noted above.

The situation with respect to function composition (and hence in the worldview here the situation with right extraction) is more complex and will be central to the punchline of this paper, so we will postpone the full discussion. But if we take the view (with Steedman) that the wh case involves function composition, then it still should at least be possible to find cases of a gap on the right conjunct and not on the left, as in (17); this also assumes free lift whereby the right conjunct VP lifts to VP/_R(VP/_LVP), as shown in (17). Note that o in (17) is showing where function composition has occurred in the combinatorics.

If and takes its arguments one at a time, then the case of and is really no different from the situation with think. Just as think allows wh-extraction from its right argument (e.g. a CP) only, so should and, regardless of whether wh-extraction involves / (passed by function composition) or | (passed by feature passing).

And indeed, the result that there should be no Coordinate Structure effects in wh-extractions is actually a welcome one, as it has often been argued that CSC effects seem to be about information structure and/or discourse coherence rather than a syntactic principle; see e.g. Lakoff (Reference Lakoff1986), Kehler (Reference Kehler, Johnson, Juge and Moxey1996). Standard counterexamples in the literature include (18) (we use __ to indicate gaps without any theoretical commitment to how gaps are represented in the grammar); see, for example, Ross (Reference Ross1967) and Goldsmith (Reference Goldsmith, Eilfort, Kroeber and Peterson1985). Note that these examples show that in wh-extraction we can find a gap in the right but not left conjunct as in (18a) as well as in the left but not right conjunct, as in (18b). As shown in (16), this is exactly as we would expect if wh-extraction involved the passing of |. We have not yet fully shown what happens if, instead, it involves function composition, but (17) shows that at least examples like (18a) (with a gap in the right conjunct only) are expected:

It is worth noting that we find cases like these not just with VPs but also with full Ss:

A common reaction to examples like these is to posit that these involve a different and – a subordinating rather than a coordinating one. First, though, if it is correct that and combines with its arguments one at a time, it is always subordinating, so it is not clear what that could mean. Second, we would need to also posit a second or:

But even more striking is data discovered in Lakoff (Reference Lakoff1986), which he used to argue for a non-syntactic account of CSC effects. His precise argument is not exactly the one I will give below, but his data provide intriguing new evidence against positing a second and and or. And this is that we also find CSC violations in chains involving silent and and silent or :

The reason I take these to be strong evidence that we do not want a syntactic CSC (with a different and and or in the counterexamples) is because it seems even more suspicious to posit yet another and which is silent (and has all the same properties as and except its phonology) as well as another item or. Although, as noted above, Lakoff’s own argument based on these examples was slightly different (and he did not deal with or ) I nonetheless refer to these as Lakoff chains. By this I mean any chain with at least one silent and or or and where some of the conjuncts/disjuncts have gaps and some do not. (I use the term gap liberally, as Jacobson Reference Jacobson2025 extends this also to cases of what one might call Left Node Raising; see Section 7.)

6.2. RNR and Lakoff chains

Leaving aside for the moment the correct treatment of wh-extraction, (17) above shows that we expect to be able to find a gap in the right conjunct and not the left in RNR as well, since this would involve ordinary function composition. It would be difficult to show this for the case of just two ordinary conjoined VPs (or Ss), but Lakoff chains provide just the evidence we need (see also Chaves Reference Chaves2014 for relevant discussion). Indeed, (23) shows that the prediction that we can find perfectly good cases of RNR with a gap in a right conjunct but not all of the others:

Here we know that this is a matter of RNR rather than e.g. 2 six packs of beer in (23a) being an ordinary object of drink because there is also a gap following bought. Thus 2 six packs of beer combines with the complex TV (VP/_RNP) went to the store, bought, bicycled home, and then proceeded to drink.

We find similar effects with full Ss, as in (24), and also similar effects with or as in (25):

6.3. But wh-extraction and RNR differ

As shown in (21) and (22), the wh-extraction cases allow for a complete mix and match in terms of where there is a gap and where not. The rightmost conjunct/disjunct can contain a gap or not and similarly for the leftmost one, and all the ones in-between can be of either variety. But the view here predicts an interesting constraint on the rightward looking Lakoff chains. Recall that we are claiming there is no S-crossing composition, which follows from the view that syntactic categories correspond to functions on strings. Further, we are claiming here that RNR is an automatic consequence of having function composition, and we have also adopted a free lift operation. With this – as shown earlier – it follows that we can get things like bicycled home and proceeded to drink __ as in (23a) (this of course is part of the larger Lakoff chain); we illustrate this again in (26) (note that what is notated here as and/and is intended to mean that either of those items can occur in that position):

Here the chain is launched by the lowest conjunct missing its object; i.e. it is of category VP/_RNP From there, this can combine with another full VP (which type lifts as in the above case), which would give us something like found his car, bicycled home, and proceeded to drink __ or it can combine with another VP/_RNP by the ordinary conjunction of likes (to give e.g. bought __, bicycled home, and proceeded to drink__). And ultimately any of these chains will find an NP on the right to give what we are calling the RNR Lakoff chain.

But to launch a chain with the full VP on the left and one with a gap on the right, we would need S-crossing composition. We show one way to try to derive such a case below (the use of * here is to indicate an illegitimate composition):

Of course, this is just one bad derivation and as such does not prove that there is no possible way to get this. But we simply invite the reader to try other possibilities; all require S-crossing composition (or some other illegitimate composition) somewhere.

In sum, the prediction is that a Lakoff chain in an RNR construction has to contain as its rightmost (lower) expression something with a gap. Once such an expression launches the chain, all further VPs on the left can have a gap or not. And indeed, the prediction constraining the right expression is borne out. (Note that (28a) is not a Lakoff chain but involves just a simple coordination – were it to be good we would probably label it Heavy NP Shift rather than RNR, but the names are irrelevant. Importantly, the analysis here predicts that (28a) should be bad.)

All the corresponding wh cases are good: We can construct the same contrasts with S-level conjoined cases (note the contrast between (29b, c) where the latter has a gap in the rightmost conjunct:

6.4. Left branch effects more generally

Assuming that and takes its arguments one at a time, the cases where there is a gap in the left conjunct and not in the right conjunct – whether it be in wh-extraction or in RNR – show that the grammar also cannot contain anything like the Left Branch Constraint. We do, however, see in the Lakoff chain RNR cases a limited kind of Left Branch effect: It is impossible to have a gap in a left conjunct unless there is one also on the right (possibly further down). This follows for the rightward looking cases from the impossibility of S-crossing composition.

Note that the case of gap passing in coordinated structures is but a special case of gap passing in anything of the form (A/_LB)/_RC. So, we make a more general prediction beyond the case of coordination: We should find Left Branch effects in rightward extraction but not in leftward. Of course, there are many questionable cases of a gap on a left branch in wh-extraction, as in (30), which is certainly at least degraded:

But again, this could conceivably have to do with information structure since we know that subject position tends to be old, given or presupposed information. But there is a very robust contrast between (30) and the corresponding right extraction case, which contrast is predicted here:

This is as predicted; the reader can confirm that (31) would have to involve S-crossing function composition, whereas (30) should be good (without additional principles) given the | passing conventions. This is exactly parallel to the case with and.

One might have the reaction here that of course (31) is bad because Heavy NP Shift targets only items within the VP. This is correct, but why? I actually assume that run-of-the-mill Heavy NP Shift cases (involving three-place verbs, as in give to Mitka a delicious bone) are a matter of a verb like give having two different specifications on its directional slashes: (VP/_INP)/_RPP as in give a bone to Mitka and a second possibility (VP/_RNP)/_RPP. Hence, run-of-the-mill Heavy NP Shift cases have nothing to do with function composition. But there remains the question as to why (31) cannot be composed using function composition: S-crossing composition should allow just this. We can also embed these in conjuncts simply to avoid any commitment about Heavy NP Shift and turn this into a clear RNR case. As predicted, the same robust contrast emerges:

The (b) cases are simply beyond (at least this author’s) tolerance, no matter how we might try to give them context.