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date: 19 June 2021

# Ellipsis in Dynamic Syntax

## Abstract and Keywords

In this chapter, we argue that ellipsis is a phenomenon that directly parallels anaphora, hence providing direct evidence of the concept of context on which natural language (NL) processing depends. From this perspective, we argue first that, in failing to give due recognition to the interactive and multimodal nature of NL processing, theoretical linguistics has entered a stalemate situation in which no unitary account of ellipsis is possible. The alternative Dynamic Syntax account that we provide next, however, presents ellipsis as a test case for the view that each NL constitutes a set of mechanisms for situated human interaction, with syntax not as a level of representation, but instead comprising a set of procedures for incrementally and predictively effecting conceptual structure–NL-string mappings. The significance of the extended set of so-called ‘elliptical’ phenomena that are examined from this perspective is that they all provide evidence for the seamless integration of NL structures and processing under domain-general action and perception processes.

# 9.1 Language as action and the phenomenon of ellipsis

From the perspective that takes language as a form of action, ellipsis is (part of) the phenomenon where use of verbal actions by an interlocutor is deemed less efficient for coordination in interaction than relying on the context, either of one’s own recent verbal actions (see both utterances in (1)), somebody else’s verbal actions ((1B), (2B), and (3B)), or of the physical environment (4):

(1)

(2)

(3)

(4)

This view of ellipsis, as a phenomenon seamlessly integrated in and enabling the joint action of conversational participants, has been obscured by theoretical linguistic approaches that abstract linguistic phenomena away from interaction and environmental resources and view natural language (NL) instead as a code, to be analysed in the model of formal languages with a specification of sentential syntactic organization and parallel mapping to propositional semantics as the explanatory basis. In such an approach, linguistic strings like those in (1) are analysed as (a) containing syntactically determined (p. 206) ellipsis sites, in the sense that the interlocutor’s presumed silence is attributed some underlying structure, which (b) needs to be ‘licensed’ by special linguistic devices so that (c) a complete proposition including the meaning of the ‘missing’ part is recovered on the basis of identity with some other linguistically derived structure. Assumptions (a) and (b) immediately exclude (2) and (3) because here there is no obvious ellipsis site, nor can there be predefined linguistic rules which determine the interactive meaning of these utterances as continuations, interruptions, or explicit commentary on (aspects of) another’s talk. Assumption (c) immediately excludes the explanation of phenomena like the one in (4) as part of the model because here there is no linguistically derived content to rely on in deriving interpretation. As a result, such accounts of ellipsis restrict their attention to strings like the ones in the individual utterances in (1) where, it is claimed, the specifically linguistic knowledge that people exhibit in interpreting them circumscribes them as a distinct phenomenon.

We argue here that this delimitation of the phenomenon, and its commitment only to explaining a subset of the data, show that the standard methodology of abstract sentence-descriptive grammars impedes proper understanding of what a unified account of ellipsis really shows: namely, language users’ know-how to employ and derive significance from multiple resources as they engage moment-to-moment with each other. For this reason, we argue, the standard competence–performance distinction that underlies the standard methodology has to be replaced by a different perspective in which the coordinated and context-dependent actions of conversational participants are central to the explanation.

In this chapter, we sketch an alternative view of ‘syntax’ as an ability to act jointly, hence displaying properties in common with those that have been assumed up to now as characteristic of semantics, pragmatics, and processing models. From this perspective, we will show how the presumed ‘syntactic’ licensing of an ‘ellipsis site’ as in (1) can be accounted for without the assumption of an autonomous level of syntactic analysis. Under the same terms, we also aim to show how recoverability of ellipsis interpretations, including those without linguistic antecedents such as (4), can be achieved on an incremental dynamic basis without assuming the necessity of sentence–proposition mappings. We do this through modelling the various phenomena within the architecture of Dynamic Syntax (DS, Kempson et al. 2001), an inherently incremental and action-oriented formalism for modelling interaction. We introduce DS in §9.2 and then show how it captures the various interactive ellipsis phenomena in §9.3 after we discuss the challenges for other standard accounts in the next subsections.

## 9.1.1 The ellipsis stalemate in competing domains of analysis

Syntactic accounts of ellipsis rely on models of linguistic ability that postulate distinct types of declarative propositional knowledge as necessarily underpinning human linguistic performance. Having adopted this perspective, they then accordingly partition the phenomena by attributing to some instances causes distinct from those attributed to other intuitively similar cases. This is because such models, by ab initio definition of their remit, exclude in principle certain cases from consideration (see, e.g., Stabler 2013). For example, the cause of the surface appearance of the strings in (1), so-called VP-ellipsis and sluicing, is assumed to be underlying syntactic structure that has remained unpronounced: since Ross (1967) and Sag (1976a), the ellipsis site is analysed as projecting complex sentential structure which is deleted at a late stage of the derivation under conditions of identity with that of an antecedent clause. However, even for this now narrowly circumscribed domain of phenomena, problems arise for such an account, which is symptomatic of the illegitimacy of this fractionating process. Firstly, the particular interpretations naturally recovered for various such ellipsis sites turn out to appear very diverse, which, due to compositionality considerations, then leads to constant differentiation of categories of ellipsis types (e.g. for VP-ellipsis: endophoric, exophoric, null-complement anaphora, tautosentential, discourse-anaphoric, etc., all terms and phenomena illustrated in Miller and Pullum 2014; for various differentiated semantic categories of sluicing, see, e.g., Fernández et al. 2007). Secondly, it has been shown that identity of surface structure is not required for the licensing and recoverability of meaning of ellipsis sites (see, e.g., Hardt 1993). And, lastly, meta-theoretically, the account lacks parsimony, since antecedents which present a single intuitive reading have to be assigned ambiguous underlying structures to allow for the multiple possible ellipsis types. From an empirical point of view, this makes such accounts psychologically unrealistic, since a left-to-right incremental version of them must invoke ambiguity to account for the subsequent interpretation of the ellipsis site. A particularly notorious such problem is the strict vs sloppy ambiguity (Sag 1976a), where, for a single fixed interpretation of the antecedent clause, the ellipsis site allows for two interpretations, e.g., in (5) his can be taken to denote either John as ‘Bill checked John’s mistakes’ (the strict interpretation), or Bill as in ‘Bill checked his own mistakes’ (the sloppy interpretation):

(5)

To avoid this problem, a competing semantic account (Dalrymple et al. 1991) presumes that ellipsis sites are syntactically simple with no hidden structure. The burden of explanation for the strict/sloppy ambiguity is then shifted to an abstraction over semantic content of a clausal antecedent, which involves either abstracting out only the subject content (the strict interpretation), or abstracting out all occurrences of the term occupying that subject position (the sloppy interpretation).

Notwithstanding their differences, syntactic and semantic accounts share the property of being sentence-based: the elliptical string is taken to correspond to a sentence which is in some sense incomplete, with interpretation recovered from a clausal antecedent. Both thus confront the difficulty of characterizing sub-sentential utterances which provide no evidence of having a sentential antecedent and yet are able to achieve illocutionary acts, which Stainton (2006b) argues require a pragmatic inference account over and above whatever semantic or syntactic accounts of ellipsis might achieve:

(6)

Moreover, there are sub-sentential utterances where no identical, linguistically provided antecedent is available on which the recoverability of some particular interpretation can be based:

(7)

## (p. 208) 9.1.2 Morphosyntactic licensing of sub-sentential talk

The difficulty confronting both semantic and pragmatic accounts of ellipsis when applied to accounts of sub-sentential utterances, is that the morphosyntactic forms of such utterances remain the same whether they appear as sentential constituents or not (Merchant 2004a; Ginzburg 2012; Gregoromichelaki 2012). For example, they display specific case requirements:

(8)

Contra Stainton (2006b), in such case-rich languages, the form has to match whatever is taken as the required interpretation, even in the absence of any sententially, or even linguistically, derived antecedent (Gregoromichelaki 2012, 2016). For example, in a context as in (9), den Arzt needs to be in accusative case:1

(9)

A further problem indicating the need to integrate formal constraints with interpretational ones, is that ellipsis is argued to be subject to island constraints (Ross 1967), until very recently, widely taken to be diagnostic of a syntactic phenomenon (see Merchant, this volume). For example, the so-called Complex NP Constraint is exhibited in so-called Antecedent-Contained Deletion/Antecedent-Contained Ellipsis constructions. In such cases, a dependency needs to be licensed within the restrictor of a quantifying element provided by the adjunction of a relative clause. A further elaboration of the restrictor provided by a second relative clause prevents such a dependency:

(10)

(11)

The challenge of defining accounts of sufficient richness to express such phenomena has been addressed in an impressively detailed manner by Ginzburg (2012) and colleagues, (p. 209) within a constructional version of HPSG formulated in the Type Theory with Records (TTR) representational framework (HPSGTTR, Ginzburg 2012; Ginzburg and Miller, this volume). In this model, sub-sentential strings, as in (7), are taken to express paraphrases of what a whole sentence formulation would denote; and so the sub-sentential elements are mapped directly onto the various semantic/pragmatic functions they are taken to accomplish. However, this attempt to analyse ‘fragments’ as commensurate to whole sentences means that the HPSGTTR framework retains conservative assumptions vis-à-vis syntax: fragments are modelled as ‘constructions’ of sentential type, involving sui generis syntactic mappings of sub-sentential constituents directly to ‘sentences’ paired with necessarily (quasi-)propositional interpretations. For example, one of the grammatically derived interpretations of the string in (7) will be ‘A asks B who A meant by the use of “Billy”’. In consequence, each such sub-sentential string is assigned multiple such pairings and is by definition characterized to be as spuriously ambiguous as the constructions it is involved in. This means that the problematic aspects of the syntactic accounts, namely ambiguity instead of general mechanisms, is not sidestepped—on the contrary, it is wholly embraced as is natural in a constructional approach. However, as argued in Gregoromichelaki (2012), the interpretational options for such fragments are open-ended, so a constructional approach faces the problem of ignoring the radical flexibility and adaptability of linguistic resources. Additionally, there remains the empirical problem that morphological/syntactic restrictions on ‘fragments’ pervade any occurrence of sub-sentential utterances whether these depend on linguistic or wholly non-linguistic contexts (see (9) and (12)):2

(12)

The defined HPSGTTR constructions apply only to linguistically provided partial antecedents which are clarifiable, so the rules specified by the grammar will not apply to the intuitively similar clarification cases such as these.

An account that aims to capture global syntactic generalizations while, at the same time, accounting for licensing idiosyncrasies without an independent level of syntactic representation over strings is the general framework of Minimalist Grammars (MG, Stabler 1997; Kobele 2006). The MG formalism, applied to elliptical phenomena in Kobele 2012b, 2015, (p. 210) requires, firstly, the relation between sentence string and semantics to be mediated by extensive transformations. This is because a copying account of ellipsis recoverability under identity is sustainable only on the basis of a decompositional mapping of surface appearance to semantic interpretation. This mapping is effected through various grammatical operations, like merge, move, and indeed e(llipsis), applying over fine-grained linguistic categories (‘types’) of expression, as constrained by global syntactic constraints such as the Shortest Move Constraint (SMC). This account presents a significant improvement on standard syntactic analyses, since an ellipsis site is considered, as in semantic accounts, syntactically atomic, i.e. no underlying syntactic structure is derived. Instead, ellipsis sites are generated due to particularized grammatical operations mapping empty or fragmentary strings to fine-grained syntactic categories. Because both syntactic categories and operations are so fine-grained, this account allows ellipsis sites to behave like pro-forms (as in Hardt 1993) whose antecedents are syntactically restricted to be particular ‘derivational contexts’, i.e. syntactic derivations that behave as functions on the potentially overt linguistic elements that are mismatched between the antecedent and the ellipsis site.

Given that this account incorporates global syntactic restrictions like the SMC, it can deal with formal licensing constraints like the island restrictions of (11). Additionally, the fact that it makes use of ‘derivational contexts’ as antecedents, instead of syntactic structure, means that it can deal with cases of mismatched antecedents, as in (5), without having to postulate destructive structural operations or unnecessary ambiguity in the antecedent itself. However, this model still maintains standard assumptions regarding syntax, in that its explanations rely on assigning psychological reality to a view of syntax that is independent and distinct from other cognitive abilities. Syntactic categories, operations, and global constraints, like the SMC, are assumed to be specifically linguistic and not attributable to general cognitive constraints (see also Stabler 2013). This has consequences: for example, in order to fully account for phenomena like (5), the grammatical characterization provided is not adequate. Given that MG is a competence model, it has nothing to say on how antecedents are defined. In order for antecedents to be provided, MG has to be integrated in a performance model, a parser/generator (Kim et al. 2011; Kobele 2012b). This is because the ‘derivational contexts’ invoked by the assumed pro-forms simply represent, as far as the grammar is concerned, decontextualized descriptions of the combinatorial licensing of linguistic elements. So, from our point of view which takes the grammar–processor distinction as unsustainable and an artifact of the view of language as a code, the MG account (a) introduces theoretical redundancy because syntactic restrictions are not modelled on the basis of general cognitive processes directly; (b) in the case of ellipsis, this has the consequence that such phenomena are analysed as involving various cognitively arbitrary category specifications or being explainable on the basis of otherwise general processing explanations; and (c) as a consequence, because the MG grammatical account is confined to linguistic structures, it is unable to account for intuitively analogous non-linguistic antecedents such as (9) and (12), since, even embedded in a performance model, there is no linguistic derivation in the context to be invoked as the antecedent grammatical operation.

Finally, along with all the accounts already examined, given that the syntactic derivations of MGs license whole sentential strings paired with propositional interpretations, it will be unable to account for dialogue phenomena like (2), as we will now argue. (p. 211)

## 9.1.3 Ellipsis as completability

Accounts of ellipsis assuming a sententialist methodology struggle to address the challenge of the dynamics of conversational dialogue. The problem posed by conversational exchanges is that people commonly and purposefully do not utter full sentences. Conversations are replete with fragmentary forms which build incrementally on what has gone before, in which participants effortlessly switch between speaker and hearer roles, and commonly no-one in the conversation will have anticipated its overall content in advance:

(13)

If one attempted to preserve the assumption that all fragments are independent incomplete sentences, one might consider data like (13) as at least five elliptical sentences each to be mapped onto representations of propositional content; but it is far from obvious what source to provide to any such posited underpinning sentential structures when the overall structure cannot be anticipated. Even the illocutionary flavour of the subparts may shift as participants are more or less authoritative, or in disagreement:

(14)

An account in terms of sentential ellipsis of the above misses the significance of B’s action in (14) as an interruption and the ones in (13) as continuations.

In any case, such an ellipsis account cannot be sustained since this split utterance phenomenon can take place at any point in an emergent structure (Gregoromichelaki et al. 2011; Howes et al. 2011), and affects every syntactic/semantic dependency: preposition–complement (15), reflexive–antecedent (16), quantifier–pronoun binding, negative polarity, quantifier–tense (17), even head–complement dependencies (18):

(15)

(16)

(17)

(p. 212)

(18)

Therefore, no account that relies on specialized constructions or syntactic types, instead of general mechanisms, can provide an adequate explanation for this phenomenon. Instead, sub-sentential strings need to be licensed by the grammar incrementally and without the requirement that a whole sentence needs to be licensed eventually (as in Kobele 2012b and others). This is because such sub-sentential strings are not only interpreted incrementally but also can be used perfectly naturally to perform speech acts that rely on their very incompleteness (Gregoromichelaki 2013):

(19)

But even incremental syntactic accounts (e.g. Poesio and Rieser 2010, or a conceivable extension of Kobele 2012b, 2015) cannot deal with such data if they maintain an independent level of syntactic analysis since, as (16) shows, splicing together the two strings will yield ungrammatical results.

Given the rapidly accumulating experimental evidence that parsing and production are both incremental and interdependent in achieving action and representational coordination during interaction (Pickering and Garrod 2013), accounts of sub-sentential utterances as somehow incomplete cannot be sustained. Firstly, as we saw in (9) and (12) for adult interaction, sub-sentential talk underpinned by the context dependency of human interaction can achieve any function that sentential and propositional units perform. Secondly, such utterances form the basis of language acquisition. Children at the one-utterance phase can perform perfectly adequate verbal actions employing sub-sentential strings relying on the adult caregiver to provide what they lack at that stage, namely, the requisite conceptual breakdown of a holistic situational representation so that new linguistically expressible concepts can be acquired:

(20)

Moreover, the split utterance data cannot be excluded from the core remit of the grammar as performance disfluencies since they also constitute effective verbal actions for the language-acquiring child to coordinate with caregivers:

(21)

(22)

(p. 213) Instead, in our view, the characterization of sub-sentential data needs to make reference to the dynamics of real-time processing expressed in a vocabulary that allows contribution from environmental resources and non-linguistic cognitive domains at a sub-sentential level. Such a model, in our view a grammar, needs to:

• include a set of mechanisms for inducing recovery of content from both linguistic and non-linguistic sources;

• model word-by-word incremental, semantic licensing;

• model the context as an evolving record of all inputs, including words, structures, and procedures that induce such incrementally developing content;

• define shared mechanisms for parsing and production.

The model we sketch below, Dynamic Syntax (DS), meets these criteria. In DS, the pervasive use of sub-sentential elements across dialogue turns and participants will not only be wholly predicted, but will be seen to serve a key purpose in communication by narrowing down the otherwise mushrooming alternative structural and interpretative analyses through the ongoing interactive coordination of participants (see Gargett et al. 2009; Eshghi et al. 2015). We will argue that this perspective not only illuminates the sharing of linguistic actions in context, as seen in (13)–(22), but also provides a processing approach which reveals a novel and surprising meta-theoretical generalization: namely, the lack of need for conceptual distinction between syntactic vs semantic vs pragmatic procedures in the integration of verbal actions with coordinated joint action. In all three domains of traditional linguistic inquiry the mechanism of jointly developing initially underspecified information operates uniformly. Just as pronominal anaphora construal has been shown not to be definable as confined within sentential, speaker-turn, or linguistic boundaries, ellipsis needs to be modelled in the same way, as an anaphoric mechanism both relying on and sustaining participant coordination and context-dependent action. This is achieved in DS by modelling both pronominal anaphora and ellipsis through the initial projection of temporarily underspecified contents imposing their resolution as a goal for all conversational participants and thus subsequently resolved by exploitation of either environmental or linguistic resources. Furthermore, we argue, in contrast to any other formalism, this perspective allows us to extend the parallelism beyond ellipsis and pronominal anaphora, to the explication of the function of syntactic mechanisms. Syntactic dependencies introduced by fragments, morphosyntactic constraints introduced by e.g. case morphemes, but also the mechanism underpinning long-distance dependency, will be modelled as introducing initially underspecified structural projections with goals imposed on either participant in a conversation to resolve them either through context or by offering an appropriate subsequent verbal action.

# 9.2 Dynamic Syntax

Dynamic Syntax (DS) is a grammar formalism based on the psycholinguistically inspired action-based modelling of NL string–interpretation mappings in context. NL syntax is reconceptualized to be no longer its own level of representation, but, instead, a set of (p. 214) licensing actions for inducing or linearizing semantic content, incrementally, predictively, and on a word-by-word basis. Parsing and production are interdefined as coordinated activities operating in tandem, each having access to the same set of construction steps. Context in DS is modelled as including an incrementally evolving record of all the actions employed and their outcomes, enabling recoverability of any of these for reuse. The interaction achieved in split utterances emerges as an immediate consequence, since both parsing and production employ predictive actions which make available to each interlocutor, at each sub-sentential step, the role of parser or generator.

## 9.2.1 String-content mappings

To model this action-directed perspective, DS is founded on a dynamic modal logic that defines the transitions among states taken to constitute the current context of processing at each point in a parse/generation task (see Kempson et al. 2001 for formal details). The accessibility relations among these states are defined through actions which license goal-driven, time-linear transitions from state to state. Such states can be taken to model the total context of each processing step, linguistic and non-linguistic, so that the whole system licenses mappings from context to context.

In DS, particular conceptualizations of eventualities are taken to involve actions of building (parsing) or linearizing (production) a semantic tree whose nodes incrementally come to reflect the content of some utterance. Keeping in mind that processing can start at any point, if we take the case of aiming to achieve a propositional structure, the first step is a one-node tree that merely states the goal to be achieved, namely, to derive a formula of propositional type (Figure 9.1, above $⇓$), indicated by the requirement $?Ty(t)$, the query symbol ? indicating this is a goal as yet unrealized. This single node tree is then incrementally enriched as word-by-word processing proceeds, eventually leading to a complete tree of propositional type with no goals left outstanding (Figure 9.1, below $⇓$), a result achieved through combining grammatical actions with content derived from context.

Figure 9.1 Processing John upset Mary in DS

DS trees are invariably binary, reflecting functor–argument structure (argument node on the left branch, functor node on the right), with a pointer ◊ identifying the node under development). Each node is annotated, not with words, but with terms of a logical language (e.g. Mary′), and their type (e.g. Ty(e)), these terms here being subterms of the (p. 215) resulting propositional representation at the root node. The representation includes an event/situation argument S of type es, enabling tense/aspect construal (we suppress details here; see Gregoromichelaki 2006; Cann 2011).3 Since event/situation arguments are first-class citizens of the combinatorial structure, predicate assignments reflect this: $Ty(e→(es→t))$ the intransitive-verb type for combining with a subject first and then the situation argument; and $Ty(e→(e→(es→t)))$, the transitive type.

## 9.2.2 Formalization of tree structure and incremental tree development

In order to talk explicitly about how such structures are constructed incrementally, trees are formally defined, so that their incremental construction can be achieved through actions that induce the requisite tree development. DS adopts a logic with modalities indicating not only what is currently true about the tree but also what is to be true at future developments of the tree (Blackburn and Meyer-Viol 1994). For example, the daughter relation is defined as $〈↓〉$: $〈↓〉α$ holds at a node if $α$ holds at its daughter (with variants $〈↓0〉$ and $〈↓1〉$ for argument and functor daughters respectively). There is also the inverse mother relation $〈↑〉α$ with argument/functor variants, $〈↑0〉$, $〈↑1〉$.

Thus a DS grammar includes a set of actions which are procedures for building/linearizing trees: ‘syntax’ is just the subset of actions which unfold tree structure under the guidance of linguistic elements. Syntax is formulated as the employment of packages (macros) comprising simple atomic actions—make(X) for creating new nodes, go(X) for moving the pointer, put(Y) for annotating nodes, where X and Y are tree relations and node annotations (labels) respectively.

Computational actions are language-general macros not needing a lexical trigger: these introduce tree relations; move the pointer ◊ around some partial tree under construction (e.g. completion, which moves the pointer out of a node once its type requirement is satisfied); remove satisfied requirements (thinning); and perform function-application (beta-reduction) operations compiling information up a tree on a bottom-up basis once all daughter decorations are suitably provided. Primary amongst these is the construction of ‘unfixed nodes’ (*-adjunction): such actions are defined using the Kleene star operator * annotating a so-called ‘unfixed’ node with the specification $〈↑*〉Tn(a)$, which indicates that this node is related to some node a along a sequence of zero or more mother relations to it. Lexical actions are macros triggered by individual words of the particular NL whose actions also perform the same tree or string development along with introducing semantic content on the nodes of the tree.

(p. 216) Partial trees: imposing constraints on update. The underpinning dynamic which drives NL processing is the gradual resolution of initial underspecifications. There are three basic types, each with an attendant requirement for update:

(1)

(2)

(3)

Such underspecifications all allow modal constraints on their resolution, giving rise to a variety of locality restrictions. For example, anaphoric expressions can impose locality constraints associated with limits on recoverability of their antecedent. Locality within a given predicate domain is definable as the tree traversal of an unbroken functor path: arguments local to a given predicate meet the characterization $〈↑0〉〈↑*1〉Tn(a)$ (i.e. there is a path up one argument relation plus a possibly empty sequence of function-path relations from the current node to the dominating Tn(a) node). Reflexive anaphors are characterized as projecting a restriction on putative antecedents that they be ‘co-argument’ terms, i.e. holding along the relation $〈↑0〉〈↑*1〉〈↓0〉Tn(a)$. Conversely, pronominals exclude as antecedent any formula at a node standing in such a local relation; and wh-pronouns contribute a metavariable (WH), defined as awaiting substitution by a term, the answer, in some future utterance, a yet further long-distance dependency effect (see Gregoromichelaki 2006, 2013 for a reformulation of Binding Theory in DS terms).

Unfixed tree relations vary as to whether or not their resolution is subject to such tight locality restrictions. An unfixed node within some tree is identified by the annotation $〈↑*〉Tn(a),?∃xTn(x)$ which defines it as unfixed but within a tree whose tree root is Tn(a). There is also a more specific localized variant defined as $〈↑0〉〈↑1*〉Tn(a)$, i.e. the tree root now encompasses a local predicate–argument sub-tree.

Morphosyntactic specifications also involve locally statable constraints. Accusative case marking, for example, is definable as imposing a requirement on a node of the form $?〈↑0〉Ty(e→(es→t))$, dictating that in the outcome, it must be immediately dominated by a predicate node.

In every case, what drives processing is the set of requirements lexically or computationally imposed: such requirements operate as predicted goals for either participant in the joint task to accomplish that constraining of future developments. Of these, it is underspecification of hierarchical position within a tree that lies at the core of the account, underpinning many discontinuities, and expressible through the construction of unfixed nodes. Figure 9.2 shows how the building of a locally unfixed node (local-*-adjunction) can feed lexical actions, so that in combination, the word order properties of each particular NL are derived. In some languages this underpins scrambling. In English, this mechanism, in combination with the lexical action of the verb, induces the imposed SVO (subject–verb–object) ordering: the DP before the verb is taken to annotate a locally unfixed node; its (p. 217) position as logical subject (or not) is determined by the action sequence projected by the following verb, which among other actions includes such specification. The left-peripheral nature of long-distance dependency is expressed through the building of an unfixed tree relation without such a single-clause locality restriction, which involves a computational action defined in the presence of a node requiring completion to a propositional type $Tn(a),?Ty(t)$ with a precondition that the node is not already developed in any other way, relative to which the action defined licenses the construction of an unfixed node annotated (p. 218) as $〈↑*〉Tn(a),$Ty(X)$,?∃xTn(x)$, i.e. with a resolution of this underspecified tree relation having to be at some possibly later point in the construction of the tree being developed from Tn(a) (this is the final step of merge4 in Figure 9.2); hence the potentially ‘long-distance’ discontinuity effect.

Figure 9.2 Unfolding structure for John upset…

In all tree developments, the closing stages invariably involve modalized function-application (beta-reduction) steps which compile up the content of all non-terminal nodes to finally yield a complete tree with no requirements outstanding (see Figure 9.1).

## 9.2.3 Linking trees through term sharing

In addition to the incremental projection of predicate–argument structures, a freely available computational action licenses paired ‘linked’ trees, which are in effect correlated through a conventionalized anaphoric device that results in a shared term appearing in both such trees. Formally, a transition from some node in the main tree onto the top node of a new tree is licensed, this new tree-beginning having imposed on its development a requirement that it include the term appearing on the node from which the transition was initiated. Relative clauses are the paradigm case: the relative pronoun triggers actions which reflect the LINK transition and some initial construction within the newly emergent tree of an unfixed node. The WH-metavariable then functions in a fixed anaphoric way to provide the required copy from the main tree, thus creating the resultant shared term in the two trees (see Figure 9.3, which displays the outcome of processing the string John, who smokes, left).5

Figure 9.3 Result of parsing John, who smokes, left

Such linked trees provide opportunities mid-sentence for NL processing to shift temporarily to a distinct structure for purposes of elaboration, expansion, explanation, etc. of terms in the main structure. And this can happen either within a single individual’s utterance, giving structures like relative clauses, Hanging-Topic Left-Dislocation, clausal and phrasal adjuncts, etc., or across speakers where the effects include clarifications, confirmations, continuations, etc. (see e.g. Gargett et al. 2009). This is because LINK- (p. 219) adjunction allows indefinite iteration of adjunct extensions of arbitrary type, a common way of extending utterance exchanges:

(23)

The fact that linked trees temporarily shift processing to an independent adjunct tree to elaborate a term on the main tree provides the basis for a requirement of anaphoricity from the one structure to the other. It also explains why this form of tree relation is what is needed for modelling sluicing (see e.g. Merchant 2001), amongst other structures which may be sensitive to island constraints as we shall see in detail in §9.3.7 for antecedent-contained ellipsis. In such cases, for example, where relative clauses constitute the linked ‘islands’, the relative pronoun provides the copy that links the newly introduced tree to the main tree. This copy process creating the shared term is not island-constrained with respect to its antecedent. Nonetheless, since that copied term has to occur on an unfixed node as the new tree is being introduced, the resolution of its position within that new tree is domain-sensitive: it must occur within the construction of that very tree. In this sense, island constraints in DS emerge from the need to shift processing to another domain along with needing to complete this structure before resuming processing of the one temporarily interrupted.

# 9.3 The Dynamics of Ellipsis

With the formal underpinnings of its semantic tree construction process to hand, we now describe the DS model of ellipsis. We show how the incremental notion of DS context can account for the varying types of elliptical forms found in interaction.

## 9.3.1 Context in DS: Mechanisms for recovery of content at the ellipsis site

The concept of context appropriate for a processing-oriented account is substantially richer than is expressible in either model-theoretic accounts or semantically blind syntactic accounts. For this reason, context in DS is conceived as a dynamic, multi-modally induced record of (a) words; (b) conceptual content notated as tree structures as described above; and (c) the sequence of actions in building the emergent strings and trees (Cann et al. 2007; Purver et al. 2010; Eshghi et al. 2015). Since a DS grammar, through the imposition of predicted goals, models the recovery from memory of the range of options available for the next processing steps, this set of options is attributed psychological reality so it also constitutes part of the model of context. To model context time linearly, we follow Sato (2011a), Purver et al. (2011), and Eshghi et al. (2015) in defining this range of options as a (p. 220) Directed Acyclic Graph (Context DAG) as in Figure 9.4, where each node represents the current (partial) tree and each edge in the graph records the action taken. The entire DAG represents the search space for parsing/generation, which will also include any conceptual content derived from context. In Figure 9.4, the top path from T0 to T12 is the chosen one given the lexical input, and corresponds to the derivation outlined in Figure 9.2.

Figure 9.4 DS parsing context as a graph: Actions (edges) are transitions between partial trees (nodes)

The context of a partial tree is then the path back to the root of this graph; and actions, as well as conceptual content notated in tree form, are recoverable through a mechanism of backwards search for reiteration/reuse in creating new construals. As a result, there are three basic mechanisms by which an ellipsis site, being an underspecified element awaiting resolution, can exploit the Context DAG for content recovery:

1. (a) Reuse of content (semantic-formulae) from some (partial) tree on the Context DAG, which can include recoverability of information direct from the utterance scenario, yielding indexical construals.

2. (b) Reuse of sequences of actions from the DAG (sequences of DAG edges).

3. (c) Direct reuse of structure, i.e. extension of some (partial) tree in context.

## 9.3.2 Content underspecification and recoverability through copying or action replay

Forms of the ellipsis site. We take first the familiar cases of English VP-ellipsis. Under DS, these involve an initial content underspecification projected at the ellipsis site, with optional triggers for content recovery in the form of strings such as do so, too, and bare auxiliaries. Auxiliaries are taken, like pronouns, to project a temporary content placeholder of predicate type (e.g. U $:e→(es→t)$) with an accompanying requirement $?∃x.Fo(x)$ which triggers the context search.

Recovering predicate content. In such cases, two types of information are recoverable from context:

1. (a) a formula content copied from some tree;

2. (b) a sequence of actions to be reiterated at the ellipsis site.

(p. 221) The two mechanisms fetching such information to the new processing task through backwards search are implemented by the pair of computational actions Substitution and Regeneration.6 Figure 9.5 displays the identical substitution process for (a) a pronominal and (b) an elliptical expression as in (24):

Figure 9.5 Substitution from context at the ellipsis site of (24): Pronominal anaphora (top) and VP-ellipsis (bottom)

(24)

Figure 9.6 then displays the regeneration process at an ellipsis site for cases like B’s answer in (25):

Figure 9.6 Action replay from context at the ellipsis site

(25)

The new content in B’s answer is derived through rebinding of the variable projected by the anaphor to the newly introduced subject. This is achieved by searching the DAG and then reusing the actions involved in constructing the question to flesh out the ellipsis site in the answer, as triggered by the metavariable placeholder projected from the auxiliary. The processing of the question in (25) involves parsing of the subject who, constructing a predicate as indicated by the verb, and constructing its object argument; these actions, (p. 222) having been stored as a sequence in context, can be reused in the next stages. But with John’ now annotating the subject node, these actions will now yield a rebinding of the object argument to the new local subject. The effect achieved is the same as the higher-order unification account of Dalrymple et al. (1991) but without anything beyond what has already been used for the processing of the previous linguistic input and, consequently, without any need to assign some distinct type of expression to the elliptical element did or the subject John. All that has to be assumed is that the metavariable U contributed by the anaphoric did can be updated by an action sequence taken from the DAG context.

This duality of mechanisms for content recovery provides a way of capturing all strict/sloppy ambiguities observed in several forms of ellipsis. Either content specifications or sequence-of-action specifications can be searched for and reiterated, the first preserving some previous construal, the other preserving only the pattern of construal:

(26)

(p. 223) This gives precisely the right basis for the ambiguity without having to invoke ambiguity of the antecedent. In (26), a strict construal λx.Help′(Students′(of – Bill′))(x), ‘help Bill’s students’, is carried over as the fixed predicate content to be predicated of the subject John′. The sloppy interpretation involves the sequence of actions associated with processing help + his + students in the first conjunct reapplied to the new subject John′.

This is not a mechanism identified specifically for ellipsis: the same type of analysis applies to the DS analysis of quotation (Gregoromichelaki 2017) and two subcases of pronominal anaphora too, i.e. coreferentiality and so-called lazy pronouns. Coreferential construals constitute a replication of some antecedently constructed content of individual type e:

(27)

Lazy construals involve recovery of actions to be rerun at the site indicated by the pronoun to yield some requisite term that is distinct from that picked out by the antecedent. In (28), them is resolved by rerunning actions used to process his keys in the previous clause:

(28)

Under this view, neither ellipsis sites nor pronominals deviate in any way from the usual processing mechanisms DS defines: like all other morphosyntactic and lexical specifications, such elements impose predictive goals constraining the subsequent actions of the interlocutors as these unfold in the DAG model of context; general processing mechanisms like backwards search, Substitution, and Regeneration can then be employed, by either interlocutor, to achieve appropriate expansions of such potentially radically underspecified content in ways that reflect their own purposes. Since the DAG unfolds and constrains these future processing options on a word-by-word basis, employing and resolving underspecification can be achieved either through the exchange of propositional contents, as seen above, or through the exchange of sub-sentential elements that exploit verbal or non-verbal actions for becoming integrated in the functioning of the participants’ joint actions.

## 9.3.3 Licensing sub-sentential utterances: Morphosyntactic constraints

Use of sub-sentential utterances in dialogue shows how particular morphosyntactic forms impose goals on interlocutors that curtail the processing paths compatible with further processing or backwards search. For example, as we saw earlier, so-called wh-pronouns project a specialized metavariable requiring instantiation externally to the tree under construction, this in question–answer pairs being the answer to that question. On the other hand, the metavariable provided by reflexives is restricted to obtaining a locally provided antecedent. These two types of constraint can combine leading to interpretations that are very finely constrained: short answers to a wh-question (as in (29)) need to be interpreted within the structure which that question projects, while the local substitution imposed by a (p. 224) reflexive as shown in Figure 9.7 will lead to a cascading effect affecting all occurrences of the WH-metavariable, thus yielding an appropriate interpretation of the answer.

Figure 9.7 A short answer with binding restrictions

(29)

Sub-sentential utterances may also bear morphological features, which are expressed in DS via imposition of predictive goals to interlocutors to pursue processing paths that conform to some particular specification of the conceptual content being developed. Like indexical pronominals, imposing, for example, gender restrictions in English, accusative case marking, as in (9)–(12), introduces the requirement: $?〈↑0〉Ty(e→(es→t))$, a restriction that a node so annotated be immediately dominated by a node of predicate type. Since backwards search through the DAG will not fetch the appropriate content in this case, the imposition of such morphological constraints has the effect of imposing particular conceptualizations of the utterance situation becoming newly available as processing options in the DAG. Since the DS-DAG is not restricted to representing specifically linguistically derived content, such morphologically triggered context enrichment does not presuppose the mediation of any syntactic derivations. Nevertheless, unlike other frameworks (e.g. Ginzburg 2012), any DS rules applicable to linguistically derived content will be able to apply unchanged to the subsequent development of such contextually derived content (as in e.g. (12)).

## 9.3.4 Licensing split utterances

Given that processing in DS is modelled as incremental and predictive, the licensing of sub-sentential utterances is achieved word-by-word without requiring necessary expansion to a propositional structure for a string to be interpreted or produced. So sub-propositional strings can be employed to perform speech acts as naturally as propositional ones, as seen in (19) and (22). The DS explanation of the licensing of split utterances without having to assume inference of propositional intentions relies on the DS modelling of the tight coupling of parsing and production (‘mirroring’). Parsing in DS incorporates aspects of production, i.e., the parser does not passively expect the scanning of input to produce structure; instead, the Context DAG is expanded at each word step with the generation of predictions (goals) in order to accommodate what will be encountered next. On the other hand, production in DS employs exactly the same mechanism and DAG as parsing, with the only difference that, instead of scanning input, every step of articulation is licensed by a richer tree, a so-called goal tree. The goal tree is a tree at least one step forward from the tree-under-construction, and a potential next processing step through the DAG is licensed by the tree-under-construction subsuming the goal tree. Subsumption means that the partial tree that is being developed must be extendible into that goal tree by following the licensed actions of the system (Purver and Kempson 2004). Put simply, whereas parsers have to follow what the speaker offers them, speakers have to have at least some partial idea of what they are going to be communicating at the next step.

So given this incrementality and predictivity of processing, first, there is nothing to prevent speakers initially having only a partial structure to convey, i.e. the goal tree may be a partial tree, perhaps only one step ahead from what is being voiced. Secondly, since the DS-grammar implements a notion of predictivity, if, at some stage during sub-sentential processing, an interlocutor has the ability to satisfy the projected goals via their own resources, e.g. via lexical access or by extending the current tree with a linked tree, it is perfectly sanctioned by the grammar for them to take over and continue extending the partial tree through DAG paths perhaps not foreseen by the original speaker (see e.g. (2) and (14)).

Moreover, since DS does not assume the mediation of any connected syntactic derivation in such cases, it is able to deal even with cases where, as we saw in (16), repeated modified here as (30), split utterances can take forms which would be ungrammatical under standard assumptions (*Did you burn myself?):

(30)

(p. 225) Figure 9.8 displays the partial tree induced by processing Mary’s utterance Did you burn, which involves a substitution of the metavariable projected by you with the term standing for the current addressee, Bob. At this point, Bob can complete the utterance with the reflexive. This is because a reflexive, by definition, just copies a formula from a local co-argument node onto the current node, just in case that formula satisfies the person/number conditions of the expression, in this case, that it designates the current speaker.

Figure 9.8 Incremental development of Mary’s/Bob’s context via processing words

Since sub-sentential/sub-propositional elements can perform various discourse functions (‘speech acts’), as seen in e.g. (19), the DS analysis of split utterances applies equally to cases like (reprise) sluicing, reprise clarifications, corrections, etc. without assuming that such sub-sentential constituents need to be sententially/propositionally expanded (Kempson et al. 2007; Gargett et al. 2008, 2009; Gregoromichelaki et al. 2009; Eshghi et al. 2015). For example, cases of elliptical clarification interaction, mid-sentence, as in (31), only involve locally attached link structures, with their discourse function modelled only as effects on the DAG (see e.g. Eshghi et al. 2015):

(31)

(p. 226) Such clarifications are construed relative to whatever constituent immediately precedes them, as in (31), where what is pertinent to the sub-sentential interruption is the immediately preceding DP the doctor. So such utterances are analysable in exactly the same terms as split utterances more generally, where the fragment is taken to directly extend its antecedent structure in context, here just the content derived from the doctor through the independently motivated link adjunction. Figure 9.9 shows the result of processing (generating for B, parsing for A) of the utterance Chorlton.7

Figure 9.9 Processing Chorlton? in ‘A: the doctor B: Chorlton?

## 9.3.5 Licensing the splitting of dependencies across turns

(p. 227) Having given a unified account of linguistic processing as mappings from context to context, making redundant extra machinery of idiosyncratic constraints applying to structure over strings, it becomes evident that the phenomena ‘anaphora’ and ‘ellipsis’ are really part of the wider phenomenon of incremental licensing of NL strings and interpretations. We therefore expect them to display parallel properties, and this is in fact what we find.

We first note the parallel potential between pronouns and ellipsis for anticipatory forward-looking resolution (‘cataphora’). In English, only some pronouns license this localized anticipatory function, with the clausal sequence following the predicate used to provide the value for the anticipatory expletive pronoun (for details, see Cann et al. 2005).8 Given our modelling of split utterances in terms of DAG options constraining the next processing actions of both interlocutors, as we would expect, the requirement of resolution of such an anticipatory device can be taken over by another party to formulate according to their own context or to serve their own purposes (see also (2)):

(32)

(33)

Further, as we show above (e.g. (4)), there is the parallelism between pronominal anaphora and VP-ellipsis in that they are both resolvable, indexically, from the utterance situation.

So ellipsis, like pronominal anaphora, is resolvable either through backwards search recovering content or actions from the Context DAG, or by just imposing a constraint for its resolution and restricting the available DAG paths for both interlocutors to those providing content for its resolution, or, indexically, by introducing in the DAG aspects of the utterance situation.

Now, a generalization missed by other frameworks (e.g. Kobele 2012b) but revealed through this modelling is that this threefold parallelism extends to ‘syntactic’ mechanisms, for example, those underpinning long-distance dependencies. First, in parallel to cases (32)–(33), the method of initially building an unfixed node and resolving its position later is the standard mechanism used in DS for long-distance dependencies. But the structure that finally resolves the structural underdetermination of such unfixed nodes can equally be provided by backwards DAG search and reiterating actions from context. For example, Mary in (34) is uttered in a context where actions are available for repeated application:

(34)

(p. 228) Here, triggered by the presence of too, Mary too is interpreted as ‘John upset Mary’ via a sequence of actions in which Mary’ is taken to annotate an unfixed node, later unified to become the internal argument of Upset’, exactly following actions used in interpreting the preceding string. And given that DS parsing and production mirror each other, resolution goals imposed on the DAG by one interlocutor both constrain and are resolvable by the other:

(35)

Completing the parallelism is the resolution of an unfixed node indexically. Of these, striking instances are children’s one-word utterances in early language acquisition, where they rely on their interlocutor to provide some open structure into which their presented fragment can be incorporated, as in (20) repeated here as (36):

(36)

Thus, from this perspective, use of fragments in split utterances (see e.g. (15)–(17)) isn’t merely an optional economy measure, it is an essential vehicle for coordination, which is crucially exploited during both language acquisition and in day-to-day human interaction. Moreover, this prediction of a parallel dynamics between pronominal anaphora, ellipsis, and long-distance dependency resolution, inexpressible in other frameworks, provides meta-theoretical foundations supporting not merely the dynamic perspective on ‘syntax’ proposed, but also the potential it provides for context-grounded interaction.

## 9.3.6 Licensing repair devices: Self-repair and corrections

But even further than this, a unified account of linguistic processing as mappings from context to context, aiming to model action coordination during interaction, can accommodate, in the same terms, the phenomena that arguably overtly promote coordination, namely, repair (see e.g. Schegloff 2007), which has traditionally been rendered a performance phenomenon unworthy of interest for theoretical linguistics. For example, self-repair, a pervasive phenomenon in dialogue (Shriberg 1994), is naturally accounted for given the DS notion of the DAG context and content recoverability employing backwards search. The same backwards-search mechanism described above for various other ellipsis cases applies again in repair cases; however, these are triggered by the current processing state being abandoned and processing resuming again from appropriate prior points in the context (see Hough 2011 and Hough and Purver 2012 for details). This strategy models common types of self-repair phenomena such as short stuttered repeats (I, I go to Paris) and substitutions (John likes, uh, loves Mary), but it can also deal with more complicated licensing phenomena where, as predicted, ellipsis interacts (p. 229) with the repairing of structure. In the following example, ellipsis reconstruction must operate across an interruption point + in a repair:9

(37)

This is a case where the content of London repairs the content derived from Paris on Monday. However, under one interpretation, the speaker continues to describe the event as one occurring ‘on Monday’, and this requires elliptical resolution after abandoning the content of Paris and replacing it with the content of London. To model this, the action sequences triggered by on Monday must be replayed after the substitution of one argument content for another. Schematically, the incremental steps leading to this can be seen in Figure 9.10, where the operation of Regeneration applies after processing has resumed from the point just before the DAG options including Paris are abandoned (characterized as state S4 in the diagram), finally arriving at the revised interpretation at S7.

Figure 9.10 Incremental interpretation of self-repair by replaying DS actions in the Context DAG

This same backtracking with Regeneration mechanism naturally extends to other-corrections, where the repair is not of one’s own utterance but another’s. It is the fact that actions are first-class citizens in the DS context that allows this straightforward integration of parsing and generation to enable the direct reflection of incremental dialogue-level coordination across interlocutors.10

Nevertheless, as we will see immediately below, such an action-based framework remains capable of expressing even presumed arbitrary formal ‘syntactic’ constraints as those applying to restrict the licensing of various forms of ellipsis, for example, antecedent-contained ellipsis as in (11). (p. 230)

## 9.3.7 Licensing in local processing domains: Island restrictions

DS takes the grammar to be a model of the joint processing actions of speakers and hearers. From this perspective, standard syntactic constraints are reconceptualized as constraints on processing DAG options, expressed in the same vocabulary, and, as we saw, expected to interact with phenomena like pronominal anaphora and ellipsis. We’ve already seen that standard, presumed sui generis linguistic constraints, like island restrictions as displayed by, for example, relative clauses, can be accounted for through the assumption of self-contained processing domains (see §9.2.3). Processing a relative clause, as we saw in §9.2.3, is taken to involve temporary shifting to a newly introduced tree structure in order to provide the context deemed necessary for proceeding with the processing of the main tree. For this reason, while processing goes on in the new domain, the fixing of an unfixed node initiated in the main tree has to await shifting of the processor back in the main tree (see Kempson et al. 2001; Cann et al. 2005).

With this perspective on island constraints, the restrictions on antecedent-contained ellipsis emerge unproblematically:

(38)

(39)

Simplifying for reasons of space here, in these cases, the DP is minimally made up of a determiner (every), a nominal (student), and a relative pronoun (who) initiating a relative clause which contains the ellipsis site (had). This relative clause is expected to provide an added restrictor to the variable bound inside the epsilon-term τ,x,Student′(x) which is the content contributed by the DP (see Figure 9.11).11

The DP word sequence has to be processed under the usual principles governing the processing of relative clauses. First, processing the determiner phrase every student involves constructing an abstract λy.τ,y,Student′(y) that will result in binding a variable x introduced by the noun student. Second, a linked tree is constructed from the node occupied by x with the requirement to include this variable as one of the arguments of this new linked tree in order to furnish it with further restrictions. Because relative pronouns in English appear as ‘left-dislocated’ elements, an unfixed node is introduced initiating the building of this linked tree in order to process the relative pronoun, who. Processing the relative pronoun, through anaphoric means, duly annotates this unfixed node with a second copy of the variable x. It is then the underspecified domination relation associated with the unfixed node, (〈↑*Tn(a)), which determines the locality of that initially unfixed node as being within the domain of a single tree. As a result, this then precludes the possibility that this unfixed node could be unified as the argument of a further linked tree as, by definition, there are no dominance relations holding across linked structures (Figure 9.11):

Figure 9.11 Successful processing of John interviewed every student who Bill had

(p. 231) Now, in coming to resolve the metavariable V which the ellipsis site had has contributed inside the relative clause, a sequence of actions from the context has to be retrieved that will result in a sub-tree of Ty(e→(est)). But now the choice of which sequence to select is constrained: the selected sequence that will resolve the ellipsis has to conform to the already mentioned independent restriction on unfixed nodes imposed on the partial tree already constructed from the relative pronoun. Hence the variable x can only appear in the local tree and cannot cross further to another linked one. This explains the island sensitivity yielding ungrammaticality in (39) where this constraint cannot be satisfied (Figure 9.12).

Figure 9.12 Ungrammaticality of (39) as impossibility to unify unfixed node with object of interview in second relative clause

(p. 232) Notice the significance of this result. In other frameworks, island constraints would be articulated within the component of syntax, independent of any interpretation/processing actions, hence not expected to interact with ellipsis/anaphora construal. In DS, however, with syntax defined in terms of update of the DAG content, such restrictions, being constraints on local processing domains, are directly predicted also to constrain ellipsis. This is because ellipsis is also modelled as a process of contextual development, therefore required to conform to any restrictions applying independently to such processes.

# 9.4 Reflections: Static vs dynamic perspectives compared

Stepping back from the details, we can see how the present account of ellipsis compares to standard accounts. Like earlier accounts, the present one also addresses the issues of the nature of the ellipsis site itself, the recovery of its content, and licensing limits on that recoverability. However, the main explanatory tool for addressing standard cases of ellipsis here does not provide descriptions of decontextualized syntax–semantics mappings (derivations, e.g. Kobele 2015). Instead, DS models directly the parser/generator actions involved in processing the skeletal information projected by some ellipsis sites. Such actions, as in routine anaphora resolution cases, include the ability to introduce, retrieve, and reuse contextual resources. Replacing a competence model embodying propositional knowledge of sentence–proposition mappings, we take grammars instead to model the know-how of interpreting and producing language in context. As such, the grammar in general, and syntax in particular, do not involve sui generis devices or representations; instead, domain-general mechanisms like underspecification and update are the core notions. As in the general domains of perception and action, the conceptualizations afforded by linguistic elements proceed incrementally and predictively, and since participants’ actions in an interaction form each other’s context, actions and conceptualizations can interleave in jointly achieving coordination across sentence boundaries and across turns. From such a perspective, participants do not need to formulate hypotheses as to each other’s intentions, since the goal-directed subpersonal mechanisms of the grammar are adequate for enabling low-level coordination without having to explicitly derive propositional descriptions of each other’s actions.

# Acknowledgements

This chapter is grounded in work done on the ESRC project The Dynamics of Conversational Dialogue (DynDial) (ESRC-RES-062-23-0962), in collaboration with Patrick G. T. Healey, Matthew Purver, Ronnie Cann, Christine Howes, and Wilfried Meyer-Viol, who have each played a central role in the project. We are extremely grateful to them for their input and to many others who have contributed to the way Dynamic Syntax has evolved, in particular, Stergios Chatzikyriakidis, Miriam Bouzouita, Jieun Kiaer, and others such as Graham White and Dov Gabbay, who have supported this work in more general ways. Eshghi’s research in this paper was supported by the EPSRC, under grant number EP/M01553X/1 (BABBLE project) and Hough’s by the DFG-funded Cluster of Excellence, Cognitive Interaction Technology ‘CITEC’ (EXC 277) at Bielefeld University, and the DFG-funded DUEL project (grant SCHL 845/5-1).

## Notes:

(1) Note that the claim here is not that a sentential structure or linguistically-based logical form needs to be recovered in order to interpret the case-marked NP (e.g. a verb like rufen in German); instead, as argued later, what is advocated here is that such morphological constraints restrict directly the role of referents within conceptualizations of events/situations (Gregoromichelaki 2006; Hough 2015), the latter conceived as non-linguistically mediated, geometric-topological structures (as in, e.g., Gärdenfors 2014), or perceptually grounded type classifications (see, e.g., Larsson 2015). There is no necessary one-to-one mapping from such conceptual structures to the words of a particular language.

(2) Again the claim here is not that Accusative vs Nominative choice in Greek indicates the presence of linguistically articulated but hidden structure; on the contrary, as in (8)–(9), morphological case, like any other linguistic constraint, restricts the conceptualization of the ongoing or envisaged event/situation, in this instance, the roles of the entities referred to; see also n. 1. Our general claim in this chapter is that exactly this function of linguistic elements is the reason why linguistic structures routinely do not have to be completed up to a sentential level in order to be interpretable.

(3) In this exegesis we ignore quantification, merely noting that NPs (DPs) in DS project actions that lead to the construction of arbitrary names denoting a witness of type e, with scope variation expressed as anticipatory statements of term dependency incrementally projected during the construction process (Kempson et al. 2001; Cann et al. 2005). Proper names will be shown here in the abbreviated form John′, Bill′, etc. Tense/aspect/modality specification, defined as sortally restricted event terms, are indicated by Si,j,…(Gregoromichelaki 2006; Cann 2011).

(4) This use of the term Merge is a unification step, not to be confused with its use in Minimalism.