Kurt Erbach and Cornelia Ebert
Affiliation: Goethe Universität-Frankfurt
Dynamic binding of discourse referents (DRs) has been shown to exist across sentences (Heim 1982, Groenendijk & Stokhof 1991) a and later also across dimensions such as across not-at-issue appositive and an at-issue host sentence (Nouwen 2007, AnderBois et al. 2015). We contribute to this ongoing semantic issue by further developing cross-modal semantics for dynamic binding across gesture–speech interaction (e.g. Ebert et al. 2020). Specifically, we suggest that there are predefined loci in gesture space that stand for free variables of rigid designators. Via semantic rules of identity, these variables are assigned specific values during derivation. These assumptions entail that the establishment of an antecedent and the retrieval of a locus are handled similarly. Background. Ebert et al. (2020) assumes that pointing gestures refer to an intended referent g and introduce a DR for this referent. Formally, a gesture denotes the rigid designator to the intended referent. The introduced DR can be anaphorically picked up by a pronoun in later discourse. Im- portantly, in this dynamic semantic framework, it is predicted that gesturally introduced DRs allow for anaphoric binding across dimensions—i.e. verbally introduced DRs can be the referents of pro-speech gestures; in this case our “gestural pronouns”. Following AnderBois et al. (2015), ges- ture semantics incorporates a dynamic system that keeps track of discourse referents (i.e. variables over individual concepts) as well propositional variables p and p⋆ which are respectively at-issue and not-at-issue content. Co-occurrence with a definite predicate, ⊔P, introduces a not-at-issue identity relation, = ⋆p, between the gestural, z, and the speech concept, x, in (1). (1) [x]∧⊔Pp(x)∧[z]∧(z =p⋆ x) Data. Schlenker (2020) presents eamples where a gestural anaphoric expression, tied to a certain locus in the gesture space, is dynamically bound by what is introduced via speech. (2) is an adaptation of Schlenker’s example wherein the speaker points to a location in the gesture space, A, when she utters the first candidate and to another location, B, when uttering the second candidate (note the actual candidates are neither present nor pointed to). The pro-speech gesture (i.e. the gesture occurring in the place of speech), pointing to location A, can be interpreted as a gestural anaphoric expression that gets bound by what is introduced via speech and located at a certain position in the gesture space earlier. In this example, the POINTING TO A gesture gets bound by the DR that is identified as that which co-occurred with the same gesture: the first candidate. (2) a. I can hire [the first candidate]POINTING TO A or the second candidatePOINTING TO B. b. I will hire POINTING TO A. Analysis. We build on Ebert et al. (2020) by assuming that there are predefined loci, L1...Ln in the gesture space, which stand for free variables of rigid designators that are assigned specific values during derivation. This way, (a) the establishment of an antecedent and (b) the retrieval of this locus are handled similarly: (2) can be formalized as (3). (3) a. [x] ∧ first.candidatep(x) ∧ [z] ∧ (z = L1) ∧ (z =p⋆ x) ∧ [y] ∧ second.candidatep(y) ∧ [z′] ∧ (z′ = L2) ∧ (z′ =p⋆ y) ∧ hirep(speaker, x) ∨ hirep(speaker, y) b. [z′′] ∧ (z′′ = L1) ∧ hirep(speaker, z′′) Conclusion. Assuming loci in gestural space can be assigned values during derivation allows for gestures towards a given locus to function as pronouns. This opens the door for further work on the values that can be assigned to space in communication.