Maria Bittner, Rutgers http://www.users.cloud9.net/~mbittner NASSLLI 2016 Rutgers, New Brunswick NJ Observation: In discourse, quantified noun phrases function both as antecedents and anaphors. e.g. (1) i. Al invited someX1 friends. ii. MostX1X2 people came, and they allX2 had a good time. iii. OneX1X3 girl had a prior engagement.

q Dynamic Plural Logic (DPlL, van den Berg 1993, 1994) § plural info-state (set of assignments) represents both drefs and relations § update relates plural info-states (i.e. input info-state to a set of outputs) § minimal info-state (no drefs) is the singleton of the dummy assignment, g , which assigns the dummy individual, , to all variables

= {g } =: G0 (1) i. Alx1 invited somex2, x3 friends.

a f3 f3 output of update by (1i),

a f4 f4 if Al (a) has 5 friends (f1, ..., f5)

a f5 and invited 4 of them (f1, ..., f4)

(1) iia. Mostx3x4 people came and ...

iib. theyx4 allx4x5 had a good time.

q UC0 with ranked sets of individuals (UCδ||, Bittner 2014) § plural info-state (set of dref hierarchies) represents both drefs and relations § local anaphors refer to ranked individuals (e.g. ⊤δ) or ranked sets (e.g. ⊤δt) global anaphors refer to ranked global values (e.g. ⊤δ||) § update function an input plural info-state to the output info § minimal info-state (no drefs) is the singleton of the empty hierarchy (as in UC0)

UC v. DPlL: maximization and distributivity built into UC update function (no need for distributive or maximizing operators, such as van den Berg's Δu, Mu, or for dummies) (1') i. Alx [invited ] some friends⊤x.

⟨⟨a⟩, ⟨f3⟩⟩ ⟨⟨a⟩, ⟨f3⟩⟩ for same model,

⟨⟨a⟩, ⟨f5⟩⟩ invited friends: f1, ..., f

c6 Pc6 output c6, if out of

c8 (= c7) Pc8 output c8, if each invited friend

[had a prior engagement ] ([hv.prior.engagement⟨⊤δ⟩]; [one{⊤δt, ⊤δ||}]))

c11 Pc11 output c11,

q Dynamic semantics, which explicitly represents context change, is motivated by evidence from a wide variety of phenomena in diverse languages. q The phenomena at issue include: nominal reference, indexicality, temporal reference, plurality and quantification, presupposition, vagueness, ... (long list, keeps growing) q To represent such phenomena, we need a logical representation system that can represent: § current discourse referents (drefs) § current rank of each dref § ranked drefs in center v. background of attention § semantic type of each dref: e.g. o individual, event, state, time, world, ... o set of individuals, set of events, set of states, set of times, set of worlds, ... § current relations between drefs

Berg, M. van den. 1993. Full Dynamic Plural Logic. Proceedings of the 4th Symposium

on Logic and Language. Berg, M. van den, 1994. A direct definition of generalized dynamic quantifiers.

Proceedings of the 9th Amsterdam Colloquium. Bittner, M. 2014. Temporality: Universals and Variation. Wiley-Blackwell.