Roberts (2023): Imperatives in dynamic pragmatics #
This file formalizes the paper's semantics and dynamic pragmatics for imperative mood. An
imperative denotes a property indexed to the addressee, its realization conditions. Over
circumstances, world–time pairs, a goal-based ordering source gives an agent's goals at a
circumstance in priority order, the timely futures of a circumstance are its possible futures at
which those goals remain in force, timelyFut, and a futurate circumstantial modal base delivers
the actual future circumstances in which realizing the prejacent is feasible, IsFuturate. The
paper's first-pass preference over circumstances ranks them by the highest-priority goal and
breaks ties by the next, which is the lexicographic order on goal profiles, profile; it
refines Kratzer's ordering, profile_le_of_atLeastAsGoodAs. The applicable circumstances are
those in whose timely futures realizing the prejacent is never worse, by the goals held there,
than not realizing it, applic, and the property holds of an addressee who in every applicable
circumstance comes to realize the prejacent in time, realizes. The content is conditional and
futurate but not deontic: an if-clause restricts the modal base, realizes_restrict, and
deontic force arises only when a direction is accepted and the realization of the property joins
the addressee's goals on the scoreboard, after which, other goals being equal, circumstances
realizing it are preferred, Scoreboard.accept_prefers. The illocutionary force linking
principle sends each type of denotation to the scoreboard coordinate it updates,
Denotation.defaultForce, and the conservativity presupposition on imperative subjects restricts
quantificational subjects to the addressees, nobody_livesOn, so that Nobody move! directs
each addressee not to move, realizes_nobody_move.
Implementation notes #
A goal-based ordering source assigns each circumstance its goals in priority order, whose set
is a Kratzer ordering source over circumstances (Background), and possible futures are
the substrate's futureHistoryBase; a goal held at a circumstance remains in force at a later
one when it is among the goals held there. The goal profile of a circumstance is the
list of its goals' truth values in priority order, so goal-relative preference is < on
List Prop, the lexicographic order with False < True, and "at least as good" in the
applicability condition is its negation ≤, which agrees with the paper's ≥ because the
order is total. The property an accepted direction adds to the goals is the imperative's
denotation, its realization conditions, and the paper leaves where it enters the hierarchy
open; here it is appended below the goals already held. The common ground is the library's
filter with the Stalnakerian assertion of Discourse/CommonGround.lean, so the scoreboard is a
HasAssertion instance. The addressee-part relation is flattened to membership in the set of
addressees, and the restriction of the property to addressees, which the paper writes as a
domain restriction on the abstracted individual, is left to the conservativity presupposition
rather than built into the domain of realizes.
TODO #
- Formulas (51c) and (53) reuse the world variable of the circumstance being rated for the realizing witness while quantifying that witness over the timely futures, which range over possible worlds; the possible-futures reading is formalized, and the gloss "it's possible ... for a to come to realize P" supports it.
- The retirement clauses of (58) and (59), a question dropped once answered and a goal dropped once realized or unrealizable, the comparison with the rival accounts of §5, the desiderata of §1, the plural-addressee derivation of Everyone gather!, embedded imperatives and free choice disjunction are discussed in the paper without a proposal formalized here.
References #
- C. Roberts, Imperatives in a dynamic pragmatics (2023)
- M. Kaufmann, Interpreting imperatives (2012)
- P. Portner, The semantics of imperatives within a theory of clause types (2004)
- P. Portner, Imperatives and modals (2007)
- C. Roberts, Information structure in discourse: towards an integrated formal theory of pragmatics (2012)
- R. C. Stalnaker, Assertion (1978)
- A. Kratzer, The notional category of modality (1981)
- F. Veltman, Notes on imperatives (2018)
Goal profiles #
The goal profile of a circumstance under goals ranked by priority: whether it realizes each
goal, highest priority first. Goal-relative preference (52), the paper's first pass, is the
lexicographic order on profiles: profile G c < profile G c' when c' realizes the first goal
on which they differ.
Equations
- Roberts2023.profile G c = List.map (fun (x : Reference.Index W T → Prop) => x c) G
Instances For
Goal-relative preference refines Kratzer's ordering: a circumstance realizing every goal another realizes has at least as good a profile.
Goal-relative preference refines Kratzer's strict ordering: a circumstance realizing strictly more goals than another has a strictly better profile.
Circumstances, goals and futures #
The timely future circumstances of a circumstance (50): its possible futures at which the goals held at it remain in force.
Equations
- Roberts2023.timelyFut history g c = {c' : Reference.Index W T | c' ∈ history.futureHistoryBase c ∧ ∀ p ∈ g c, p ∈ g c'}
Instances For
A futurate circumstantial modal base (51) for the realization of P by a: every
circumstance compatible with the base at a circumstance lies in its world, later than it, and
has a timely future at which a realizes P.
Equations
- One or more equations did not get rendered due to their size.
Instances For
The applicable circumstances (53) for the realization of P by a at c: those
compatible with the modal base at c in whose timely futures a realizer of P is at least as
good as a non-realizer by the goals held there.
Equations
- One or more equations did not get rendered due to their size.
Instances For
The realization conditions (54): a has the property at c when in every applicable
circumstance a comes, at a timely later time in the same world, to realize P.
Equations
- Roberts2023.realizes history g f P a c = ∀ c' ∈ Roberts2023.applic history g f P a c, ∃ (t' : T), c'.time < t' ∧ P (c'.world, t') a ∧ (c'.world, t') ∈ Roberts2023.timelyFut history g c'
Instances For
Applicable circumstances are actual future circumstances: in the world of evaluation and later than it.
Realization is later still: the property is futurate.
A circumstance at whose timely futures realizing the prejacent is worse than not, by the goals held there, is not applicable: a goal already accomplished or no longer relevant makes no circumstance applicable.
The first pass agrees with Kratzer wherever Kratzer decides: a circumstance at whose timely futures some non-realizer is strictly better than a realizer by the goals held there is not applicable.
An if-clause adds its proposition to the modal base, which shrinks the applicable circumstances.
A futurate modal base stays futurate under an if-clause.
Imperatives are conditional: a direction entails its restriction by an if-clause, which only makes explicit some of the conditions on applicability.
The scoreboard and the pragmatics of direction #
The central coordinates of the scoreboard: the common ground, the questions under discussion, and each interlocutor's evident goals in priority order.
- cg : Filter (Reference.Index W T)
The common ground, the propositions the interlocutors accept.
- qud : List (Question (Reference.Index W T))
The questions under discussion, the immediate one first.
- goals : I → List (Reference.Index W T → Prop)
Each interlocutor's evident goals, highest priority first.
Instances For
The denotation of a root sentence: a proposition, a question, or a property indexed to the addressee, an imperative's realization conditions.
- proposition
{I : Type u_4}
{W : Type u_5}
{T : Type u_6}
(p : Set (Reference.Index W T))
: Denotation I W T
A declarative's proposition.
- question
{I : Type u_4}
{W : Type u_5}
{T : Type u_6}
(q : Question (Reference.Index W T))
: Denotation I W T
An interrogative's question.
- property
{I : Type u_4}
{W : Type u_5}
{T : Type u_6}
(P : Reference.Index W T → I → Prop)
: Denotation I W T
An imperative's property, indexed to the addressee.
Instances For
The illocutionary force linking principle (56): the default force of a root sentence, assertion, interrogation or direction, is fixed by the type of its denotation.
Equations
Instances For
Assertion (57) is Stalnaker's: an accepted proposition joins the common ground.
Equations
- One or more equations did not get rendered due to their size.
Accepting a move (57), (58), (59): an asserted proposition joins the common ground, a
posed question the questions under discussion, and a property directed to i adds its
realization by i to i's goals, below those already held.
Equations
- K.accept i (Roberts2023.Denotation.proposition p) = HasAssertion.assert K p
- K.accept i (Roberts2023.Denotation.question q) = { cg := K.cg, qud := q :: K.qud, goals := K.goals }
- K.accept i (Roberts2023.Denotation.property P) = { cg := K.cg, qud := K.qud, goals := Function.update K.goals i (K.goals i ++ [fun (x : Reference.Index W T) => P x i]) }
Instances For
A direction leaves the common ground untouched.
A direction leaves the questions under discussion untouched.
A direction leaves the goals of every other interlocutor untouched.
Deontic force is pragmatic: once i accepts a direction, among circumstances alike with
respect to i's prior goals one in which i realizes the property is preferred to one in
which i does not.
Imperative subjects #
Nobody restricted to the addressees (68). The second-person pronoun (66), overt or null,
is the Montague lift NP.individual of an addressee, which lives on the set of addressees by
NP.individual_livesOn.
Equations
- Roberts2023.nobody addr = Quantifier.GQ.no addr
Instances For
The derivation (42′) of Nobody move!: the addressees have the property when in every applicable circumstance there is a timely later time at which none of them moves, so each of them is directed not to move in the applicable circumstances.