Seth Cable Topics in Semantics Spring 2020 Linguistics 753 ‘Predicates of Relevance’ and the Analysis of Responsive Predicates: Elliot et al. (2017)
1. Analyzing Responsive Predicates Through ‘Shifting’ Operators: A Review
(1) The Challenge of Responsive Predicates 1
• It is typical to analyze interrogative CPs as having a different semantic type (
• Ceteris paribus, this predicts that a single embedding predicate should only be able to combine with one of these two types of clauses:
o Predicates that can combine only with interrogatives: rogatives o Predicates that can combine only with declaratives: anti-rogatives
• However, responsive predicates (e.g., know, tell, be certain) are able to combine with both interrogative and declarative CPs
a. Behavior of Reponsive Predicates: Bill knows what / whether / that Dave ate.
• Conceivably, one might be able to capture the behavior of responsives by positing a lexical type-ambiguity… but there’s good reason for not doing that.
(2) Further Evidence for the Non-Ambiguity of Responsives: Coordinated CPs
a. Fact: It is possible to coordinate declarative and interrogative CPs together under a single responsive.
(i) Mary knows [ [ who ate ] and [ that Bill ate fish ] ]
b. First Conclusion: The meaning of know in (2a) must be compatible with either a declarative or interrogative CP.
c. Second Conclusion: If only phrases of the same type can be conjoined, then somehow the declarative and the interrogative CPs in (2a) must be the same type!
d. Major, Interrelated Questions:
o What is the type of the verb know in (2a)?
o What is the type of the coordinated CP in (2a)?
1 I haven’t mentioned this yet, but the terms ‘responsive’, ‘rogative’, and ‘anti-rogative’ are attributed to Lahiri (2002).
1 Seth Cable Topics in Semantics Spring 2020 Linguistics 753 (3) First Possibility: Interrogative-to-Declarative Shifting
a. Core, Informal Intuition:
o Responsive predicates are ‘inherently anti-rogative’ (type
o There is a means in the grammar for an interrogative CP to be interpreted as a proposition, typically the strongest true answer to the CP.
o Thus, where V is a responsive predicate and Q is a question, ‘V Q’ is equivalent semantically to ‘V P’, where P is the strongest true answer to Q.
b. One Possible Implementation: The ‘Answer’ Operator (Review)
w (i) [[ knows ]] = [ lp
(ii) The ‘Answer Operator’: Takes a question Q as argument and returns the most informative true proposition in Q.
w. [[ Ans ]] = [ lQ
1. [ Bill [ knows [ Ans [ what Dave ate ] ] ] ]
2. [[ (3biii.2) ]]w = T iff
Epi(Bill,w) Í ip . p Î [[ what Dave ate ]]w & p(w) = T & "q . (qÎ [[ what Dave ate ]]w & q(w) = T) à p Í q
Bill’s knowledge entails the strongest true answer to ‘what did Dave eat?’
(4) Second Possibility: Declarative-to-Interrogative Shifting
• Contrary to (3a), responsive predicates are ‘inherently rogative’ (type <
• There is means in the grammar for a declarative CP to be interpreted as a set of propositions (type
• Thus, if V is a responsive predicate and P is a declarative, ‘V P’ is equivalent to ‘V Q’, where Q is a kind of ‘degraded question’ whose only answer is P
2 Seth Cable Topics in Semantics Spring 2020 Linguistics 753 (5) Implementation of Declarative-to-Interrogative Shifting (Elliot et al. 2017)
a. Semantics of Knows: [[ knows ]]w =
[ lQ
• This function is only defined for Q if there is a true proposition (answer) in Q
• When defined for Q, it yields T for Q and x iff x’s epistemic state (knowledge) entails every true answer to Q
w b. The ‘Singleton’ Operator: [[ Sgltn ]] = [ lp
c. Illustration: Responsive Predicates with Interrogatives
(i) Sentence: Bill knows who ate
(ii) LF: [ Bill [ knows [ who ate ] ] ]
(iii) Truth-Conditions: 1. [[ (5cii) ]]w is defined only if $p. p Î { { w’ : x ate in w’ } : x Î De } & p(w) = T (i.e., There is some true proposition of the form ‘x ate’)
2. [[ (5cii) ]]w = T iff
"p. (p Î { { w’ : x ate in w’ } : x Î De } & p(w) = T) à Epi(Bill,w) Í p (i.e., Bill knows every true proposition of the form ‘x ate’.)
d. Illustration: Responsive Predicates with Declaratives
(i) Sentence: Bill knows Dave ate
(ii) LF: [ Bill [ knows [ Sgltn [ Dave ate ] ] ] ]
(iii) Truth-Conditions: 1. [[ (5dii) ]]w is defined only if $p. p Î { { w’ : Dave ate in w’ } } & p(w) = T (i.e., Dave ate in w)
2. [[ (5dii) ]]w = T iff
"p. (p Î { { w’ : Dave ate in w’ } } & p(w) = T) à Epi(Bill,w) Í p (i.e., Bill knows that Dave ate.)
(6) Crucial Result: ‘X knows that S’ presupposes that S is true!
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(7) Major Claim of Elliot et al. (2017)
For the ‘predicates of relevance’ (e.g., care, matter, be relevant) – which are all responsive – only the ‘Declarative-to-Interrogative’ analysis in (5) makes the right predictions.
2. Empirical Argument: Predicates of Relevance with Declaratives vs. Interrogatives
As illustrated below, ‘predicates of relevance’ (PoRs) all seem to responsive.
(8) The Responsivity of Predicates of Relevance
a. ‘Care’ (i) Mary cares who ate (ii) Mary cares that Dave ate.
b. ‘Matter’ (i) It matters to Mary who ate. (ii) It matters to Mary that Dave ate.
c. ‘Relevant’ (i) It’s relevant who ate. (ii) It’s relevant that Dave ate.
(9) Independence of PoRs with Interrogatives from PoRs with Declaratives, Part 1
• Sentences (8ai) & (8bi) – where the PoR combines with an interrogative CP – do not presuppose/entail that the attitude holder believes any answer to the interrogative CP.
• Sentences (8aii) & (8bii) – where the PoR combines with a declarative CP – do presuppose that the attitude holder believes the proposition denoted by the CP.
a. Scenario: Mary is concerned whether her advisor was awarded an institutional grant, which will support her own research. Therefore, she is very eager to know which professors at the university were awarded such grants, even though they haven't been announced, and she has no idea who might have gotten one.
b. Sentences and Judgments:
(i) Mary cares who was an awarded a grant. (True) (ii) Mary cares whether her professor was awarded a grant. (True) (iii) Mary cares that her professor was an awarded a grant. (Infelicitous)
4 Seth Cable Topics in Semantics Spring 2020 Linguistics 753 (10) The Challenge for ‘Interrogative-to-Declarative’ Shifting
a. The Core Intuition Behind ‘Interrogative-to-Declarative’ Shifting:
If V is a responsive predicate and Q is a question, ‘V Q’ is equivalent semantically to ‘V P’, where P is the strongest true answer to Q.
b. Consequence of the Core Intuition in (10a) for Predicates of Relevance:
If V is a predicate of relevance and Q is a question, ‘X V Q’ is equivalent to ‘X V P’, where P is the strongest true answer to Q.
c. The Challenge / Problem:
The facts in (9) above and (11) below demonstrate that the prediction in (10b) is just not true for predicates of relevance.
(11) Independence of PoRs with Interrogatives from PoRs with Declaratives, Part 2
a. Scenario: Alice is concerned that John may have left the party. She’s therefore eager to know who left the party. As it turns out, however, only Bill left the party.
b. Sentences and Judgments:
(i) Alice cares who left the party. (True)
(ii) Alice cares that Bill left the party. (Infelicitous)
(12) Major Conclusion: ‘Interrogative-to-Declarative’ Shifting Fails for PoRs
If V is a predicate of relevance and Q is a question, ‘X V Q’ is not equivalent to ‘X V P’, for some answer P to Q.
• Thus, one cannot ‘reduce’ cases where PoRs combine with interrogatives to cases where they combine with declaratives…
(13) New Direction This Suggests
• Perhaps, however, we can ‘reduce’ cases where PoRs combine with declaratives to cases where they combine with interrogatives…
• That is, if V is a predicate of relevance and P is some proposition, then ‘X V P’ is equivalent to ‘X V Q’, for some question Q built from P…
5 Seth Cable Topics in Semantics Spring 2020 Linguistics 753 3. A ‘Rogative’ Semantics for Predicates of Relevance
For reasons of space, Elliot et al. (2019) focus their attention to the predict ‘care’… It is assumed that parallel approaches could be extended to the other PoRs…
(14) Rogative Semantics for ‘Care’
a. Informal Intuition: Where Q is some question, ‘X cares Q’ presupposes that:
(i) There is a true answer to Q (ii) X believes there is a true answer to Q
b. Formalization:
[[ care ]]w =
[ lQ
(i) Observations: • [[care]]w is defined for Q only if Q contains a true proposition • [[ care ]]w is defined for x only if x believes Q contains a true proposition
(15) Analysis of ‘Care’ with Interrogative CPs
a. Sentence: Bill cares who ate.
b. LF: [ Bill [ cares [ who ate ] ] ]
c. Predicted Truth-Conditions:
(i) [[(15b)]]w is defined only if:
1. $p. p Î [[who ate]]w & p(w) = T (i.e., Somebody ate)
2. Dox(Bill,w) Í {w’ : $p. p Î [[who ate]]w & p(w’) = T}
(i.e., Bill believes somebody ate)
(ii) [[(15b)]]w = T iff care(w, Bill, [[who ate]]w)
Thus far, our formal semantics capture our core intuitions in (14a)…
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(16) Analysis of ‘Care’ with Declarative CPs
a. Sentence: Bill cares that Dave ate.
b. LF: [ Bill [ cares [ Sgltn [ Dave ate ] ] ]
c. Predicted Truth-Conditions:
(i) [[(16b)]]w is defined only if:
1. $p. p Î {{ w’ : Dave ate in w’ }}& p(w) = T (i.e., Dave ate)
iff Dave ate in w
2. Dox(Bill,w) Í {w’ : $p. p Î {{ w’ : Dave ate in w’ }} & p(w’) = T}
iff Dox(Bill,w) Í { w’ : Dave ate in w’ }
(i.e., Bill believes Dave ate)
(ii) [[(16b)]]w = T iff care(w, Bill, { {w’: Dave ate in w’} })
(17) The Crucial Result
• The rogative semantics for care in (14) and the ‘Sgltn’ operator in (5) together correctly predict the facts in (9)-(11):
o ‘Care’ with a declarative CP presupposes that the CP is true, and that the subject believes the CP…
o But ‘care’ with an interrogative CP doesn’t presuppose/entail that the subject believes any particular answer to the CP (let alone the ‘strongest true answer’)
• This follows because the rogative semantics in (14) only requires that the subject believes there is some true answer within the (interrogative) CP it takes as argument.
• However, when the CP argument of cares is declarative, the only ‘answer’ in the denotation to the CP is the ‘classical proposition’ denoted by the CP…
o Consequently, it follows that when cares combines with a declarative CP, the subject must believe that that proposition is true…
7 Seth Cable Topics in Semantics Spring 2020 Linguistics 753 (18) Some Further Discussion
• The preceding discussion is entirely couched within the assumption that interrogative CPs have a different type (
o After all, it is ‘Sgltn’ the ‘shifts’ the denotation of a declarative CP to interrogative type…
• However, as Elliot et al. (2017) also note, this approach is even more at home in a system where all subordinate CPs are of type
• Indeed, as students are invited to confirm:
o Our analysis of ‘care’ in (14)-(16) would work equally well if the denotations of interrogative/declarative CPs were downward closed sets of propositions.
• However, the proposed presupposition for ‘care’ in (14) will be vacuous with interrogatives, if interrogatives are always non-informative…
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