Modelling Selectional Super-Flexibility?

Kristina Liefke

Department of Philosophy, Ruhr University Bochum, Germany [email protected]

Abstract The selectional flexibility of some attitude verbs (e.g. know) between declarative and interrogative complements is a core topic in con- temporary formal . Despite this , little attention has been paid to verbs (e.g. see, remember, observe) that embed an even wider vari- ety of complements (incl. subject-controlled gerundive clauses and con- crete object-denoting DPs). Since the familiar types of some of these com- plements resist an embedding in the type for questions [= sets of proposi- tions], these verbs challenge Theiler et al.’s (2018) uniform interpretation strategy for the complements of declarative/interrogative-neutral verbs. Our paper answers this challenge by interpreting the complements of selectionally super-flexible verbs like remember in a generalized type for questions, viz. as parametrized centered questions. The resulting seman- tics captures the intuitive entailment pattern of these verbs.

Keywords: Responsive verbs · Experiential attitude verbs · Comple- mentation · Cross-categorial entailment · .

1 Introduction Responsive verbs, i.e. verbs like know that are selectionally flexible between de- clarative (e.g. (1a)) and interrogative clauses (e.g. (1b); see [11, 17]), have been at the center of much recent work in formal semantics (see e.g. [8, 36, 37, 41, 42, 44]). (1)  a. that Mary was wearing a crazy hat (declarative clause) John knows b. whether Mary was wearing a crazy hat (interrogative) Responsive verbs are particularly interesting since their flexibility cannot be attributed to an between a declarative- and an interrogative-embedding use. Such attribution is excluded by the fact that declaratives can be coordinated with interrogatives in the complements of these verbs (see (2); ff. [12, p. 93]): (2) John knows [that Mary was wearing a crazy hat] and [whether she bought it at the party supply store] Interest in responsive verbs is further fuelled by the observation that their de- clarative and interrogative complements can stand in semantic inclusion relations (see (3) [for uni-directional inclusion] and (4) [for mutual inclusion]): ? I thank my anonymous reviewers for SALT 31 for valuable comments on the abstract of this paper. The paper has profited from discussions with Floris Roelofsen, Frank Sode, Markus Werning, and Ede Zimmermann. The research for this paper is suppor- ted by the German Research Foundation (via Ede Zimmermann’s grant ZI 683/13-1). 2 K. Liefke

(3) a. John knows [that Mary was wearing a crazy hat (when she arrived)] ⇒ b. John knows [whether Mary was wearing a crazy hat ...] (4) a. #John knows [whether Mary was wearing a crazy hat] and [that she was wearing a rainbow squid hat] (redundant) ≡ b. John knows [that Mary was wearing a rainbow squid hat] The validity of entailments like (3) is typically ascribed to the observation that the information content of the interrogative clause in (3b) (i.e. ‘Mary was or was not wearing a crazy hat’) is contained in the content of the declarative in (3a). The redundancy – and attendant markedness – of (4a) is due to the fact that the true answer to the question denoted by the first conjunct in the complement of (4a) (‘Mary was wearing a crazy hat’) is already informationally contained in the content of the second conjunct in (4a), where rainbow squid hats are crazy hats. The informational relations between embedded declaratives and interroga- tives pose an important empirical constraint on any adequate semantics for resp- onsive verbs. However, a suitable account of this constraint is challenged by the fact that declaratives and interrogatives are typically associated with objects of a different semantic type: while declaratives are commonly interpreted as proposi- tions (analyzed as [characteristic functions of] sets of possible worlds, type1 (s; t); see [16, 26]), interrogatives are interpreted as questions (analyzed as [characteris- tic functions of] sets of , type ((s; t); t); see [7, 13, 16]). The different types of declaratives and interrogatives block an easy2 analysis of the relation be- tween the complements in (3a) and (3b) as set-theoretic inclusion and disable the familiar interpretation of natural language and in (2) and (4a) as set intersection. To answer the above challenge, Theiler et al. [36] propose that declaratives and interrogatives are uniformly interpreted in the type for questions, ((s; t); t). In this type, the common of declaratives can be represented through the type-shifter λp(s;t)λq(s;t)(∀ws)[q(w) → p(w)] that sends sets of worlds p to their powersets P(p), i.e. to downward-closed sets of propositions (see [7, 8, 36]). The downward closure of these sets effects that, if these sets include p, they also include every informationally stronger /set of worlds q, where q ⊂ p.3 The results of this type-shift meet the type-requirement (viz. type-identity) on entailment and coordination, and capture the intuitive relations between de- clarative and interrogative complements (see [8, 33]). Consequently, they readily account for the data in (3) and (4). My simplified account of this data (in (6), (7)) 1 To distinguish centered propositions from properties (see below), I here use multiary function types (see [30, 38]). The latter are types of the form (α1× ...×αn) → αn+1 that are associated with functions from n-tuples of objects of the types α1, ..., αn to objects of type αn+1. Following Tich´y[38], I write (α1 × ... × αn) → αn+1 as (α1 . . . αn; αn+1) and identify the type (α) with α. 2 Arguably, one can enable this analysis by coding propositions as questions (see [40]). However, Theiler et al. argue (in [36, p. 413], [37]) that this move fails to explain the selectional restrictions on non-responsive verbs (e.g. the anti-rogativity of believe). 3 This differs from [13], Possibility Semantics [8], and Uegaki’s [40] semantics, which identify questions with the maximal elements in these sets (cal- led alternatives). For reasons against this move, the reader is refereed to [7, 8, 33]. Modelling Selectional Super-Flexibility 3 uses the semantics for know in (5), where know := λT ((s;t);t): ∃q ∈ T [q(w)]. λws e 0 w 0 0 λz . ∃p ∈ T [p(w) ∧ (∀w . DOXz (w ) → p(w ))] (see [40, p. 631]). For better read- ability, the semantic complement of know is highlighted in (6) and (7):4 ((s;t);t) s e (5) know = λT λw λz [knoww(T )(z)] J K 0 0  (6) a. knoww λp ∀w . p(w ) → (∃x. crazy-hatw0 (x) ∧ wearw0 (x)(m)) (j) 0 0 0 b.( ∀T )(∀w)(∀z)[knoww(T )(z) → (∀T .T ⊆ T → knoww(T )(z))] 0 0 ⇒ c. knoww λp.(∀w . p(w ) → (∃x. crazy-hatw0 (x) ∧ wearw0 (x)(m))) ∨ 0 0  (∀w . p(w ) → ¬(∃x. crazy-hatw0 (x) ∧ wearw0 (x)(m))) (j)

0 0 (7) a. knoww λp. ((∀w . p(w ) → (∃x. crazy-hatw0 (x) ∧ wearw0 (x)(m))) ∨ 0 0 (∀w . p(w ) → ¬(∃x. crazy-hatw0 (x) ∧ wearw0 (x)(m)))) ∧ 00 00  (∀w . p(w ) → (∃x. squid-hatw00 (x) ∧ wearw00 (x)(m))) (j)

b.( ∀x)(∀w)[squid-hatw(x) → crazy-hatw(x)] 0 0  ⇔ c. knoww λp ∀w . p(w ) → (∃x. squid-hatw0 (x) ∧ wearw0 (x)(m)) (j ) In particular, (6) models the entailment in (3) through the inclusion of P{w0 | ∃x.  0 crazy-hatw0 (x)∧wearw0 (x)(m)} (see (6a)) in the union of P {w | ∃x. crazy-hatw0  0  (x)∧wearw0 (x)(m)} and P {w | ¬∃x. crazy-hatw0 (x)∧wearw0 (x)(m)} (see (6c)).

2 The Challenge from Experiential Attitude Verbs

Its merits notwithstanding, Theiler et al.’s semantics fails to capture the selec- tional flexibility of a particular, but salient, subclass of responsive verbs: veridical experiential attitude verbs (see [14, 35]). The latter are verbs like see, remember, and observe that also combine with direct object DPs (e.g. (8e)) and with subject- controlled and non-controlled gerundive clauses (e.g. (8d, c); see [1, 14, 44]): (8)  a. that Mary was wearing a crazy hat( s; t); generally:((ss; t)   b. whether Mary was wearing a crazy hat(( s; t); t) Ron  remembers c. Mary wearing a crazy hat( s; t) or v (event)  d. PRO wearing a crazy hat( (se; t)   e. a / Mary’s crazy hat( (s; ((s;(e; t)); t)) Like the complements of know in (3) and (4), the complements of the different occurrences of remember from (8) stand in semantic/informational inclusion rela- tions to each other. These relations are exemplified in (9) to (11). They include – next to the familiar relations between declarative and interrogative complements (see (9)) – the entailment from gerundive small clauses to that-clauses (e.g. (10); as argued by [31, 43]) and to concrete object-denoting DPs (e.g. (11); see [2, 35]): (9) a. Ron remembers [that Mary was wearing a rainbow squid hat] ⇒ b. Ron remembers [whether Mary was wearing a crazy hat]

4 For simplicity, we neglect tense and aspect of the matrix verb. 4 K. Liefke

(10) a. Ron remembers [i. PRO / ii. Mary wearing a crazy hat] 6⇐ ⇒ b. Ron remembers [that there was a crazy hat (which i. he himself / ii. Mary was wearing)] (11) a. Ron remembers [i. PRO / ii. Mary wearing a crazy hat] 6⇐ ⇒ b. Ron remembers [a crazy hat] The modelling of the above relations is impeded by the observation that some of the above complements (viz. the red-marked ones in (8)) resist an interpre- tation as questions. This holds especially for concrete object-denoting DPs (see (8e)) and for subject-controlled complements (see (8d)). Surprisingly, this resis- tance even holds for some embedded declaratives (see (8a)). The particular chal- lenges that are posed by these kinds of complements are discussed below:

2.1 Challenge 1: concrete-object DPs Most contemporary formal semantics interpret the direct object DPs of intensio- nal transitive verbs as intensional generalized quantifiers (type (s; ((s;(e; t)); t)); see [25, 26]) or as properties of individuals (type (s;(e; t)); see [45, 46]). In par- ticular, these semantics interpret (8e) as (12a) resp. (12b), where the complement is over- or underbraced. Since remember takes different-type arguments in these interpretations, we interpret it through different non-logical constants, viz. rem- ember 0 (which takes a quantifier-argument) and remember00 (which takes a proper- ty-argument): type (s; ((s;(e; t)); t))  z }| { (12)  0 0 (s;(e;t))  a. rememberw (λw λP ∃x. crazy-hatw0 (x) ∧ Pw0 (x))(r) (8e) 00 b. rememberw (crazy-hat)(r) J K  | {z }  type (s;(e; t))

Noticeably – depending on the size of Ds and De –, already the ‘simpler’ (= low- er-type) interpretation of the DP a crazy hat (in (12b)) can have a larger cardi- nality than the domain of questions. As a result, there is no true, information- preserving embedding of properties in the domain of questions. But embeddabil- ity (or injectivity) is a key requirement on any admissible type-shift (see [3, 48]).

2.2 Challenge 2: parasitic complements Surprisingly, even declaratives like (8a) cannot always be represented as ques- tions (see [4, 5, 24, 27]). This is the case when these declaratives are parasitic on other attitudes, i.e. when their intuitive interpretation requires their contents to be evaluated at worlds other than the evaluation world (w) and the alter- natives (w0) that are introduced by the matrix attitude verb. Such evaluation is prompted either by the presence of other attitude predicates (in (13): by the presence of see; inspired by [29]) or by the lack of adequate truth-conditions in the absence of these predicates (as is the case in (14a), inspired by [4, 5]): (13) Ralph remembers [that the man whom he has seen sneaking around on the waterfront was wearing a hooded sweater] Modelling Selectional Super-Flexibility 5

In particular, in (14a), the evaluation of her [= some/the female tattoo model] at the relevant scene from Fred’s dream is triggered by the observation that (14a) is false on its de re-reading (in (15a), paraphrased by (14a-ii)) and is contradic- tory on its de dicto-reading (in (15b), paraphrased by (14a-i)): (14) : Fred has been dreaming of some female tattoo model (no parti- cular one that he has come across in real life) a. Now, he falsely (!) remembers [that she had clear (= untattooed) skin] 6≡ i. de dicto: Fred remembers an inconsistent situation (in which the model simultaneously does and does not have tattoos) 6≡ ii. de re: There is a tattoo model whom Fred remembers (as) ha- ving clear skin ≡ b. F. remembers [that the tattoo model from his dream had clear skin] The interpretation of her at Fred’s oneiric scene is then prompted by the obser- vation that (14a) has plausible truth-conditions on a ‘parasitic’ reading (viz. (15c), paraphrased in (14b)) that interprets the DP the tattoo model at some other world/attitudinal alternative5 (different from w and from the mnemonic alterna- tives, w0). In (15c), this alternative is denoted by X : (15) a. [the model-in-w][λt. Fred remembers-in-w [λw0. t has-...-in-w0]] b. Fred remembers-in-w [λw0. the model-in-w0 has-clear-skin-in-w0] c. Fred remembers-in-w [λw0. the model-in-X has-clear-skin-in-w0] To capture the dependence of the constituents in (14a) on different attitudinal alternatives, we posit distinct variables for the alternatives that are introduced by the matrix [= parasite] attitude verb (i.e. remember; below: w2) and for the alternatives that are introduced by the host attitude verb (i.e. dream; below: w1). This move has been proposed by Blumberg [4, 5]. (In line with the above naming pattern, the variable for the evaluation world, w, is then renamed ‘w0’.) The reading (15c) (on which (14a) is true) then has the interpretation in (16). There, remember 000 takes as arguments (characteristic functions of) sets of pairs of worlds (type (ss; t)). In [4], such sets are called paired propositions.6 (16) (14) @ = remember000 (λhw , w i ∃x. model (x) ∧ clear-skin (x))(f) w0 1 2 w1 w2 J K | {z } type (ss; t) 2.3 Challenge 3: -complements Another challenging case for the question-interpretation of experiential attitude complements is posed by subject-controlled gerundive small clauses (e.g. (8d)): following Chierchia [6], the latter are obligatorily interpreted de se, viz. as (char- acteristic functions of) sets of centered worlds (type (se; t); see (17)), called cen- tered propositions. The members of such sets are commonly analyzed as world/ individual-pairs hw, yi, where y is the center of w (see [18, 34]). 5 In this paper, I use alternative in the sense of ‘attitudinal alternatives’ (see [15]). 6 Since Blumberg’s framework only has unary function types, it analyzes paired propo- sitions as functions from worlds to propositions (type (s;(s; t))). 6 K. Liefke

(17) (8d) = remember0000 (λhw , yi∃x. crazy-hat (x) ∧ wear (x)(y))(r) w0 1 w1 w1 J K | {z } type (se; t)

Admittedly, the domain of centered propositions, D(se;t), potentially has a smaller cardinality than D((s;t);t). However, since there is no principled connection be- tween De and Dt (:= {0, 1}), there is still no good embedding of D(se;t) in D((s;t);t). The absence of a suitable embedding of semantic de se-complements in the domain of questions is sharpened by observation that – like their non-de se-relati- ves – self-directed experiential attitudes can parasitically depend on other atti- tudes. Such dependence is assumed by the remember-report in (18a), which pre- supposes the context from (14).7 To capture the parasitic de se-nature of this re- port, its complement requires an interpretation in the type (s;;(se; t))) (i.e. as a set of pairs of worlds whose second (world-)element is centered; see (18b)). I will hereafter call objects of this form parametrized centered propositions.

(18) a. Fredi remembers [PROi being scared by the model (from his dream)] ≡ Fred remembers [that he himself was being scared by the model ...] b. remember00000(λw λhw , yi ∃x. model (x) ∧ scare (y)(x))(f) w0 1 2 w1 w2 | {z } type (s;(se; t)) Aggravating the above, interrogatives can also be parasitic and de se (see (19a)). Complements of this form even require an interpretation in the type (s (se; t);; t)): (19) a. Fred remembers [whether he himself was being scared by the model] b. remember000000 λhw ,C(se;t)i[(∀w . (∀y. C(w , y) → (∃x. model (x) ∧ w0 1 2 2 w1 | {z } scarew2 (y)(x)))) ∨ (∀w2. (∀y. C(w2, y) → ¬(∃x. modelw1 (x) ∧ scarew2 (y)(x))))] (f) | {z } type (s (se; t); t) The interpretation of the occurrences of remember from (12) and (16)–(19) suggests that these occurrences are each associated with a different(-type) lexical entry. But this makes it difficult to model the semantic relations from (9)–(11).

3 A Uniform Type for Parasitic and de se-Complements

I propose to answer the above challenge by generalizing Theiler et al.’s [36] type for questions, ((s; t); t), to the type for parametrized centered questions (s (se; t); t) (abbr. ‘PCQ’; inspired by [23] resp. [9]). Objects of this type are (characteristic functions of) sets of ordered pairs of worlds (type s) and centered propositions (= sets of centered worlds; type (se; t)). The first element of such pairs is a ‘host’ attitudinal alternative (in (14a): a world that is compatible with what Fred has been dreaming). The second element is the content of the matrix attitude (in 7 For reasons of simplicity, I (na¨ıvely) assume that gerundive small clauses (e.g. the complement in (18a)) make the same semantic contribution as declarative clauses (here: that he himself was being scared by the model from his dream). For a sophistica- ted account of the semantics of these clauses, the reader is referred to [20, 22, 35]. Modelling Selectional Super-Flexibility 7

(14a): the content of Fred’s remembering). Below, I show that the different se- mantic objects from Section 2 all have a true embedding in the domain of PCQs. I start by demonstrating that my account preserves Theiler et al.’s results from [36] (i.e. that there is a true PCQ-embedding of propositions and questions):

3.1 Embedding simple questions and propositions I have assumed above that ‘simple’ interrogatives (i.e. non-parasitic, non-de se clauses like (8b)) are interpreted in the type ((s; t); t), where ‘s’ is associated with the worlds/alternatives that are introduced by the matrix attitude verb. This as- sumption suggests that, in PCQ-representations of questions (in the type (s(se; t); t)), the ‘host’ attitudinal alternative and the individual center(s) of the ma- trix attitudinal alternatives are semantically ‘inert’. My question-to-PCQ type- shifter (in (20)) reflects this inertness by assuming that its value is independent8 of w1, and by universally quantifying over the individual centers in all (centered world-)members of C. To capture the type of its arguments, we call this type- shifter ‘E-inq’ (for inquisitive [or interrogative] Embedder):

((s;t);t) (se;t) (20) E-inq := λT λhw1,C i[T (λw2 ∀y. C(w2, y))] In the formulation of this type-shifter, universal quantification over the type-e elements in C is motivated by the wish to identify sets of centered worlds with se- mantically inert centers as boring centered propositions (following [10]; see above). The latter are characteristic functions of sets of centered worlds whose value does not depend on the worlds’ center, i.e. (∀w2)(∀x)(∀y)[C(w2, x) ↔ C (w2, y)] (see (s;t) [28, p. 553]). This is the case if C := λhw2, yi[p (w2)], where p is a non-logical constant. By applying E-inq to the familiar interpretation of the polar interrog- ative from (8b) (see (6c)), we yield the PCQ-representation in (21): (21) E-inq whether Mary was wearing a crazy hat  J 0 0 K ≡ E-inq λp. (∀w . p(w ) → (∃x. crazy-hatw0 (x) ∧ wearw0 (x)(m))) ∨ 0 0  (∀w . p(w ) → ¬(∃x. crazy-hatw0 (x) ∧ wearw0 (x)(m)))

= λhw1,Ci[(∀w2. (∀y. C(w2, y)) → (∃x. crazy-hatw2 (x)∧wearw2 (x)(m))) ∨

(∀w2. (∀y. C(w2, y)) → ¬(∃x. crazy-hatw2 (x) ∧ wearw2 (x)(m)))] Given the possibility of representing propositions as questions (through the function λqλp(∀w)[p(w) → q(w)]; see Sect. 1), one would expect that E-inq also provides a true PCQ-embedding of propositions. This is indeed the case, as is evidenced by (22) for the interpretation of the declarative complement in (8a): (22) E-inqλqλp[∀w. p(w) → q(w)] that Mary was wearing a crazy hat  J K = λhw1,Ci[∀w2. (∀y. C(w2, y)) → (∃x. crazy-hatw2 (x) ∧ wearw2 (x)(m))] As desired, the PCQ-representation of the complements in (8a) and (8b) preser- ves the intuitive informational relation between these complements. Since it uses Ciardelli et al.’s analysis of questions as downward-closed sets of propositions (see the uni-directional material conditional in (21) and (22)), my semantics also

8 The ‘curried’ version this shifter, i.e. λw1λC [T (λw2 ∀y. C(w2, y))], is constant for w1. 8 K. Liefke straightforwardly captures the semantic inclusion relation between the comple- ments in (9) (see (23)): (23) a. E-inqλqλp[∀w. p(w) → q(w)] that M. was wearing a squid hat  J K = λhw1,Ci[∀w2. (∀y. C(w2, y)) → (∃x. squid-hatw2(x)∧wearw2(x)(m))] ⊆ b. E-inq whether Mary was wearing a crazy hat  J K = λhw1,Ci[(∀w2.(∀y.C(w2, y)) → (∃x.crazy-hatw2(x)∧wearw2(x)(m)))

∨ (∀w2. (∀y. C(w2, y)) → ¬(∃x. crazy-hatw2 (x) ∧ wearw2 (x)(m)))]

3.2 Embedding paired propositions Above, I have identified the first element in world/centered proposition-pairs with a host attitudinal alternative. My type-shifter E-para (in (24)) – which pro- vides PCQ-representations of paired propositions – makes use of this identifica- tion. To capture the non-de se status of simple paired propositions, this shifter treats C in its range as a boring centered proposition (analogously to E-inq). To associate the ‘second’ world in paired propositions with matrix alternatives, it identifies these boring propositions with subsets of {hw2, yi | R(w1, w2)}: (ss;t) (24) E-para := λR λhw1,Ci[∀w2. (∀y.C(w2, y)) → R(w1, w2)] By applying E-para to Blumberg’s semantics for the parasitic declarative complement in (14b) (see (16)), we obtain the PCQ in (25). The latter is a set of ordered world/centered proposition-pairs whose first member is one of Fred’s oneiric alternatives and whose second member is a set of (oneirically dependent) centered worlds that constitute Fred’s mnemonic alternatives. (25) E-para that the model (from Fred’s dream) has clear skin  J K = λhw1,Ci[∀w2. (∀y. C(w2, y)) → (∃x. modelw1 (x) ∧ clear-skinw2 (x))] I will show below that the type-shifter E-para is easily generalized to parame- trized centered propositions (e.g. the familiar of the complement in (18a)). Following my treatment of centered propositions (in Sect. 3.3), I will also show that my PCQ-representation of paired propositions captures intuitive en- tailment relations between parasitic declarative and interrogative complements.

3.3 Embedding centered propositions My earlier considerations have associated the individual elements in PCQs with the center of the matrix attitudinal alternatives (in (8d)/(17): the center of Ron’s mnemonic alternatives). To preserve this association, my type-shifter for cen- tered propositions, E-dese, (in (26)) identifies the second element, C, of all or- dered pairs in a PCQ with a subset of the represented centered proposition: (se;t) (26) E-dese := λG λhw1,Ci[∀w2. (∀y. C(w2, y) → G(w2, y))] By applying this type-shifter to Chierchia’s semantics for the complement in (8d) (see (17)), we yield the PCQ in (27): (27) E-dese PRO wearing a crazy hat  J K = λhw1,Ci[∀w2. (∀y. C(w2, y) → (∃x. crazy-hatw2 (x) ∧ wearw2 (x)(y)))] Modelling Selectional Super-Flexibility 9

The attentive reader may have noticed that – like the values of the type- shifter E-inq – the values of E-dese do not depend on w1. While this is desir- able for a PCQ-representation of the semantic complement in (8d), this blocks an adequate interpretation of parasitic de se-complements like the one in (18a). To give a suitable PCQ-semantics for such complements, we use a combination of the type-shifters E-dese and E-para. The resulting shifter (in (28)) sends parame- trized centered propositions S (type (s;(se; t))) to sets of pairs whose first ele- ment is the parameter of S (below, the world w1) and whose second element is a subset of S’s value at w1: (s;(es;t)) (28) E-pa/se := λS λhw1,Ci[∀w2.(∀y.C(w2, y) → S(w1)(w2, y))] The above shifter enables a suitable PCQ-interpretation of the complement in (18a), as expected (see (29)): (29) E-pa/se PRO being scared by the model (from his dream)  J K = λhw1,Ci[∀w2. (∀y. C(w2, y) → (∃x. modelw1 (x) ∧ scarew2 (y)(x)))] The different type-shifters that are required for a uniform (i.e. PCQ-)interpre- tation of the diverse experiential attitude complements are given in Table 1. In this table, the type-shifters from Sections 3.1 to 3.3 are printed in black. Type- shifters that will be introduced in subsequent sections are printed in grey.

Complemnt Input Name Definition interrogative ((s; t); t) E-inq λT λhw1,Ci[T (λw2. (∀y. C(w2, y)))] declarative/ (s; t) —— λq.[E-inq (λp∀w. p(w) → q(w))] non-contr. SC E-decl ≡ λq λhw1,Ci[∀w2.(∀y. C(w2, y)) → q(w2)] parasitic decl. (ss; t) E-para λRλhw1,Ci[∀w2.(∀y. C(w2, y)) → R(w1, w2)] controlled SC (se; t) E-dese λGλhw1,Ci[∀w2.(∀y. C(w2, y) → G(w2, y))] para.contr. SC (s;(se; t)) E-pa/se λS λhw1,Ci[∀w2.(∀y. C(w2, y) → S(w1)(w2, y))] de se-interrog. ((se; t); t) -inq/se λQλhw1,Ci[Q(C)] (see Sect. 3.4) object DP GQ E-qtf λQλhw1,Ci[∀w2.(∀y.C(w2, y)) → Qw2 (E)] 0 0 object DP (s;(e; t)) E-pty λP.[E-qtf (λw2 λP .(∃x. Pw2 (x) ∧ Pw2 (x)))] Table 1. ‘Familiar denotation’-to-PCQ type-shifters.

3.4 Embedding centered questions I have shown above that the black-printed type-shifters in Table 1 enable the PCQ-embedding of more complex objects than the familiar propositions or ques- tions. Unsurprisingly, this is also the case for centered questions (see [9]). The latter are sets of centered propositions (type ((se; t); t)) that are denoted e.g. by interrogative clauses with a reflexive subject (e.g. by the complement in (30)): (30) Ron remembers [whether he himself was wearing a crazy hat] A combination of the type-shifters E-inq and E-dese (in (31)) allows us to repre- sent the semantic complement in (30) as the PCQ in (32): 10 K. Liefke

((se;t);t) (31) E-inq/se := λQ λhw1,Ci[Q(C)] (32) E-inq/se whether he himself was wearing a crazy hat  J K = λhw1,Ci[(∀w2. (∀y. C(w2, y) → (∃x. crazy-hatw2 (x)∧wearw2 (x)(y)))) ∨

(∀w2. (∀y. C(w2, y) → ¬(∃x. crazy-hatw2 (x) ∧ wearw2 (x)(y))))] The PCQ-representation in (32) captures the intuitive semantic inclusion re- lation between the complements of the reports in a de se-analogue of (9) (s. (33)): (33) a. (that he himself was) wearing a rainbow squid hat J K = λhw1,Ci[∀w2.(∀y.C(w2, y) → (∃x.squid-hatw2(x)∧wearw2(x)(y)))] ⊆ b. whether he himself was wearing a crazy hat = (32) J K This entailment is explained by the inclusion of the set P {hw2, yi | ∃x. squid-hatw  2 (x) ∧ wearw2 (x)(y)} in the union of the sets P {hw2, yi | ∃x. crazy-hatw (x) ∧   2 wearw2 (x)(y)} and P {w2 | ¬∃x. crazy-hatw2 (x)∧wearw2 (x)(y)} . Similar obser- vations hold for the intuitive entailment between remember-reports with parasitic de se-declarative and interrogative clauses (see (18b) resp. (19b)).

4 A PCQ-Interpretation of Concrete-Object DPs

4.1 Embedding intensional generalized quantifiers I have shown above that PCQs enable a true embedding of paired and/or center- ed propositions and questions. This success notwithstanding, it seems that my uniform type for experiential attitude complements, (s(se; t); t), blocks an ade- quate semantic representation of concrete-object DPs. This is due to the fact that – on certain assumptions about the cardinality of Ds and De – intensional generalized quantifiers do not have a true embedding in the domain of questions (see Sect. 2.1) and that, in envisioned PCQ-representations of intensional quanti- fiers, the ‘host’ parameter (w1) and the individual center of the matrix attitudi- nal alternatives (y) in a PCQ need to be semantically inert (a similar observa- tion is made in [47]). For matrix centers y, failure to respect this inertness would result in an inability to capture relations between concrete object-denoting DPs (e.g. a crazy hat) and subject-controlled gerundive small clauses (e.g. PRO wear- ing a crazy hat) that have this DP in complement object position (see (11-i)). Despite the above, concrete DP complements of remember still allow for a representation in the type for PCQs. This is due to the intuitive equivalence of embedded object DPs with gerundive small clauses of the form ‘there being [dp ] (in the subject’s remembered scene)]’ (see [21, 35], based on [31]): (34) a. Ron remembers [a (viz. Mary’s) crazy hat] ≡ b. Ron remembers [a crazy hat being there (in Ron’s contextually rel- evant remembered event/scene)] My quantifier-to-PCQ shifter E-qtf (in (35)) exploits this equivalence. This shif- ter sends quantifiers Q to sets of world/centered proposition-pairs whose second element is a subset of the set of ‘boring’ centered worlds in which Q has a type-e referent. In (35), E is a world-relative existence (see [19, p. 117 ff.]). Modelling Selectional Super-Flexibility 11

(s;((s;(e;t));t)) (35) E-qtf := λQ λhw1,Ci[∀w2. (∀y.C(w2, y)) → Qw2 (E)] By applying E-qtf to the intensional quantifier-interpretation of the object DP in (8e) (see (12a)), we obtain the PCQ in (36). The last line of (36) uses the assumption that any object that is a crazy hat in some world exists in this world:   (36) E-qtf a crazy hat ≡ E-qtf λwλP ∃x. crazy-hatw(x) ∧ Pw(x) J K = λhw1,Ci[∀w2. (∀y. C(w2, y)) → (∃x. crazy-hatw2 (x) ∧ Ew2 (x))]

≡ λhw1,Ci[∀w2. (∀y. C(w2, y)) → (∃x. crazy-hatw2 (x))] Granted the availability of a type-shifter from properties to intensional gener- alized quantifiers (viz. an intensional version of Partee’s [32] type-shifter BE, aka , ∃-clos; in (37)), E-qtf also enables the PCQ-representation of property-based semantics for object DPs (see (12b)). This representation (in (39); see (38)) is exactly the PCQ in (36), as desired.

(s;(e;t)) 0 0 (37) ∃-clos := λP λwλP (∃x)[Pw(x) ∧ Pw(x)] (38) E-pty := λP (s;(e;t))[E-qtf(∃-clos(P ))]

≡ λP λhw1,Ci[∀w2.(∀y.C(w2, y)) → (∃x. Pw2 (x) ∧ Ew2 (x))]

(39) E-pty(crazy-hat) = λhw1,Ci[∀w2. (∀y.C(w2, y)) → (∃x. crazy-hatw2 (x))]

4.2 Capturing semantic relations between complements The uniform representation of the different semantic complements of remember straightforwardly captures the semantic relations in (10) and (11). In particular, the semantic inclusion relation between the complements in (11-i) takes the form of a set-theoretic containment of the powerset P {hw2, yi | ∃x. crazy-hatw (x) ∧   2 wearw2 (x)(y)} in P {hw2, yi | ∃x. crazy-hatw2 (x)} (see (40)). This containment is due to the inclusion of the set {hw2, yi | ∃x. crazy-hatw2 (x) ∧ wearw2 (x)(y)} in the set {hw2, yi | ∃x. crazy-hatw2 (x)}. (In virtue of this inclusion, any subset of the former is also a subset of the latter.) (40) a. E-decl PRO wearing a crazy hat  J K = λhw1,Ci[∀w2. (∀y. C(w2, y) → (∃x. crazy-hatw2 (x)∧wearw2 (x)(y)))] ⊆ b. E-qtf a crazy hat  J K = λhw1,Ci[∀w2. (∀y.C(w2, y)) → (∃x. crazy-hatw2 (x))] ≡ ≡ λhw1,Ci[∀w2. (∀y.C(w2, y)) → (∃x. crazy-hatw2 (x) ∧ Ew2 (x))] = E-decl a crazy hat being there  J K Notably – in line with our intuitions – my uniform semantics for remember- complements does not predict the obtaining of a semantic inclusion relation be- tween the complements in (41). This is due to the fact that P {hw2, yi | ∃x. crazy-  hatw2(x)} is not contained in the union of P {hw2, yi | ∃x. crazy-hatw (x)∧wearw2   2 (x)(y)} and P {hw2, yi | ¬∃x. crazy-hatw2(x) ∧ wearw2(x)(y)} . (41) a. Bill remembers [whether he himself was wearing a crazy hat] 666⇒ b. Bill remembers [a crazy hat] 12 K. Liefke

5 Future Work

In this paper, I have focused on the uniform interpretation of the different syn- tactic complements of remember. To provide a fully explanatory account of the entailment relations in (9)–(11), we would also need to specify the compositional semantics of the verb remember itself. The previous sections suggest that such specification can proceed analogously to the interpretation of responsive verbs in [36], resulting in a single, type-(s; ((s (se; t); t); (e; t))), interpretation of remem- ber. However, this interpretation fails to account for the difference between the complements in (42a) and (42b) (granted that non-controlled gerundive small clauses commonly receive the same interpretation as that-clauses; see e.g. [35]).

(42) a. Ron remembers [that Mary was wearing a crazy hat] ≡ Ron remembers [the fact that Mary was wearing a crazy hat] 666⇒ b. Ron remembers [Mary wearing a crazy hat] ≡ R. remembers [a (specific) event in which Mary was wearing ...]

To capture the semantic difference between (42a) and (42b), I have proposed (in [22]) to distinguish two same-type lexical entries for remember that are associated with semantic [≈ propositional] (e.g. (42a)) and with episodic [≈ event-]memory (e.g. (42b); see [39]). I leave the transfer(-to-PCQ) of these ideas for future work. I close this paper with a comment on the selection behavior of non-veridical experiential attitude verbs (e.g. imagine, dream, hallucinate): The possibility of coding the different semantic complements of experiential attitude verbs as PCQs suggests that the complements of non-veridical experiential attitude verbs can also be uniformly interpreted in this type. However, such interpretation would wrongly predict that these verbs also take interrogative complements (see (43b)):

(43)  a. that Mary is wearing a crazy hat   b. ??whether Mary is wearing a crazy hat Ida imagines c. Mary / d. PRO wearing a crazy hat   e. a crazy hat To provide an explanatory account of the anti-rogativity of non-veridical experi- ential attitude verbs, it does not suffice to stipulate a type-difference (viz. (s (se; t); t) vs. (s (se; t))) between the complements of veridical and non-veridical experi- ential attitude verbs (see [37, 42]). Rather, such account requires to in- dependently observable lexical-semantic properties of these verbs. I conjecture that relevant properties will include the presence (for veridical) resp. absence (for non-veridical experiential attitude verbs) of a ‘decidability’- on the verb’s complement. This presupposition assumes the existence of a fact of the matter that determines whether the complement is true at the evaluation world. In some respects, this move resembles Uegaki and Sudo’s [42] account of the anti- rogativity of non-veridical preferential verbs (e.g. wish, hope, fear). It remains to be seen whether this account can be used to explain the anti-rogativity of non- veridical representational verbs like imagine. Bibliography

[1] Anand, P.: Suppositional projects and subjectivity. Ms. https://l.rub. de/80d3047e (2011) [2] Barwise, J.: Scenes and other situations. J. of Philosophy 78(7) (1981) [3] van Benthem, J.: Language in Action. North-Holland, Amsterdam (1991) [4] Blumberg, K.: Counterfactual attitudes and the relational analysis. Mind 127(506), 521–546 (2018) [5] Blumberg, K.: Desire, Imagination, and the Many-Layered Mind. Ph.D. thesis, NYU (2019) [6] Chierchia, G.: and attitudes de se. Semantics and Contextual Expression 11, 1–31 (1989) [7] Ciardelli, I., Groenendijk, J., Roelofsen, F.: Inquisitive Semantics. OUP, Oxford (2018) [8] Ciardelli, I., Roelofsen, F., Theiler, N.: Composing alternatives. Linguistics & Philosophy 40(1), 1–36 (2017) [9] Coppock, E., Wechsler, S.: The proper treatment of egophoricity in Kath- mandu Newari. In: Jaszczolt, K.M. (ed.) Expressing the Self, OUP. https: //open.bu.edu/handle/2144/27880 (ta) [10] Egan, A.: Secondary qualities and self-location. Philosophy and Phenomeno- logical Research 72(1), 97–119 (2006) [11] Grimshaw, J.: Complement selection and the lexicon. Linguistic Inquiry 10(2), 279–326 (1979) [12] Groenendijk, J.A.G., Stokhof, M.J.B.: Studies on the Semantics of Ques- tions and the of Answers. Ph.D. thesis, U. of Amsterdam (1984) [13] Hamblin, C.L.: Questions in Montague English. In: , pp. 247–259, Elsevier (1976) [14] Higginbotham, J.: Remembering, imagining, and the first person. In: Bar- ber, A. (ed.) Epistemology of Language, pp. 496–533, OUP, Oxford (2003) [15] Hintikka, J.: Semantics for propositional attitudes. In: Models for Modali- ties, Synthese Library, vol. 12, pp. 87–111, Springer, Dordrecht (1969) [16] Karttunen, L.: Syntax and semantics of questions. L & P 1(1), 3–44 (1977) [17] Lahiri, U.: Questions and Answers in Embedded Contexts. OUP (2002) [18] Lewis, D.: Attitudes de dicto and de se. Phil. Review 88(4), 513–543 (1979) [19] Liefke, K.: A Single-Type Semantics for Natural Language. Ph.D. thesis, Tilburg University (2014) [20] Liefke, K.: Reasoning with an (experiential) attitude. In: Fujikawa, N. (ed.) New Frontiers in AI, LNCS/LNAI, vol. 12331, pp. 276–293, Springer (2020) [21] Liefke, K.: Saving Hamlet ellipsis. In: Logic and Algorithms in Computa- tional Linguistics 2018, SCI, vol. 860, pp. 17–43, Springer (2020) [22] Liefke, K.: Two kinds of English non-manner how-complements. Ms. https: //ling.auf.net/lingbuzz/005455 (2020) [23] Liefke, K., Werning, M.: Evidence for single-type semantics: an alternative to e/t-based dual-type semantics. J. of Semantics 35(4) (2018) 14 K. Liefke

[24] Maier, E.: Parasitic attitudes. L & P 38(3), 205–236 (2015) [25] Moltmann, F.: Intensional verbs and quantifiers. Nat. Lang. Sem. 5 (1997) [26] Montague, R.: Universal grammar. Theoria 36(3), 373–398 (1970) [27] Ninan, D.: Imagination, Content, and the Self. Ph.D. thesis, MIT (2008) [28] Ninan, D.: De se attitudes: ascription and communication. Philosophy Com- pass 5(7), 551–567 (2010) [29] Ninan, D.: Counterfactual attitudes and multi-centered worlds. Semantics & Pragmatics 5(5), 1–57 (2012) [30] Orey, S.: Model theory for the higher order predicate calculus. Transactions of the American Mathematical Society 92(1), 72–84 (1959) [31] Parsons, T.: Meaning sensitivity and grammatical structure. In: Dalla Chiara, M.L. (ed.) Structures and Norms in Science, pp. 369–383, Springer (1997) [32] Partee, B.: Noun phrase interpretation and type-shifting principles. In: Groenendijk et al., J. (ed.) Studies in Representation Theory and the Theory of Generalized Quantifiers, pp. 115–143, Dordrecht (1987) [33] Roelofsen, F.: Algebraic foundations for the semantic treatment of inquisi- tive content. Synthese 190(1), 79–102 (2013) [34] Stephenson, T.: Control in centred worlds. J. Sem. 27(4), 409–436 (2010) [35] Stephenson, T.: Vivid attitudes: centered situations in the semantics of remember and imagine. In: Proc. of SALT XX, pp. 147–160 (2010) [36] Theiler, N., Roelofsen, F., Aloni, M.: A uniform semantics for declarative and interrogative complements. Journal of Semantics 35(3), 409–466 (2018) [37] Theiler, N., Roelofsen, F., Aloni, M.: Picky predicates: why believe doesn’t like interrogative complements, .... Nat. Lang. Sem. 27(2), 95–134 (2019) [38] Tich´y,P.: Foundations of partial . Journal of Symbolic Logic 48(2), 525–525 (1983) [39] Tulving, E.: Episodic and semantic memory. In: Tulving, E., Donaldson, W. (eds.) Organization of Memory, pp. 381–402, Academic Press (1972) [40] Uegaki, W.: Content nouns and the semantics of question-embedding. J. of Semantics 33 (2016) [41] Uegaki, W.: The semantics of question-embedding predicates. Language and Linguistics Compass 13(1), e12308 (2019) [42] Uegaki, W., Sudo, Y.: The ∗hope-wh puzzle. Natural Language Semantics 27(4), 323–356 (2019) [43] Umbach, C., Hinterwimmer, S., Gust, H.: German wie-complements: Man- ners, methods and events in progress. http://tinyurl.com/wxm5lp5 (Ms) [44] White, A.S., Rawlins, K.: A computational model of S-selection. In: Proc. of SALT XXVI, pp. 641–663 (2016) [45] Zimmermann, T.E.: On the proper treatment of opacity in certain verbs. Natural Language Semantics 1(2) (1993) [46] Zimmermann, T.E.: Painting and opacity. In: Von Rang und Namen: Philo- sophical essays in honour of Wolfgang Spohn, pp. 427–453, Mentis (2016) [47] Zimmermann, T.E.: Quantification over alternative . Semantics & Pragmatics 10(8), 1–25 (2017) [48] Zimmermann, T.E.: Towards a general theory of type shifting. Invited talk at SALT XXX (2020)