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On Krifka’s “Nominal Reference, TemporalConstitutionandQuantification in Event Semantics”

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Abstract

Krifka, in his paper “Nominal reference, temporal constitution and quantification in event semantics”, provides the first formal mereological (algebraic) analysis of the relation between nominal reference and temporal constitution (also based on his 1986 PhD thesis). The focus is on two manifestations of this relation in the grammar of natural languages. First, as many observed, there are direct structural analogies between the following two sets of distinction: namely, mass/count and atelic/telic. They are clearly reflected in their parallel cooccurrence patterns with quantifiers, numerical and measure expressions. Second, nominal reference and temporal constitution interact and mutually constraint each other in the derivation of meaning of complex verbal predicates. One key example is aspectual composition(ality) e.g., eat soup (atelic) versus eat two apples (telic). In order to provide an adequate analysis of the relevant data Krifka’s principal innovation is to assume a single join semi-lattice structure, undetermined with respect to atomicity, relative to which he defines two higher-order, cross-categorial predicates for reference types of natural language predicates: namely, quantized and cumulative. Specifically in the case of aspectual composition, the interactions and mutual constraints between the structure of objects and eventualities stem from the systematic mappings (homomorphisms) whose source is the lexical semantics of verbs. Such mappings are also independently motivated by other phenomena exhibiting systematic interactions objects and eventualities.

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Notes

  1. 1.

    The term ‘temporal constitution’is a translation of the German ‘Zeitkonstitution’, coined by François (Francois, 1985).

  2. 2.

    The use “count nouns (or NPs)” and “mass nouns (or NPs)” here reflects the fact that there is no general agreement concerning the level of linguistic description on which these categories are grammatically relevant. Starting with Verkuyl (1971, 1972) at least, there have been debates whether the telic/atelic distinction, and subsequently also the mass/count distinction (Pelletier & Schubert, 2002), are distinctions that are relevant at the level of lexical items at all, and whether they should instead be viewed as distinctions at the level of phrasal constructions, as constructional properties of NPs, VPs and sentences.

  3. 3.

    For Krifka (1989, 1998), these two sets of distinctions are taken to be semantic properties of nominal and verbal predicates, rather than being inherent in entities in the domain, in the external world. There are debates and numerous misunderstandings concerning the status of these categories. The key question is whether these are ontological categories (Bach, 1986; Parsons, 1990, i.a.) or whether these are categories that are properties of verbal and nominal predicates (Krifka, 1986, 1989; Filip Filip, 1993a, b; Partee, 1999, i.a.) (See Filip, 2011, 2012 for summaries of these debates.)

  4. 4.

    There is a long-standing tradition of observations related to aspectual composition(ality), which can be traced to the nineteenth century philology (e.g., Streitberg, 1891). Some notable precursors are Poutsma (1926) and Jacobsohn (1933) (cited by Verkuyl, 1971, 1972, also 2005 and elsewhere, who credits them as the major sources of inspiration for his theory of aspectual compositionality), Garey (1957) (inspiration for Filip, 1985 and Krifka, 1986) and Leech (1969, p.137) who speaks of ‘semantic concord’ between nominal arguments and complex verbal predicates.

  5. 5.

    The interpretations that are relevant for this test concern the temporal extent of singular eventualities denoted by predicates in the scope of these temporal modifiers. The interpretations that are irrelevant are iterative and generic interpretations. Moreover, for time-span modifiers, we need disregard the shifted inchoative interpretation of atelic predicates under which the time-span modifier denotes the measure of time until the onset of denoted eventualities from ‘now’ or some other reference point (see also Vendler, 1957, p. 147) (e.g., The children ran in an hour understood as meaning they started running after an hour from some understood reference point), and for durative modifiers, the irrelevant interpretations regard the duration of the result state that follows the set terminal point in the denotation of telic verbal expressions (e.g., John put the wine into the fridge for half an hour).

  6. 6.

    This, among others, obviates the minimal part problem posed by the putative divisive reference of mass nouns and process-denoting (atelic) predicates (Taylor, 1977; Bach, 1981, i.a.), and also unintuitive results such that there is a sharp sortal difference between what walk (atelic, non-atomic domain) and walk a mile (telic, atomic domain) describe, even though it arguably is the same eventuality in the world under two different descriptions (Krifka, 2001).

  7. 7.

    In compliance with later developments in event semantics, here the term ‘eventuality’ (coined by Bach, 1981) is used instead of ‘event’, given that ‘event’ is now restricted to mean an entity in the denotation of telic (accomplishment, and also achievement, according to some at least) predicates, and given that by ‘events’ Krifka (1989) intends to cover the domain from which both telic and atelic predicates draw their denotation.

  8. 8.

    Krifka (1989) uses S, rather than O, for the relevant predicate variable.

  9. 9.

    For a formal definition of an extensive measure function see Champollion and Krifka, 2016, §13.21.

  10. 10.

    Schwarzschild (2002, 2006) relies on a closely related property of monotonocity in his analyses of closely related phenomena.

  11. 11.

    Measure phrases, such as five meters, are of type [N/N] and analyzed by means of the number (n) expressed by the numerical word (five) and a measure function (μ), expressed by some measure word (meter). Syntactically speaking, numericals (five) belong to a basic category NM (numerical number), and consequently measure words (meter) have the category [N/N, NM] (see (4), Krifka (1989, p.83).

  12. 12.

    Krifka (1989) analyzes extensive measure phrases (such as five ounces(of)) as ‘quantizing modifiers’ that derive quantized predicates from non-quantized ones, namely, denoted by mass terms (beer, gold) and plural terms (apples): ∀P∀P[qmodo(P,P) ↔ ¬qua(P) ∧ qua(P(P))] (Krifka, 1989, D28, p.82). In later works, he specifies the input of measure phrases in terms of the property of cumulative reference.

  13. 13.

    This is reminiscent of Strawson’s (1959) view that the possibilities for identifying eventualities without reference to objects are limited, because eventualities fail to provide “a single, comprehensive and continuously usable framework” of reference of the kind provided by physical objects (Strawson, 1959, p. 46ff.).

  14. 14.

    “An hour full of running is naturally assumed to be without gaps, like a bathtub full of water. A year full of winning (iterative) has got to have gaps, like a street full of policemen” (Vlach, 1981, p. 282, fn. 17).

  15. 15.

    As Krifka (1998, and elsewhere) also observes, similar notions and relations mediating between participants and eventualities were proposed by others: e.g., [+ADD-TO] V property (Verkuyl, 1972, 1993), ‘measuring out’ tied to the internal direct object DP (Tenny, 1987, 1994), ‘structure-preserving binding relations’ (Jackendoff, 1996).

  16. 16.

    Dowty’s (1987, 1989, 1991) treatment of Incremental Theme as one of the lexical determinants of argument selection is not entirely uncontroversial. For instance, Jackendoff (1996), Rappaport Hovav and Levin (2002, 2005, pp. 284–285) argue that Incremental Theme is not a factor in argument selection, while agreeing that the intuition behind it, which concerns structure-preserving mappings between eventualities and some suitable objects, plays an important role in a variety of aspectual phenomena.

  17. 17.

    Related observations were also made by L. Carlson (1981), Mittwoch (1988), Dahl (1991) and Moltmann (1991).

  18. 18.

    Borer (2005) argues that a telic interpretation must be licensed by a quantity DP, with a definite DP being one subtype, including definite mass nouns and definite plurals.

  19. 19.

    This idea is inspired by the Localist Theory (Gruber, 1965), which inspired the framework of Conceptual Semantics of Jackendoff (1991, 1996).

  20. 20.

    Kagan (2013) applies this idea to a full-fledged scalar approach to the semantics of Russian prefixes.

  21. 21.

    The line between incremental and non-incremental verbs is not always easy to draw, given that nearly all episodic verbs may be interpreted as incremental in a suitable context, cp. ‘latent incremental theme verbs’ (Rappaport Hovav & Levin, 2005).

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Appendix

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(1)

Temporal trace function τ: E → T

Krifka (1989), p. 97 (D 40)

 

∀e∀e’[τ(e ∪E e’) = τ(e) ∪T τ(e’)]

 
 

The run time of the sum of two events e and e’ is the sum of the run time of e and the run time of e’.

(2)

Locative trace function: π: E → L

Lasersohn (1995), Krifka (1998)

 

∀e∀e’[π(e ∪Ee’) = π(e) ∪L π(e’)]

 

The path trace of the sum of two events e and e’ is the sum of the path trace of e and the path trace of e’.

 

Example: [[walk two miles]] = λx,e[walk(x,e) ∧ agent(e,x) ∧

 

mile(π(e)) = 2]

 

A set of sums of walking eventualities, each to the amount of two miles

(3)

a derived measure function μ’. Intuitively, it describes the transfer of a measure function from one domain to another, on the assumption that there is a homomorphism h from one domain to the other, i.e., a function that preserves some structural relation defined on its domain in a similar relation defined on the range (Krifka, 1989, p.80). For example, a measure function μ for times like hour, week or year can be used as a derived measure function μ’ on temporal traces of eventualities:

 

(a) ∀e[μ’(e) = μ(τ(e))] Krifka (1989), p. 97 (D41)

 

 where τ(e) = t, the temporal trace of e

 

(b) hour’(e) = hour(τ(e))

 

(c) ⟦sing for an hour⟧ = λx,e[sing(e) ∧ agent(e,x) ∧ hour’(e) = 1]

(4)

Two-place predicates that capture the structure-preserving ‘transfer’ properties of thematic relations that mediate between objects and eventualities (Krifka, 1998, D 29-D 33, p. 92, and 2001)

 

 • Summativity (cumulativity)

 

 ∀R[sum(R) ↔∀e,e’,x,x’ [R(e,x) ∧ R(e’,x’) → R(e∪Ee’, x∪Ox’)]]

 

 A general condition for the relation between thematic relations and the join operations. For example, two events of drinking a glass of wine yield an event of drinking two glasses of wine (Krifka, 1989, D29, p.92).

 

 • Uniqueness for Objects

 

 ∀R[uni-o(R) ↔∀e,x,x’[R(e,x) ∧ R(e,x’) → x = x’]]

 

 There canbenotwo distinctobjectswhichbearthethematicrelationR to the same event (Krifka, 1989, D30).

 

 • Uniqueness for Eventualities

 

 ∀R[uni-e(R) ↔ ∀e,e’,x[R(e,x) ∧ R(e’,x) → e = e’]]

 

 There can be no two distinct events which bear R to the same object, that is, an event is related to a specific object. E.g., adrinking of aglass of wine is rela -ted only to this glass of wine as a theme/patient and to nothing else (Krifka, 1989, D31).

 

 (o.k.: eat, write; not o.k.: read, see, push, ride)

 

 • Mapping to Subobjects

 

 ∀R[map-o(R) ↔∀e,e’,x [R(e,x) ∧ e’ ⊂ Ee → ∃ x’[x’ ⊂ Ox ∧ R(e’,x’)]]

 

 If an event bears R to anobject,anysubpart of the event bears R to some subpart of the object. E.g. every proper subpart of anevent eof drinking aglass of wine corresponds to a proper subpart of the glass of wine (Krifka, 1989, D32).

 

 (o.k.: eat, write; not o.k.: read, see, push, ride)

 

 • Mapping to Subeventualities

 

 ∀R[map-e(R) ↔∀e,x,x’[R(e,x) ∧ x’ ⊂ Ox → ∃e’[e’ ⊂ Ee ∧ R(e’,x’)]].

 

 If an event bears R to an object, any subpart of the object bears R to some subpart of the event (Krifka, 1989, D32).

 

 (o.k.: eat, write, read; not o.k.: see, push, ride)

(5)

Classification of thematic relations (Krifka, 1989, p. 96 (14), 1998, 2001)

Example

sum

uni-o

map-e

map-o

uni-e

 

eat an apple, write a letter

+

+

+

+

+

Strictly Incremental Theme

read a book

+

+

+

Incremental Theme

push a cart,see a movie

+

+

Theme/Stimulus

(6)

a.

Strictly Incremental Theme:

∀R[sinc(R) ↔ uni-o(R) ∧ map-o(R) ∧ map-e(R) ∧ uni-e(R)]

 

b.

Incremental Theme:

∀R[inc(R) ↔ uni-o(R) ∧ map-o(R) ∧ map-e(R)]

(7)

Maximal Participant:

 

∀x[max(P, x) ↔ P(x) ∧ ¬∃y[P(y) ∧ x < y]] Zucchi and White (1996, 2001)

 

An individual is a maximal P iff it is P and it is not a proper part of another P.

(8)

write a sequence ⟧ = λyλe∃x[write’(e) ∧ ag(y, e) ∧ pat (x, e) ∧

 

max (λz∃e’[write’(e’) ∧ ag(y, e’) ∧ pat(z, e’) ∧ sequence’(z) ∧ τ(e’) ≤ tR], x)]

 

Zucchi and White (2001), p. 261)

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Filip, H. (2022). On Krifka’s “Nominal Reference, TemporalConstitutionandQuantification in Event Semantics”. In: McNally, L., Szabó, Z.G. (eds) A Reader's Guide to Classic Papers in Formal Semantics. Studies in Linguistics and Philosophy, vol 100. Springer, Cham. https://doi.org/10.1007/978-3-030-85308-2_14

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