1 Gradient Grammaticality of the Indefinite Implicit Object Construction in English Tamara Nicol Medina IRCS, University of Pennsylvania Collaborators: Barbara Landau 1, Géraldine Legendre 1, Paul Smolensky 1, Philip Resnik 2 1 Johns Hopkins University, Department of Cognitive Science 2 University of Maryland, Department of Linguistics, Department of Computer Science

2 The (Indefinite) Implicit Object Construction (in English) John is eating John is reading Verb selects for an object, but none is overtly specified. Interpretation is of an indefinite and non- specific object. (something / some food). (something / written material). * John is reading (War and Peace). Grammaticality varies across verbs. * John is pushing. * John is opening. Verb Semantic Selectivity Aspect (Telicity, Perfectivity)

3 Overview 1. Factors that Affect Grammaticality of an Implicit Object Verb Semantic Selectivity Aspectual Properties (Telicity, Perfectivity) 2. Grammaticality Judgment Study 3. Linguistic Analysis (Optimality Theory) 4. Estimation of Constraint Ranking Probabilities 5. Implications for Acquisition

4 Verb Semantic Selectivity The omitted object tends to be recoverable from the verb. John is eating (some food) / drinking (a beverage) / singing (a song). Verbs that select for a wide variety of semantic complements, and therefore there is no one recoverable interpretation, tend to resist implicit objects. John is bringing *(something) / making *(something) / hanging *(something). Indefinite implicit objects are allowed to the extent that they are recoverable.

5 Selectional Preference Strength (SPS) (Resnik, 1996) Don’t push your brother. Move that chair. Do you want an apple? “like” Tony likes that girl. I don’t like this couch. I really like bananas. “eat” Eat your lunch. He’s eating cereal. She always eats avocados. An information-theoretic model of verbs’ strength of semantic preferences. Calculates the strength of a verb’s selection for the semantic argument classes from which its complements (or objects) are drawn. For all argument classes (c), PRIOR, Pr(c) – the overall distribution of argument classes POSTERIOR, Pr(c|v i ) – the distribution of argument classes, given a particular verb The greater the difference between Pr(c) and Pr(c|v i ), the higher SPS will be. (Argument classes were those listed in WordNet.)

6 Selectional Preference Strength (SPS) (Resnik, 1996) SPS correlated with experimental measures of recoverability and ease of inference (Resnik, 1996). –SPS corresponds to what people know about verbs’ selectional preferences. SPS correlated with rate of object omission in Brown corpus of American English (adult written English) (Resnik, 1996). –SPS directly affects syntax.

7 SPS and Implicit Objects Relative SPS is correlated with the relative frequency of an implicit object. Brown corpus of American English ( Francis and Kučera, 1982 ) SPS % Implicit Objects SPS r = 0.48, p < 0.05

8 Verb Semantic Selectivity High SPS is a necessary, but not sufficient condition on object omissibility. –Some verbs with high SPS do not occur with implicit objects, e.g., hang. –Not an inviolable rule. SPS is a continuous measure. How to incorporate this into a formal grammar? –As a statistical component to the grammar.

9 TELIC Existence of an inherent endpoint. ATELIC No inherent endpoint. “The ship sank.” Telicity (Lexical Aspect) “The ship floated.” A direct object serves to measure out the event. [+ Telic] “Kim is eating an apple.” incremental T HEME (Once the apple is gone, the event is over.) [+ Atelic] “Kim is eating.” [+Telic] “Kim arrived.” Requires an overt object. Does not require an overt object.

10 Telicity (Lexical Aspect) Atelicity is a necessary, but not sufficient condition on object omissibility. –Some atelic verbs do not occur with implicit objects, e.g., push, pull. –Not an inviolable rule.

11 Perfectivity (Grammatical Aspect) [+ Perfective] “Kim had written */? (something).” [+ Imperfective] “Kim was writing.” Requires an overt object. Does not require an overt object. PERFECTIVE Perspective of event endpoint. IMPERFECTIVE Perspective of ongoing event. have + past participle “The ship has sunk.” be + “-ing” “The ship is sinking.”

12 Perfectivity (Grammatical Aspect) Imperfectivity is a necessary, but not sufficient condition on object omissibility. –Perfectivity doesn’t render a sentence with an implicit object completely ungrammatical, while Imperfectivity doesn’t necessarily make it grammatical. Michelle had written ? (something).PERFECTIVE Michelle was hearing *(something).IMPERFECTIVE –Not an inviolable rule.

13 Putting the Puzzle Together No single factor completely distinguishes verbs that omit objects from verbs that do not. –SPS continuous measure which is related to the relative frequency of an implicit object. –Some Telic verbs do allow implicit objects, while some Atelic verbs do not. Michelle packed.TELIC Michelle wanted *(something).ATELIC –Perfectivity doesn’t render a sentence with an implicit object completely ungrammatical, while Imperfectivity doesn’t necessarily make it grammatical. Michelle had written ? (something).PERFECTIVE Michelle was hearing *(something).IMPERFECTIVE

14 Method Grammaticality Judgment Study Subjects 15 monolingual adult native speakers of English Stimuli 30 verbs, 160 sentences SPS (Resnik, 1996) Telicity Perfectivity Verb-Argument Structure Sentence Type Direct ObjectExample Sentence Two-Argument Verbs (n = 30) TargetImplicit Objects Michael had brought. Michael was bringing. ControlOvert Objects Sarah had brought a gift. Sarah was bringing a gift. One-Argument Verbs (n = 10) Filler No Objects Emma had slept. Emma was sleeping. Overt Objects Andrew had slept a blanket. Andrew was sleeping a blanket.

15 Results Grammaticality Judgment Study

16 Verb Semantic Selectivity (SPS) Grammaticality Judgment Study r = 0.66, p < 0.05

17 Telicity Grammaticality Judgment Study F = , p < 0.05

18 Perfectivity Grammaticality Judgment Study F = 3.63, p = 0.06

19 Summary of Findings Grammaticality Judgment Study Gradient across verbs. Effects of Verb Semantic Selectivity (SPS), Telicity, and Perfectivity.

20 Optimality Theory (Prince and Smolensky, 1993/2004) An Optimality Theoretic Analysis Formulate conditions as violable constraints, not inviolable rules. Take advantage of the component in OT called "CON", in which constraints are ranked with respect to one another. –It is the evaluation of the output candidates against the set of ranked constraints that determines the optimal output. –This will allow some constraints to have a greater effect than others.

21 Optimality Theory (Prince and Smolensky, 1993/2004) An Optimality Theoretic Analysis A strict ranking hierarchy (as in standard OT) will be shown to be too strong. Take insights from partial ranking approaches. Furthermore, will incorporate a statistical component to the ranking of constraints, which will allow for the derivation of GRADIENT grammaticality. However…

22 OT Framework catch (x,y) x = David, y = unspecified SPS=2.47 Telic, Perfective David had caught. David had caught something. * I NTERNAL A RGUMENT (* I NT A RG ) The output must not contain an overt internal argument (direct object). * I NT A RG  F AITHFULNESS TO A RGUMENT S TRUCTURE (F AITH A RG ) An internal argument in the input must be realized by an overt object. F AITH A RG    * I NT A RG F AITH A RG   T ELIC E NDPOINT (T ELIC E ND ) The internal argument must be overtly realized in the output, given Telic aspect. P ERFECTIVE C ODA (P ERF C ODA ) The internal argument must be overtly realized in the output, given Perfective aspect. T ELIC E ND P ERF C ODA  eat (x,y) x = David, y = unspecified SPS=3.51 Atelic, Imperfective David was eating. David was eating something.

23 Ranking of Constraints catch (x,y) x = David, y = unspecified SPS=2.47 Telic, Perfective David had caught. David had caught something. * I NT A RG  F AITH A RG    T ELIC E ND P ERF C ODA   * I NT A RG F AITH A RG  p(*I » F) p(*I » T) p(*I » P) * A RG OF H IGH SPS V ERB p(*I » F) x p(*I » T) x p(*I » P) = p( *I » {F, T, P} ) p(*I » F) = p(*I » T) = p(*I » P) = p(*I » F) x p(*I » T) x 1- [ p(*I » P) ] = p( P » *I » {F, T} ) Problems How to find perfect cut off value? Strictly ranked constraints won’t give rise to gradient grammaticality. What about SPS?What is needed is a flexible ranking of constraints. Partial Ranking: One or more constraints “floats” among other ranked constraints. Current Approach: NO ranked constraints, only a floating constraint. If * I NT A RG is highest ranked, then the implicit object is optimal. If F AITH A RG is highest ranked, then the overt object is optimal. Similar for T ELIC E ND and P ERF C ODA. Linear Function: As SPS increases, so does the relative ranking of * INT ARG. Joint Probabilities = Set of Rankings (a partial ranking of constraints) For each pairwise probability, such as p(*I » F), given a total probability of 1, there is the opposite probability, 1 - p(*I » F). Incorporating these gives rise to different partial rankings with different optimal outputs. catch (x,y) x = David, y = unspecified SPS=2.47 Telic, Imperfective

24 Total Set of Possible Partial Rankings Telic Perfective Telic Imperfective Atelic Perfective Atelic Imperfective *I » {F, T, P}implicit P » *I » {F, T}overtimplicitovertimplicit T » *I » {F, P}overt implicit {T, P} » *I » Fovert implicit F » *I » {T, P}overt {F, T} » *I » Povert {F, P} » *I » Tovert {F, T, P} » *Iovert 12.5% The various combinations of pairwise rankings can be captured by 8 partial rankings. –Give rise to OVERT or IMPLICIT object output depending on the aspectual properties of the input. 12.5%25% 50% NON-equiprobability p(*I » F) = 0.75 p(*I » T) = 0.85 p(*I » P) = %63.8%41.2%75% 35.1% 28.7% 6.2% 5.1% 11.7% 2.1% 9.6% 1.7% Probability of Implicit Object Calculate the probability of an IMPLICIT object output as the total proportion of rankings that give rise to it. –This is equivalent to the grammaticality of an implicit object output. –If equiprobable: 1/8 = 12.5%. Calculate the probability of an IMPLICIT object output as the total proportion of rankings that give rise to it. –This is equivalent to the grammaticality of an implicit object output. –If equiprobable: 1/8 = 12.5%. –But they are not equiprobable, since they depend on the joint pairwise ranking probabilities that compose them, and these are tied to SPS.

25 Summary of OT Analysis The grammaticality of an implicit object for a particular verb… is equivalent to the probability of the implicit object output for that input, which… depends upon the probabilities of each of the possible partial rankings, which… depends on the probabilities of *I » F, *I » T, and *I » P, which… are a function of SPS.

26 Finding the Probabilities So what are the pairwise probabilities of *I » F, *I » T, and *I » P in English? Can we even find probabilities that would work for all verbs? Use grammaticality judgment data to estimate the probabilities.

27 Estimation of the Constraint Rankings for English = p(*I » F)  p(*I » T)  p(*I » P) p(implicit) Telic Perfective = p(*I » {F, T, P}) = grammaticality judgment1.93 = x x.23

28 Estimated Probability Functions for English p(*I » F)p(*I » T)p(*I » P) Taking the grammaticality judgments as a direct reflection of the probabilities of an implicit object being generated by the grammar. Estimated what the pairwise rankings must be in order to produce these results. The probability of * I NT A RG ranked above each of the other three constraints increased with SPS. Steepest function for the relative ranking of * I NT A RG with T ELIC E ND.

29 Overall Predicted Grammaticality of An Implicit Object Best for Atelic Imperfective, worst for Telic Perfective. Increase as a function of SPS, but differentially depending on aspect type. -Telic Imperfectives show greatest effect of SPS.

30 Correlations between Judgments and Model Telic Perfective r = 0.84, p < 0.05 Telic Imperfective r = 0.88, p < 0.05 Atelic Imperfective r = -0.09, p > 0.05 Atelic Perfective r = 0.26, p > 0.05

31 What is the nature of the indefinite implicit object construction in the adult grammar? OT Analysis The grammaticality of an implicit object across verbs is –Gradient. –Reduced in accordance with SPS, Telicity, and Perfectivity. For any verb, if you know SPS, Telicity, and Perfectivity, then the grammar generates a relative grammaticality for the implicit object output with that verb.

32 Linguistic Analysis Turning to acquisition, we can now ask what the learner’s task must involve: Find p(*I » F), p(*I » T), and p(*I » P). How? The model’s values were estimated from grammaticality judgments. But children don’t “hear” grammaticality judgments! -Occurrence of implicit indefinite objects: increase ranking of * I NT A RG. -Occurrence of overt indefinite objects: reduce ranking of * I NT A RG.

33 Implications for Acquisition For example, Assign a grammaticality of 0 for any verb that never occurs with an implicit object. Assign a grammaticality of 1 for any verb that occurs with an implicit object at least 20% of the time. Assign a grammaticality of 0.50 for any verb that occurs with an implicit object infrequently: 0 – 20% of the time.

34 Conclusions The grammaticality of the indefinite implicit object construction is –Gradient, as shown in the Grammaticality Judgment Study. –Determined by a combination of factors, including Verb Semantic Selectivity (SPS), Telicity, and Perfectivity. It is possible to derive gradient grammaticality, by allowing constraints to "float" and assessing grammaticality over the total set of possible rankings. Estimation of the constraint ranking probabilities for English showed that it is, in fact, possible to find rankings that capture the phenomenon with low error. Raises interesting questions for acquisition: –What is the state of the child's early grammar? –How does the learner adjust her grammar in accordance with what she hears in the child-directed input (not grammaticality judgments) in order to arrive at a grammar that displays gradient judgments?