Gradient Grammaticality of the Indefinite Implicit Object Construction in English

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

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

4. Verb Semantic Selectivity 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. The omitted object tends to be recoverable from the verb. Indefinite implicit objects are allowed to the extent that they are recoverable. John is bringing *(something) / making *(something) / hanging *(something).

5. Selectional Preference Strength (SPS) (Resnik, 1996) 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. “eat”Eat your lunch.He’s eating cereal.She always eats avocados. “like”Tony likes that girl.I don’t like this couch.I really like bananas. Don’t push your brother.Move that chair.Do you want an apple? For all argument classes (c), PRIOR, Pr(c) – the overall distribution of argument classes POSTERIOR, Pr(c|vi) – the distribution of argument classes, given a particular verb The greater the difference between Pr(c) and Pr(c|vi), 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) % Implicit Objects SPS 4.80 SPS r = 0.48, p < 0.05 0.72

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. Telicity (Lexical Aspect) TELICExistence of an inherent endpoint.ATELICNo inherent endpoint. “The ship sank.” Requires an overt object. “The ship floated.” Does not require an overt object. A direct object serves to measure out the event.[+ Telic]“Kim is eating an apple.”incremental THEME(Once the apple is gone, the event is over.)[+ Atelic]“Kim is eating.”[+Telic]“Kim arrived.”

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

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. Grammaticality Judgment Study Method Subjects 15 monolingual adult native speakers of English Stimuli 30 verbs, 160 sentences SPS (Resnik, 1996) Telicity Perfectivity

15. Grammaticality Judgment Study Results

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

17. Grammaticality Judgment Study Telicity F = 11.357, p < 0.05

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

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

20. An Optimality Theoretic Analysis Optimality Theory(Prince and Smolensky, 1993/2004) • 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. An Optimality Theoretic Analysis Optimality Theory(Prince and Smolensky, 1993/2004) However… • 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.

22. OT Framework catch (x,y) x = David, y = unspecified SPS=2.47 Telic, Perfective eat (x,y) x = David, y = unspecified SPS=3.51 Atelic, Imperfective FAITH ARG * INT ARG FAITH ARG * INT ARG TELIC END PERF CODA      David had caught. David had caught something. David was eating. David was eating something.    * INTERNAL ARGUMENT (* INT ARG) The output must not contain an overt internal argument (direct object). FAITHFULNESSTO ARGUMENT STRUCTURE (FAITH ARG) An internal argument in the input must be realized by an overt object. TELIC ENDPOINT (TELIC END) The internal argument must be overtly realized in the output, given Telic aspect. PERFECTIVE CODA (PERF CODA) The internal argument must be overtly realized in the output, given Perfective aspect.

23. Ranking of Constraints catch (x,y) x = David, y = unspecified SPS=2.47 Telic, Imperfective catch (x,y) x = David, y = unspecified SPS=2.47 Telic, Perfective * ARGOF HIGH SPS VERB * INT ARG FAITH ARG FAITH ARG * INT ARG TELIC END PERF CODA      David had caught. David had caught something.    If * INT ARG is highest ranked, then the implicit object is optimal. • 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. What about SPS? • Problems • How to find perfect cut off value? • Strictly ranked constraints won’t give rise to gradient grammaticality. p(*I » F) p(*I » T) p(*I » P) p(*I » F) x p(*I » T) x p(*I » P) = p( *I » {F, T, P} ) Joint Probabilities = Set of Rankings (a partial ranking of constraints) • If FAITH ARG is highest ranked, then the overt object is optimal. • Similar for TELIC END and PERF CODA. p(*I » F) x p(*I » T) x 1- [ p(*I » P) ] = p( P »*I » {F, T} ) 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. p(*I » F) = Linear Function: As SPS increases, so does the relative ranking of * INT ARG. p(*I » T) = p(*I » P) =

24. Total Set of Possible Partial Rankings Probability of Implicit Object NON-equiprobability p(*I » F) = 0.75 p(*I » T) = 0.85 p(*I » P) = 0.55 12.5% 35.1% 63.8% 25% 41.2% 25% 75% 50% 12.5% 35.1% 12.5% 28.7% 6.2% 12.5% 5.1% 12.5% 12.5% 11.7% 12.5% 2.1% 12.5% 9.6% 12.5% 1.7% • 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. • 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%. • 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.

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(implicit)Telic Perfective = p(*I » {F, T, P}) = p(*I » F)  p(*I » T)  p(*I » P) = x x = grammaticality judgment 1.93 .23

28. Estimated Probability Functions for English • 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. p(*I » F) p(*I » T) p(*I » P) • The probability of * INT ARG ranked above each of the other three constraints increased with SPS. • Steepest function for the relative ranking of * INT ARG with TELIC END.

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 Perfectiver = 0.84, p < 0.05 Telic Imperfectiver = 0.88, p < 0.05 Atelic Perfectiver = 0.26, p > 0.05 Atelic Imperfectiver = -0.09, p > 0.05

31. OT Analysis What is the nature of the indefinite implicit object construction in the adult grammar? • 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 * INT ARG. • Occurrence of overt indefinite objects: reduce ranking of * INT ARG.

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?