Prepositions Matter in Quantifier Scope Disambiguation (2022)

Abstract: Although it is widely agreed that world knowledge plays a significant role in quantifier scope disambiguation (QSD), there has been only very limited work on how to integrate this knowledge into a QSD model. This paper contributes to this scarce line of research by incorporating into a machine learning model our knowledge about relations, as conveyed by a manageable closed class of function words: prepositions. For data, we use a scope-disambiguated corpus created by AnderBois, Brasoveanu and Henderson, which is additionally annotated with prepositional senses using Schneider et al’s Semantic Network of Adposition and Case Supersenses (SNACS) scheme. By applying Manshadi and Allen’s method to the corpus, we were able to inspect the information gain provided by prepositions for the QSD task. Statistical analysis of the performance of the classifiers, trained in scenarios with and without preposition information, supports the claim that prepositional senses have a strong positive impact on the learnability of automatic QSD systems.

## introduction qsd is a problem in natural language processing that arises in connection with sentences that contain multiple quantified nps: sentence (1) can be understood to mean that every kid climbed a possibly different tree. this is the so-called surface scope reading where the first quantified np has wider scope than the second, corresponding to the surface ordering of the two nps in the sentence: every @xmath0. the other, and usually less preferred, reading is the one in which there is a single tree that all the kids climbed. this is the inverse scope reading where the second quantified np has wider scope than the first, reversing the order of the two nps in the sentence: a @xmath1. many studies on quantifier scope have dealt with the issue of generating the set of possible scope readings for a sentence like (1), both from a theoretical perspective @xcite @xcite @xcite and computationally @xcite @xcite @xcite @xcite @xcite . a much smaller number of studies have focused on statistical and automatic qsd and the problem of identifying the set of factors relevant to scope preferences @xcite @xcite . these studies have shown, mostly in line with what was proposed in the semantics literature and borne out in psycholinguist work @xcite @xcite @xcite @xcite @xcite , that the grammatical role (i.e., subject and object) and lexical realization of a quantifier have an effect on scope-taking; linear precedence in a sentence has an effect as well. 1 the above factors are certainly not sufficient to predict quantifier scope. it has been repeatedly stressed in previous work that world knowledge also plays a significant part in real world qsd, and any successful model for the qsd task should make use of it @xcite @xcite @xcite . to the best of our knowledge, however, @xcite have been unique in using a model explicitly geared towards world knowledge (in particular, numerical typicality) in the qsd task. drawing on @xcite , they decided on the preferred scoping by comparing the size of two classes, e.g., person and city, standing in a relation such as the living-in relation. for example, the surface scope reading is dispreferred in a sentence such as a person lives in every city because it would require a person to live in an atypically large number of cities. the present study seeks to contribute to this scarce line of research through incorporating into a qsd model our knowledge about relations, as conveyed by a manageable closed class of function words: prepositions. relations between objects (but also times, events) are often signaled with prepositions @xcite @xcite . prepositions serve, among other things, to convey place and time (there is a restaurant at every corner, john taught on each monday), to express configurational relationships like possession or part/whole (someone with every key, a day of every month), and to indicate semantic roles in predicate-argument structure like agent or instrument (a study sponsored by a consumer group, a store filled with lots of food). recent work argues that certain prepositional senses are special in that they encode dependencies that have an effect on scope-taking @xcite . for example, the preposition of expressing 'part-whole sense' -as in a day of every month -introduces a dependency between each whole (month) and its respective parts (days). by quantifying over this dependency, we obtain the inverse scope read-ing for the example in question: for every month, there is a different day that belongs to it (every @xmath2. the surface scope reading (a @xmath3, namely that we can have many parts (days) belonging to the same whole (month), but a single part (day) cannot belong to more than one whole (month). conversely, the 'whole-containing-part sense' of the preposition of -as in a group of four homeownersencodes a dependency between a group and its respective members, thus only allowing surface scope (a @xmath4. furthermore, universal quantification in locative and temporal prepositional phrases tends to support inverse scope. for example, the locative preposition at -as in a restaurant at every corner -implies 'disjointness' (objects do not occupy more than one place at a time), and hence can be interpreted as a dependency between each corner and the respective restaurants located at that corner. quantifying over this dependency yields the inverse scope reading: for every corner, there is a different restaurant located at it. the surface scope reading is excluded because one restaurant cannot occupy more than one place (every corner) simultaneously. our study takes its theoretical inspiration from the above work and contributes to research on automatic qsd by examining the previously unexplored predictors of quantifier scope: prepositions and their senses. for the experiments undertaken in this study, we use a scope-disambiguated corpus created by @xcite , additionally annotated with prepositional senses using the semantic network of adposition and case supersenses (snacs) scheme proposed in @xcite . our results indicate that prepositional senses have a strong role in the qsd task and encourage further research and deeper analysis in this area. the structure of the paper is as follows. section (2) introduces our corpus and discusses its annotation process. section (3) explains the methodology of our study. in (4), we introduce our experimental setup and discuss the features we have used in our models. section (5) presents our results and (6) concludes with a summary and some directions for future work. ## corpus the present study uses a scope-disambiguated corpus which was created for the purposes of the 2012 study by anderbois, @xcite . it consists of 680 sentences with multiple quantified nps from the reasoning section of the law school admission test -the so-called logic puzzles. logic puzzles provide a good corpus for qsd for they use quantifiers frequently, providing a fair number of sentences containing scopally interacting quantifiers. every sentence of anderbois et al.'s corpus is labeled with the relative scope of the quantified nps involved. scope is coded numerically, with 1 corresponding to widest scope and smaller numbers indicating narrower scope; cases with no relative scope like logical equivalence (e.g., two universals or two existentials) are co-tagged with the same number. the scope predictors incorporated into the annotation in the corpus include sentence order (it is not explicitly tagged, since it can be recovered from the linear order of the tags themselves), grammatical function (subject, object, adjunct, etc.) and lexical realization of quantifiers. the beginning of the tag is marked by & and the end is marked by ♯: since the sentences in the corpus were chosen for quantified nps, they would be expected to provide no bias with respect to prepositions. the most common prepositions in english identified by @xcite do indeed overlap in eight cases with those in the corpus, although in some cases the frequency distribution is different: of, in, on, at, to, for, with, and from. while individual prepositions in prepositional phrases are tagged separately in the corpus (as illustrated by example (2)), the prepositional senses are not. it is, however, prepositional senses (rather than prepositions) that induce or block inverse scope. for example, as discussed above, the 'part-whole sense' of the preposition of induces inverse scope, while its inverse 'whole-containing-part sense' blocks it. for our study, we additionally annotated the corpus with prepositional senses, using the semantic network of adposition and case supersenses (snacs) scheme proposed in @xcite . ## method as mentioned above, manshadi and allen build their method on the fact that quantifier scopings (qs) form partial orders. hence, they define qsd as a task of creating partial orders and show that ## experimental setup a support vector machines (svm) classifier, python's scikit-learn implementation @xcite , was fitted to the data (@xmath5: wide scope, narrow scope or incomparability. once the probabilities were predicted by the classifier, in order to restore a full sentence's quantifier scoping, a predicted tdag was built. foot_2 ## summary and future work this study dealt with the qsd task following the methodology established by @xcite @xcite which allows to consider any sentence, with no restriction on the number of quantifiers involved, in a ternary classification task. applying this method to the scope-disambiguated corpus @xcite , additionally tagged 11 we also experimented with a model that includes both preposition lexicalizations and preposition supersenses (just the ss2 part). performance of this system is as follows (mean, sd): (83.01, 2.29), (87.52, 2.17), (89.12, 1.88) for similarity, precision and recall, respectively. statistical analysis of this system's results led to exactly the same conclusions as when the model including only supersenses was used. that is, it performed significantly better with respect to the baseline but not with respect to the system involving only preposition lexicalizations. thus, there is no theoretical reason to believe that preposition lexicalizations would encode any relevant information that is not already captured by preposition supersenses. with the snacs scheme @xcite , allowed us to investigate the question of whether information encoded by prepositions, or preposition senses to be exact, proves useful in the qsd task, as inspected with svm. our results confirm the formulated hypothesis -preposition senses, but not preposition lexicalizations, positively impact the learnability of the models and, hence, it may be inferred that they do convey world knowledge in a manner beneficial for the algorithm. note that, out of 1679 tagged quantified nps in the corpus, only around a third (581 to be exact) are nested in prepositional phrases; this fact further strengthens our conclusions. the fact that the methodology followed in this paper reduces the qsd problem to a pairwise comparisons task has its benefits. for instance, it significantly expands our sample from 680 sentences into 1451 pairwise comparisons. however, it comes at the price of a simplification, which might lead to information loss since each pair of quantified nps in a sentence is treated independently of other nps in that sentence, which in reality is not the case. another way to approach the qsd problem would be to treat it on a sentence level, making use of modern deep learning techniques such as pre-trained transformer neural networks. however, that might require larger quantifier scope-disambiguated corpora which do not yet exist. 12