The Vagueness of Vagueness in Noun Phrases

is not always precise – and sometimes intentionally so . In this position paper , we study vagueness in noun phrases . We manually analyze the frequency of vague noun phrases in a Wikipedia corpus , and find that 1/4 of noun phrases exhibit some form of vagueness . We report on their nature and propose a categorization . We then conduct a literature review and present different definitions of vagueness , and different existing methods to deal with the detection and modeling of vagueness . We find that , despite its frequency , vagueness has not yet be addressed in its entirety . 1 . Introduction . Natural language can be vague in many different ways : many verbs admit a wide range of interpretations ( consider , e.g. , “ to work ” , which can mean a paid activity as well as a serious effort – and not always simultaneously ) . Noun phrases can be vague , too ( as in “ several countries ” ) . Sometimes entire sentences do not have a clear-cut truth value ( e.g. , if they start with “ In many cases , ... ” ) . Naturally , such phenomena can hinder the interpretation of natural language by automated means , e.g. , in natural language understanding tasks , automated dialog systems , or intelligent assistants . Vagueness also poses a challenge for knowledge extraction . Consider for example this ( condensed ) excerpt from a featured article on Wikipedia : “ An anti-tobacco sentiment grew in many nations from the middle of the 19th century. ” This sentence is clearly factual and thus interesting for knowledge extraction . Yet , all noun phrases in the example are vague : what constitutes a “ sentiment ” ? How many nations are “ many ” ? Does the “ middle of the 19th century ” cover the 1930 ’ s ? Thus , if we want to use this sentence for the construction of a knowledge base ( KB ) , we face at least 3 challenges : How can we detect vague entities ? Current information extraction approaches for KB construction often focus on named entities , and do not deal with phrases such as “ anti-tobacco sentiments ” . How can we model vague entities in a KB ? Current large-scale KBs can not make statements about sets of unknown size such as “ many nations ” . How can we reason on vague entities ? If the sentiments grew in “ many nations ” , we can deduce that there were more than “ in few nations ” , but current KBs can not do that type of reasoning . We can , of course , choose to suppress vagueness , e.g. , by reducing “ many nations ” to a single placeholder entity of type “ nation ” , or by replacing it by a concrete number . However , this may not always be possible . It may not even always be desirable . Vagueness avoids being overly specific , when more information is not known or irrelevant at this point [ Van Deemter , 2012 , Lim and Wu , 2018 ] . Thus , vagueness is an important feature of natural language . Yet , it makes the sentence inaccessible to current information extraction methods for building KBs . In this position paper , we shed light on the phenomenon of vagueness in noun phrases . We first review different definitions of vagueness in the literature , and propose a categorization ( Section 2 ) . Then , in Section 3 , we study a corpus that was written with the intention to be least vague : a collection of featured Wikipedia articles . Our work is thus the first to actually quantify and categorize vagueness on real Web corpora . We find that 1/4 of noun phrases exhibit some type of vagueness . Finally , we discuss how vagueness has been treated in existing works . We find several works to detect vagueness in application-specific scenarios , such as privacy policies , requirement specifications , or ontologies ( Section 4 ) . In Section 5 , we discuss how vagueness can be modeled from logical and probabilistic perspectives . Section 6 describes how all of these approaches could be put together . However , we also find that vagueness in general has not yet been addressed well in the literature . It remains , until now , a vague concept . 2 . Defining Vagueness . Definition . We concentrate here on the vagueness of noun phrases . This type of vagueness has been studied extensively in philosophy [ Sorensen , 2018 ] . One classical illustration is the Heap Paradox , which is attributed to the Greek philosopher Eubulides of Miletus : A single grain of sand is not a heap . Nor does adding one more grain to some collection of sand make that collection a heap . But when does a collection of grains become a heap then ? The Old Norse tale of Loki even suggests that any concept can be debatable and vague : When two executioners want to cut off Loki ’ s head , Loki confuses them with a debate over where his head actually starts – thereby avoiding his execution . Thus , it appears that vagueness itself is a vague concept . We found two criteria that can help identify vagueness : One is the definition that a concept is vague if it admits borderline cases [ Alexopoulos and Pavlopoulos , 2014 , Liu et al. , 2016 ] . Another is to take inspiration from the vagueness doctrine in American constitutional law : a concept is vague if it would not be admissible in a law . Both criteria are imperfect , but they make the “ heap ” vague , and the “ head ” not . Existing Categorizations . Several works have proposed categorizations of vague noun phrases . Liu et al . [ 2016 ] study vagueness at the sentence level and at the noun phrase level . They identify vagueness at the sentence level along the dimensions of condition ( “ as needed ” ) , generalization ( “ generally ” ) , and modality ( “ might ” ) , and at the noun phrase level in the dimension of quantity ( “ some ” , “ many ” ) . Lassiter and Goodman [ 2017 ] distinguish two kinds of vagueness that can apply to noun phrases : scalar vagueness , where some expression can hold to some degree ( with adjectives such as “ tall ” , or modifiers such as “ many ” ) , and non-scalar vagueness , which they see in words such as “ bird ” and “ fruit ” ( presumably because of a lack of more precision ) . Bennett [ 2005 ] identifies 3 types of vagueness : Threshold ( where a property can hold to some degree ) , Partiality ( where a certain proportion of a whole is concerned ) and Deep Ambiguity ( where a word regroups several disjoint but overlapping concepts ) . We first tried to annotate a corpus ( see Section 3 ) with these definitions from previous work . However , these definitions proved to be too abstract for our manual annotation of natural language text . For example , the concept of “ beauty ” is clearly vague . Yet , it is neither a vagueness of quantity ( as in [ Liu et al. , 2016 ] ) , nor is it comparable in vagueness to a “ bird ” ( as in [ Lassiter and Goodman , 2017 ] ) , nor would we characterize it as an overlapping of disjoint but overlapping concepts ( as in [ Bennett , 2005 ] ) . The same applied to other vague noun phrases , either because they were carrying an opinion ( like “ beauty ” , “ sophistication ” or “ fame ” ) , or because they were hard to assess objectively ( like “ power ” or “ great ability ” ) . Therefore , we adapted and completed these categories as follows . Proposed Categorization . We propose three categories of vagueness . Scalar vagueness appears in expressions that can be interpreted as a scalar that ranges over a numerical scale and for which an unspecified threshold gives a truth value . For example , in “ Mary is a tall woman ” , the height of Mary could range from 40 cm to 220 cm , and the assertion is true if Mary is taller than a certain implicit threshold ( e.g. , 180 cm ) . This type of vagueness also appears in [ Rosadini et al. , 2017 , Bennett , 2005 ] and in the Heap Paradox . Quantitative vagueness appears in expressions that refer to an unspecified portion of an entity ( as in “ a part of the film ” ) , or to a set of entities whose number is not identified ( as in “ many scientists ” , or just “ scientists ” ) . This concept includes the numerical vagueness of [ Liu et al. , 2016 , Bennett , 2005 ] . It applies generally to plural nouns without a definite article or cardinal , except if they refer to the concept itself ( as in “ Apples are fruits ” ) . Subjective vagueness appears in expressions that can apply to a certain degree , and where there is no consensus on how to measure this degree . These often carry a subjective valuation , and correspond to Walter Bryce Gallie ’ s “ essentially contested concepts ” [ Gallie , 1955 ] . They include nouns such as “ beauty ” or “ ingenuity ” and echo the verse of the poet Fernando Pessoa : “ To define the beautiful is to misunderstand it. ” Practical Considerations . Some noun phrases exhibit several types of vagueness . For example , a “ long-lasting fame ” exhibits both scalar vagueness ( how long ? ) and subjective vagueness ( “ fame ” ) . “ Talented statesmen ” is both subjectively vague ( “ talented ” ) and quantitatively vague ( how many statesmen ? All ? Some ? ) . Furthermore , vagueness can not be decided on the noun phrase alone . It depends on the context in which the phrase is used . For example , the word “ computer scientists ” exhibits quantitative vagueness in the sentence “ Computer scientists believe that AES encryption is safe ” ( because it is not clear how many share this belief ) , but no vagueness in “ Computer scientists did not exist in the Middle Ages ” ( as there is no doubt about the quantity in this sentence ) . Vagueness appears usually in non-named concepts . Named entities , such as the city of “ Paris/ France ” , are not vague under most definitions of vagueness ( except Loki ’ s ) . Thus , the treatment of vagueness is inherently related to the treatment of non-named entities in natural language text [ Rosales-Méndez et al. , 2020 , Paris and Suchanek , 2021 ] . However , not all non-named entities are vague . For example , “ my garage ” is not vague , even though it is not a named entity . Vagueness is different from ambiguity [ Zhang , 1998 ] : Ambiguity applies when a word has several distinct meanings , and only one of them is intended ( as , e.g. , “ bank ” for the financial institution and the river bank ) . A vague expression , in contrast , has one meaning but more than one interpretation , and these blend into each other . Vagueness is different from underspecification . For example , the phrase “ 15 adults ” is not vague – even though it does not specify who these people are . Phrases can nearly always be made more specific , by adding more details about the concerned entities . However , what matters for vagueness is not the amount of detail , but whether the phrase is concrete enough to appear in a law or contract . “ 15 adults ” clearly is , whereas “ many people ” is clearly not . With all of this in mind , we can now reconsider the example about the anti-tobacco sentiments from Section 1 : Anti-tobacco sentiments are subjectively vague , because it is not clear when something counts as a “ sentiment ” . “ Many nations ” exhibits quantitative vagueness , because the number of nations is in question . Finally , the “ middle of the 19th century ” shows scalar vagueness , because a given year can be more or less covered by that notion . The distinction between scalar and quantitative vagueness may seem redundant , but we will see in Section 5 that they are treated in different ways by existing approaches : scalar vagueness concerns a concept to which an individual instance can belong to a certain degree . Quantitative vagueness concerns a concept to which instances do or do not belong , although their number is unclear .

Summary: This paper presents a discussion of vagueness of noun phrases along with a categorization of types of vagueness, and a corpus study that measures their prevalance in English Wikipedia. There ais a nice related work section that discusses efforts to identify and reason with vagueness in NLP, with a focus on formal reasoning systems. The authors suggest that their corpus could e a useful resource in creating detectors of vague NPs in a system that then has special reasoning capabiilties designed to deal with this vagueness.