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<?xml version="1.0" standalone="yes"?> <Paper uid="C94-2124"> <Title>A DISCRETE MODEL OF DEGREE CONCEPT IN NATURAL LANGUAGE</Title> <Section position="1" start_page="0" end_page="0" type="metho"> <SectionTitle> A DISCRETE MODEL OF DEGREE CONCEPT IN NATURAL LANGUAGE </SectionTitle> <Paragraph position="0"/> </Section> <Section position="2" start_page="0" end_page="0" type="metho"> <SectionTitle> Abstract </SectionTitle> <Paragraph position="0"> Degree words in natural lauguage, such as 'often' ~md %ometinies,' do not ha.ve (ieln)t,~tions in the reid world.</Paragraph> <Paragraph position="1"> This causes some interesting clmracteristics tor degree words. For exami)h; ~ the correspondence between the.</Paragraph> <Paragraph position="2"> English word 'often' :rod the intuitively corresponding aa>nese word is not ebvhms. This paper proposes a conceptual representat;ion to describe a wide range of linguistic phenomelul, which are rehtted to degree concepts in natural language.</Paragraph> </Section> <Section position="3" start_page="0" end_page="775" type="metho"> <SectionTitle> 1 Introduction </SectionTitle> <Paragraph position="0"> Degree words in natural l;mguage, which are exemplllied by the tbllowing, exist across p~rts of speech and across specific languages.</Paragraph> <Paragraph position="1"> (:) a. qua.ntifiers: b. adw.'rbs: e. adjectiw!s: ~/li I lllally) SOllle I t'e~,v) llO always, oftell~ SOlIletil\[les~ seldom, never tall, short Degree words haw,. S()llle interesting characteristics. First, quantities in the real workl which can be repre sented by degree words w~.ry pragmatically, depending on speakers, situa.tions, etc. (Fauconnier, 1.975). This means that degree words do not have denotations in the rea,1 world. IIowever, lllalty degreL' expressions are used in daily life and it; is not tblt thai, they are particula.rly incomprehensil~le. The authors do not think thaC to underst~md the lneanhtgs of degree words is to understan(\[ tit(; rea.l quantities in the real world. Second~ it is difficult to compare: degree words in different languages, in the case of the English non-degree word ~dog, ~ we may think that the word semantically corresponds to the ;lapanese word 'iml' because these two words reli!r to ~he same object 'clog' in the real world. However, this correspondence is not true of degree words. Tim English woM %ften' intuitively corresponds to Lit('. Japanese word %hitmshib% ~ but this correspondence is not ol)vious. 'Fhat is because these words do not have. denota.tions in the real world. These chttra.cteristics a, re related to the b~vse of Machine Tr~tnslation and its dietionaries. Even when the real quantity, which is reti?rred to by ~t degree word in ~t text, is not clearly understood, it is usually believed that it is possible to translate the word into ~tnother language. When building bi-lingual dictiomtries, it is necessary to consider the correspondence between (lm gree words in each htnguage. A new reference framework is needed by which to investigate to what extent the two words correspond to each other. These issues are. also related to conceptual descriptions in btrge scale knowledge l)aae projects, wlfieh have started recently. Third, degree words tuwe some ch~racteristics which are indepelMent from in~rts of speech. One of the phenomena degree words have in comnlon is modification restrictions between degree words and rlegree intensi.tiers. Each degree word ha.s its own modification restriction (Bolinger, 1972; Quirk, 1985; Kamei, 1988, 1990). For example, %IP and qm ~ can be modified by 'Minos(,' but 'tall,' 'short,' hnany~' and 'few' cannot usually be so h~mdled. On the other hand, %all,' %hort,' 'many,' and 'ihw' rail be modified by ~ve.ry,' but 'all' a,nd %0' cannot. 'Some' trod 'sometimes' cannot be modified by either %ery' or ~ahnost.' Previous researchers pointed out a lot of important linguistic phenonmna~ which ~re related to degree words but, the issues described abow ~. were left uninw~stigated. Barwise trod Cooper (1981) investigate relations I)c~ taween determiners in English and ge,mrMized quantltiers in logic. Howew.'r, they did not focus so much on degree words, such ~s ~tdjeetiw'.s and adverbs in general. it is still undetermined how to fully comprehend such words as 'ma.ny' and % i'ew.' Oazdar (1979) and IIirsehberg (1985) introduced ideas of a linear ordering of degree words and treated ~ wide range of phenomelut related to degree words. However, they directly htmrlled real words and treated ~positive words ~ such as %11' and hnany,' ~nd qmgative words ~ such as flew' and %o ~ separ~ttely. Relations between the positive and negative words were not clear. In order to con,prehend these, unsolwM linguistic phenomena~ the authors propose a semantic model of degree, concepts.</Paragraph> </Section> <Section position="4" start_page="775" end_page="777" type="metho"> <SectionTitle> 2 Discrete Degree Primitives </SectionTitle> <Paragraph position="0"> and a List Expression This section introduces discrete degree priinitives and a list expression 'co represent mea.nings of degree concepts. From the perspective of quantities in the real world, hnany' and 'some' are sfmilar. However, The modification restriction be.tween degree words and degree intensifier shows that e~mh word is normally modified by intensifiers selectively. This suggests the existence of DISCILETE degree concept primitives, which are independent from parts of speech. The authors introduce five basic semantic primitives (~A,' ~M,' ~S ,' 'F,' and 'N') indicating degree that are abstracted from the meanings of %.11,' hnany,' 'some,' ~fcw,' and ;no.' A list of degree primitives is used to describe meanings of degree words in terms of relative positions in the list expression.</Paragraph> <Paragraph position="1"> {A, M, S, l>, N} The list expression above is a basic list of the discrete model. The ,utthors divide meanings of degree words inte two parl;s. For example, 'tall' and %hort' can be divided into the semantic axis regarding 'tallness' and the degree concepts 'many (much)' ~md 'few (little).' Tables 2 and 3 represent the htter part of meanings of degree words. In these lists, '-' means that the value in that pa.rtict,la.r position is lacking.</Paragraph> <Paragraph position="2"> Basic list {A, M, S, F, N} ~dl, always {A, -, -, -, --} many, often {-, M, -, -, -- } some, sometimes {-, -, S, -, -} few, seldonl {., -, -, F, -} no, llever {--, --, --, --, N} Ttd)le 2: List Examples (2) Basic list {M, S, F} tall {M, --, -} not tall and not short {-, S, -} short {-, -, F} The authors think that degree words are identified by their relative positions in the list expression. It is true that quantities in the real world, which are expressed by degree words, are continuous, tIow('.ver, the authors think that language treats degree concepts in a discrete way. T~d)le 3 shows modificatiou restrictions on degree intensifiers using the primitives. In this table, %' shows that the intensifiers can lnodify the (legree primitives, and '-' shows the intensifiers cannot modify the prinfitives. Note that these primitives are not real words and that they consistently describe relationships that are independent from parts of speech. These are important differences between this model and previous research reports.</Paragraph> <Paragraph position="3"> It is pointed out that degree words convey non-literal 'conversational' meanings when they are used. The dig ference between a literati meaning and a converst~tional meaning is called 'CouversationM Imf)licature' (Grice, 1967). This section explains how this model treats this aspect of degree concepts.</Paragraph> <Section position="1" start_page="775" end_page="776" type="sub_section"> <SectionTitle> 3.1 Question and Answer </SectionTitle> <Paragraph position="0"> (17o exemplify Conversational Implicature, let us consider the following sentence, which includes a number.</Paragraph> <Paragraph position="1"> (3) I solved three of the problems.</Paragraph> <Paragraph position="2"> A natural interpretation of this sentence is &quot;I solved just three of the prol)lems, not all or four or two or one or none of them.&quot; Kowever, in a logical way, this statement is true, when &quot;I solved FOUR of them.&quot; For example, if the border line between success and failure of a test is three, this sentence is naturally spoken, even when, in fact, the person solved four of the i)roblems (Chomsky, 1972; Ota, 1980; Ikeuehi, 1985). The following is a Yes/No question corresponding to sentence (3) and its answers. Interestingly, both of the answers below are possible in this case.</Paragraph> <Paragraph position="3"> (4) A: Did you solve three of the problems ? B: - Yes, in fact i solved four.</Paragraph> <Paragraph position="4"> - No, I solved four.</Paragraph> <Paragraph position="5"> In order to handle these phenomena, more complex states than just 'three' for the meaning of the nu,nber thre.e are needed. The authors think that five states are a.ctually needed fbr clarity: (1) All problems are solved. (2) The mmlber of solwxl problems exceeds the number which aI)pears in the sentence (=three in this case). (3) The number of solved problems is exactly the number which appears. (4) The number of solved problems does not total tilt: mnnber which appears. (5) No l)roblenls are solved. The authors introduce the five primitives, 'A,' '>n\] ~: 1 h' 'In,' and 'N,' corresponding t/) these five states, respec.tively. A list expression is introduced as follow.'< {A, >:1, <u, N} 'l'he live sta.t, es are represent, e.d with rela,tive l>O~d * tiens shown in Talfle 4.</Paragraph> <Paragraph position="6"> {A, , -., --, -} {-., >::, --, - , -} {-, -, , -} {-., -, -, in, -} To expre~,~ tit('. Conver~;ational lmlfliea, ture, the authi)rs ri,presiutt the mea.ning <>f tit(: number l>art in sentence (3) with a dual list.</Paragraph> <Paragraph position="7"> I The upper row (the direct meaning row) it: this tel> resentation shows the state wherifin the number of solved probh;m.~ is the number that appear.~ in sentcnce (3). The h)wer row (the possible interpretation row) expr(~sses the l)os>dbh: rm:nl><'.rs of solved l)rol)ferns, whet: aeutence (3) is q)oken. For examph', this statement is false, wh,m &quot;I solved TWO o'f theln.&quot; Logica.iiy, however, this star(relent is TR.UI~, when &quot;l solved FOUR of theuC' The dual llst; represents the first \]>hen(line:m::, The ditl'erence I:)etwee:~ the two rows, 'A' and '>u' in this case, cxl>resses the l>OSSlbili ties of C<>nviusatl<ma.l lnll:)liea,ture. \Y=hen this sentence is Sl,ok(m , tim degree part <>\[ this seiltenee conveys th(; meatfings which correslx)nd to BOTH of the rows in the dual list. That is, it not (rely is indicated by the upper 'dir<!cC row, but also by the lower 'possil>h/row. In an atIirmativc sen~,enci:, t.he upper ~direct' lrleilAling may be dominant, ilowever, in the case of an interrogative sentence, the h)w(:r 'pos.~ibh? meaning plays a more imp/)r taa:t role. This model explains the two pos~dl)h' a n,~wers in ntwranee (d) in a. simph' way, In Fig. :\[, the meauing o\[' the que.,a.i/)n is expre,~sed with a dual list,. The meaning of the real sit, uathm (the iii('.anillg of 'fonr' in this ci~se) is express(!d with a single list (in the nfiddle), because it; is not. an interpretation, but is a situa.th)m ~C/'Vhell Cmnl)ariu Z the upl)er row of the quest.ion and t;he row expressing the ~dtuation 'tour,' there iS Ill) cotnnlon vii,lit(!, rF\]lel'e is tto intersection between them. 'i\['his case c(>rre.N)(>nds to the ~tnswer with ~No. ~ \;ghen comparing the lower ~l)ossible' row and the sit-uation, t;here is an inti;rsecl, ion, that is, the wdue ~>n.' Therefore the answer is ~Yes.' This intersection operation is a simple and naturM way to calculate possible answers to a question which includes a number.</Paragraph> </Section> <Section position="2" start_page="776" end_page="777" type="sub_section"> <SectionTitle> 3.2 Negation Operations </SectionTitle> <Paragraph position="0"> This section introduces Neg~tion Operations, which axe. deti.ed on the dual list representation. Sentence (7) is a negative smite,we which correslmnds to sentence (3). A negative sentence like this tuus several interpretations which previous research has pointed out but has not been able to treat satisNctorily. This model calculates all the possible interpretations of a negative sentence fi'om the representation of the origina.l Mlirmative sentenc.e.</Paragraph> <Paragraph position="1"> (7) 1 didn't solve three of tile problems.</Paragraph> <Paragraph position="2"> One possible interpretation of sentence (7) is that there ~rc three problems that &quot;i (lid uot solve&quot; (Interpretation A). In tllis interprets.lion, the n/tmber %hree ~ is not under the influence of the negation; the number in out of the scope of negation. '1'o obtain this interpretation, it is not necessary to change the dtml list for the originM affirmative sentence (6). It is necessary to change the meaning of the values from the number of tim solved problems to the number of unsolved problen:s in the representation of the original Mfirmatiw~ sentence (Fig. 2). The lower row expresses the possibility that the number of the unsolved problems exceeds t hl.et:.</Paragraph> <Paragraph position="3"> Where the musher (=three in this case) is within the scope of negation, the negative sentence requires other interpretations.</Paragraph> <Paragraph position="4"> (8) A: Did you solve three of the t)rot)lems? B: No, i didn't (get to) solve three of the problems.</Paragraph> <Paragraph position="5"> .--- Interpretation (B) were solved, but that the munber did :tot reach three. This interpretation can be obtained from tile model shown in Fig. 3, and the negation operation is shown in Table 5.</Paragraph> <Paragraph position="6"> tire Dual List 1. Reverse e~mh atlirmative row.</Paragraph> <Paragraph position="7"> 2. Select the COMMON part of the two rows.</Paragraph> <Paragraph position="8"> The result is a new possible interpretation row. 3. Omit t, he edge values (A aud N).</Paragraph> <Paragraph position="9"> The resnlt is a. new direct ineauing row.</Paragraph> <Paragraph position="10"> Tabh~ 5: Negation Operation tbr Interpretation B Step 1 in Table 5 rea.lizes a primitive negation opers, tion on each row. This i,~terpretation of the negative sentence is consistent with the negations of both the direct meaning and the possible implic~tion. Step 2 realizes this condition. This interpretation usually implies that there are some solved problems. This means the negation usually does not deny the. existence of tile solw~d prol)lems, ttowever, in a logical way, no problem being solved is a possible situation. Step 3 realizes this condition.</Paragraph> <Paragraph position="11"> (9) A: l)id you solve three of tke problems? C: No, I didn't solve THREE of the probh;ms: I solved ALL of them.</Paragraph> <Paragraph position="12"> - Interpretation (C) The above is a possible utterance, which requires ~nother interpretation. Table 6 shows the way to calculate this interpretation (I:~terl)retation (C)). 1. Reverse each affirmative row, 2. Select the DIFFERENT part of the two rows.</Paragraph> <Paragraph position="13"> The result is a new possible interpretatiou row. 3. Omit the edge wdues (A and N).</Paragraph> <Paragraph position="14"> The result is a new direct meaning row.</Paragraph> <Paragraph position="15"> This interpretation differs from interpretation B, only at Step 2, that is, 'to select the DIFFERENT p~rt of the two rows.' This means that the interpretation is consistent with only the negation of tile direct meaning, and does not satisfy the negation of the possibh.&quot; implication. Step 2 realizes this condition. This exemplifies that the Conversational Implicature can be canceled. In speech~ stress is put on THREE and ALL in this interpret,~tion, and this linguistic phenomenon is accounted for in Step 2.</Paragraph> </Section> </Section> <Section position="5" start_page="777" end_page="780" type="metho"> <SectionTitle> 4 Negation of Degree Expres- </SectionTitle> <Paragraph position="0"> sions in Natural Language In this section~ the dual list representation and the operations introduced in the previous section are applied to degree words other than numbers.</Paragraph> <Section position="1" start_page="777" end_page="778" type="sub_section"> <SectionTitle> 4.1 'All,' ~no,' ~some,' and ~not all' </SectionTitle> <Paragraph position="0"> Here, we will apply the same model to the relations between 'all/~some~' 'no,' and blot all' in natural language. Sentence (10-1) logically entails sentence (102). Sentence (10-2) usually implies senteuce (10-3).</Paragraph> <Paragraph position="1"> Itowever, sentence (10-3) contradicts the original sellfence (10~1). A careless mixture of logical implication and usmd implication in language makes the inference of (10-3) from (10-1) unreasonable (t-Iorn, 1972; Ota, 1980; McCawley 1981).</Paragraph> <Paragraph position="2"> (10-1) All students are intelligeut.</Paragraph> <Paragraph position="3"> (10-2) Some students are intelligent. (10-3) Some students are NOT intelligent.</Paragraph> <Paragraph position="4"> The discrete model is ~ usethl tool for describing these relations. List (11) is used to express relations 1)etween 'all,' 'some,' 'no,' ~tnd 'not all (= some ... not).' In this case, only three primitives are used. (H) {a, s, N} In this list, the w~lue ~S' corresponds to the state wherein there are SOME students who are intelligent and SOME other students who are NOT intelligent. The me,~nings of these words are also expressed with a dual list. Figure 7 graphically represents this. Ill Fig. 4, the second 'possible' rows of Call' ~nd ~sorne' ha.ve an intersection at the wdue ~A.' ~No' au,d 'not ~dl' hatw; a, simila.r intersection. This re~dizes ent~dhnent between tile two concepts. \].&quot;igure 4 also ex~ presses the differeuce between 'eontra.ry' and %:ontr~v~ dietory.' If '~dl' is true,qlo' is faJse, if 'no' is tru% qdP is fa,lse. Both exl)ressions etLlllll)t be trite at the same time. Itowever, these two CAN BE FALSE art tile s~mm time, beca.use it is 1)ossible that some students a.re intelligent auld seine students are not. The term %:ontra.ry' expresses this rela.tion. ()t~ the other h~tnd, 'MI' and hu)t all' h~w', :~ ditli~rent rel,ttionship. '.\['hes(~ two Call.liO~ \])e trl.le at tim same time, and e.~Lll.not 1)e false at the SS,llle ~il\]\[le. ~No 1 and ~SOllle' h~Lve the S&llle constra.int. The term 'contradictory ~ in Fig. 4 expresses this rela.tion.</Paragraph> <Paragraph position="5"> An iml>orta.nt poiut her(~ is that the s;mm oper~ttion of nets.lion, ~I'able 5, used fl)r numl)ers will also obt;dn tile representattion of h~ot all' front that of bdl' ill Fig. 4. Tim other nets.glen operation, q'able 6, produces nothing in this (:ase. (Fig. 5). The negation oper~tions a.re basic tuld general.</Paragraph> <Paragraph position="6"> Note th~tt 'S' in list (11) in this section mentions only the existence of intelligent st.ud~mts and non-intolllg('nt students. In Section 2, the same symbol 'S' was used for the rnea.ning of 'seine' which is relatively defined ill the {A, M, S, F, N } (list (2)). \]h, tha.t ease, the value ~S' r(;presents a quantlt~ttlve aspect of {SOllle.' A relation betwc'eu ~S' in list (11) and %S+ ' = ~S' in list (2) is described as iollows: S- ( M, S +, F ) YIowever, the authors used the same vadue ~S' in both list:;, 1)ecaa:se the difl'erence~ between these two ~S's is represented by the set of values in list expres.sions. These two 'S's correspond to ambiguities which the. word 'some' in natural la:Dguage has.</Paragraph> </Section> <Section position="2" start_page="778" end_page="779" type="sub_section"> <SectionTitle> 4.2 ~Not many' and 'not a few ~ </SectionTitle> <Paragraph position="0"> This section tel)resents lne~tnlngs 'nt~tny,' h~ few,' ~nd q'ew', ~nd applies the negation operations on these concepts. Figure 6 shows du~d list representations for these three concepts. This figure shows that the ditference between 'few' and 'it few' is in the lower possible mei~n-ing row. It is the first time tht~t ~he difference betweem the two is explicitly shown.</Paragraph> <Paragraph position="1"> ~u:d q,ot t~ few,' which ~tre c~dcub~ted from the me~tn~ ing of hna.ny' ~utd %t fe.w' using tile neg~ttion ol>ertttions introduced in the previous section. The neg~tion Ol'erations produce two possible interpretations for qlot m~uy.' However, the direct me~udng row for one inter~ pretattion is htcking. Tills shows t, hatt this interpret~lion is logically possible, lint unusu\[d (this interpret~ttion is hdl'). The other is *t usual interpret~tiou of blot lnatny.' q'he dual llst of the usmd interpretation shows that blot m:~ny' does not clahn 'few,' but it rues.us less th~.ul j'ttst ~soi:te ... tier. ~ Th(~ s~ttite negation operations also I)roduce m(,anh:gs of 'not a few.' The dual list of its usual interpretation shows that ~not a few' does not ('.l~dm hmtny,' but it meatus more tha.D, just ~some.' Note that the dual list ret,resentattion and tile negation oper~ttions on it exphdn vagueness of htot nt~tny ~ atnd 'not a few', a~s well as ~unbiguities of their interpretatlions. null This paper introduced eight basic degree primitives for degree concept, that is, 'A,' 'M,' 'S,' 'F,' 'N,' '>n,' '=n,' and '<n.' ttowever, the authors do not claim that these eight primitives are sufficient to indicate all degree concepts. Instead~ the authors clMm that people comprehend degree concepts in a discrete way, and that degree concepts are identified by their relatlw~ positions in the fl'amework of understanding. Consider the following cxan~ples concerning ,~nother degree concept 'several,' which differs from these eight degree concepts.</Paragraph> <Paragraph position="2"> (13) They legally have several wives.</Paragraph> <Paragraph position="3"> Quantities, which are refl.'rred to by 'sew'.ral' and 'a few,' seem to be close. It is often said that quantities ret>rred to by 'several' include fiw.' or six, and more tha.n the quantities referred to by '~t few.' However, sentence (13) shows th~tt 'several' means more than one in this case. Previous researchers have not been successflfl in describing the diflhrence between 'sevend' and 'a few.' The authors think that 'sew.'ral' should be in a list including 'several' and 'one,' while 'a few' should be in a list which contains 'a few' ~tnd 'many.' 'Several' implies 'not one,' while '~ few' implies 'not many.' An important point is that the ditference between 'several' and ~a few' is not the exact quantity involved, but a framework of understanding, that is, the set of vahms in the lists and their relative positions. null</Paragraph> </Section> <Section position="3" start_page="779" end_page="780" type="sub_section"> <SectionTitle> 4.3 'OR' in Natural Language and Negation </SectionTitle> <Paragraph position="0"> It has been shown that the logical operator ~OR' has characteristics similar to degree concepts (Gazdar, 1979). This is because 'of in natural language generally has two interpretations, the 'inclusive or' and the 'exclusiw'. or.' This section applies the same model for degree concepts to a logical operator 'OIL' and 'or' in natural language.</Paragraph> <Paragraph position="1"> It is difficult to conceptualize the ne.gation of 'or' in natural language, in a usual sense, although negation of 'and' is easy. Logically, however, the negation of the logical operation 'OR' (that is, 'Inclusive or') is 'NOR.' However, in a sense in natured language, 'AND' instead of 'NOR' can also be a negation of 'Oil..' and or nor</Paragraph> <Paragraph position="3"> and exclusive 'or' and their negations. The authors use three states: (,-+), (+-/-+), and (--). 'Exclusive or' is a direct meaniug of 'or' ~tnd 'inclusive or' is a possible interpret~tion of 'or' in this framework. The same negation operations will produce the two neg> th)ns of 'or 1' tha.t is, both NOR and AND. Tim direct mea, ning rows in the two interl)ret;~tlons of nega.tions of 'or' ha.ve no values. This corresponds to the Met tha.t it. is difficult to consider the nega.tion of %r' in mttura,l language. No~(; that the dual list fbr 'or' and the du;d list. for 'somo' in Fig. 4 ha.ve an ido.ntical structure. It is equally explained that the nega.tion of 'some' is diflicttlt to consider in na.tural language., while the neg~tion of %11' is easy.</Paragraph> </Section> </Section> class="xml-element"></Paper>