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<?xml version="1.0" standalone="yes"?> <Paper uid="C92-2087"> <Title>Logical Form of Hierarchical Relation on Verbs and Extracting it from Definition Sentences in a Japanese Dictionary</Title> <Section position="3" start_page="0" end_page="0" type="metho"> <SectionTitle> 2 Logical Form of Hierarchical Relation on Verbs </SectionTitle> <Paragraph position="0"> Verbs correspond to predicates on entities. If VL(rh, ...,~,~) is the subordinate predicate of vU(~x,...,~,,), both predicates have the same arity ( i.e. m = n ), there is a one-to-one correspondence C/ from {1, ..-,n} to {1, ...,n}, and if VL(~I, &quot;&quot;,~n) is true, Vv(~f(U,...,~O(n) ) is also true at the same time. That is,</Paragraph> <Paragraph position="2"> where boldface ~e stands for a tuple of variables.</Paragraph> <Paragraph position="3"> Strictly speaking, the logical form of the hierarchical relation on verbs is (1).</Paragraph> <Paragraph position="4"> For example, &quot;fiktr 1&quot; is the subordinate verb of &quot;~F ,5 1&quot;- To describe this logically,</Paragraph> <Paragraph position="6"> where '~ 1 (rh, ~1~)' means that r/~ drink ~12 and '~A~ ,5 ~ (Yl, r~2)' means that ~\]1 take 712.</Paragraph> <Paragraph position="7"> But there are v L and v U such that some arguments in vL(~h,...,~,~) don't correspond to any arguments in Vu((t, * &quot;',(m) or some in Vu((I, &quot;&quot; ',(,n) don't correspond to any arguments in VL(rlx, ...,tin), although v L is a subordinate verb of v ~. In this case, we conclude that the predicate denoted by 9yV~(~,y) is a subordinate one of the predicate denoted by qzVU(~e, z). Therefore, by generalizing (1), we get * Syntactic role is represented by meazts of a postpo~ition, such as &quot;7) 9, and &quot;~&quot;, in Japanese. that is, We expand (2) further to restrict the domain of z, and define the logical form of the hierarchical relation on verbs as follows.</Paragraph> <Paragraph position="8"> Definition I v L is a subordinate verb of v v, if for some N w~ \[v~(~,~)~ N(~)^ V~(~,~)\], where bohlface N stands for a tuple of predicate letters and N(z) means Nl(Zl) A... A N,(z,,).</Paragraph> <Paragraph position="9"> A small letter, such as n, v, and v L, stands for a linguistic expression and a capital letter, such as N, V, and V L, stands for the predicate symbol corresponding to the linguistic expression represented by its small letter.</Paragraph> <Paragraph position="10"> I~br example, &quot;~ 5 1&quot; is a subordinate verb of &quot;~ rY 7., 1&quot; because the following formula holds,</Paragraph> <Paragraph position="12"/> </Section> <Section position="4" start_page="0" end_page="0" type="metho"> <SectionTitle> 3 Extraction </SectionTitle> <Paragraph position="0"/> <Section position="1" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 3.1 Extracting the Hierarchical Ex- </SectionTitle> <Paragraph position="0"> pression in a Definition Sentence Definition 2 77re relation between an entry verb v ~ t and its definition sentence s is</Paragraph> <Paragraph position="2"> For example, the definition sentence for &quot;~tr 1 &quot;(drink) is &quot;~ C/~/.# 7o l'(to take a drink) and the definition sentence for &quot;il~ 5 1&quot; is &quot;TJ~</Paragraph> <Paragraph position="4"> We get tFor convenience, we will omit the number of the meaning of an entry verb.</Paragraph> <Paragraph position="6"> We call the main predicate verb of a definition sentence the definition verb. If the definition sentence of a entry verb v e corresponds to</Paragraph> <Paragraph position="8"> then we can easily derive the hierarchical relation between v* and its definition verb v d from Definition 2. In this paragraph, we assume that the meaning of the definition verb has been selected correctly and we will omit the number of the meaning of definition verbs. How to select it will be given in 8.2.</Paragraph> <Paragraph position="9"> A definition sentence does not always correspond to the logical form as (3). But if we can get the sentence s ~ which is a part of the definition sentence s and corresponds to the logical form as (3) and S D S d, then we can also derive the hierarchical relation between the entry verb and the definition verb. We call s ~ the hierarchical expression in a definition sentence (HED). Now, we will discuss which part of the syntactic structure of the definition sentence is HED.</Paragraph> <Paragraph position="10"> Definition 3 We get rid of modifiers out of a simple sentence s. We call the rest of s the kernel sentence s ~ of s.</Paragraph> <Paragraph position="11"> Since there isn't a expression corresponding to a universal quantifier in the definition sentence of a verb, we can conclude the following characteristic. null Characteristic 1 lf s ~ is the kernel sentence of a simple sentence s, then S D S ~ and the logical form of ~* is (3).</Paragraph> <Paragraph position="12"> For example, the kernel sentence of &quot;~ (c) ~i ~--I~ lz~JT&quot;(to kill a pain in the body temporally) is &quot;~ ~'Y&quot;(to kill a pain) and its logical form is a~d the following formula holds, V?\]1~2~8\[S(~1,7J2,718) 3 where S(711, r\]~, 7/8) is the formula corresponding to &quot;~(c)~i~C/C/--I~=~T&quot; and means that 112 is a pain, 7/s is a body, and ~\]1 kill 7/2 in ~/3 temporally. '~ (r/)' means that ~/is a pain.</Paragraph> <Paragraph position="13"> ~T Qh,r/2)' means that 711 kill ~/2.</Paragraph> <Paragraph position="14"> There is a sentence s which satisfies the following characteristic.</Paragraph> <Paragraph position="15"> Characteristic 2 A sentence s includes a sentence s ~ and S D S'.</Paragraph> <Paragraph position="16"> If the definition sentence s of a verb is complex, then s satisfies Characteristic 2 and s * is its main clause. For example, the main clause of the sentence &quot;~C/~ ~ ~ J: 5 ~zt~- ~3&quot; (something adheres to X as it covers X) is &quot;~ ~,~ ~ ;5 &quot;(something adheres to), and it corresponds to the following formula,</Paragraph> <Paragraph position="18"> and the following formula holds, V~l~\[s(~, ~) where S(~\]l,r/~) is the formula corresponding to &quot;~;O~ ~ .~ 3: ~) {:~T.~,, and means that something rh adhere to r/2 as r/1 covers r/~, '~fi~ 0l)' means that ~/ is something, and '{'~ T ~ 0/1, r/~)' means that r/1 adhere to r/~. Meaning of the compound sentence s, in which two sentences (81,82) are connected by a conjunction corresponding to 'and' in English, is either 'S\] ^ $2' or 'after $1, $2'. Therefore, an operator needs to decide the relation between 81 and s~. In the former case, s satisfies Characteristic 2 and s ~ can be both 81 and s~. For example, a sentence &quot;~r~ ~-~#&quot; ~:~,~ ~ < ~ ?~ &quot;C/ * &quot;(to throw something and have it touched AcrEs bE COLING-92. NAI,~ES. 23-28 AO13T 1992 5 7 6 PROC. OF COLING-92. NANTES, AUG. 23-28. 1992 hard) consists of two sentences. One is &quot;/,J'~, ~k il~;:r&quot; ;b&quot; (to throw something), the otimr is &quot;~ 3: < :~ ~ 4- ,5 &quot;(to have it touched hard), and two sentences correspond to following formulae respectively, ~, z < ~ 4-~ (~t~,~\]~,~3).</Paragraph> <Paragraph position="19"> And two sentences are simultaneous. So following formulae hold,</Paragraph> <Paragraph position="21"> where S(O\], ~/~, ~/3) is the formula con'esponding to &quot;/~D)~ ~ ~17 T~w 3: < ~ ~7~&quot;and means that r/1 throw 7/2 and have Y2 touched hard to ~a. '@$~ (~/)' means that ~\] is something. '~E</Paragraph> <Paragraph position="23"> touched hard to fla.</Paragraph> <Paragraph position="24"> To apply Characteristic 2 repeatedly, we conclude that there is a definition sentence s which include a simple sentence s ~ and S D S' aud that the kernel sentence of s ~ is HED. ~br exa~nple, the sentence s &quot;~b ,5 ~o (~)~k ~ oT<&quot; ~:2 null ;5 t,: ~ l:- -{- (c) ~ C/) 1~ ~ ~ :~ o &quot;( ~ T lhJ 1:-2 C/ }911 &quot;Z &quot; (to hold both ends of something and apply force to both sides in order to make it straight) is complex. It therefore satisfies Characteristic 2 and S D S1, where Sl is its main clause &quot;~- q) ~(c)~C/~o'~l~lfil~aJ3 ~-')JllP~ 7~ '' (to hold both ends of something and apply force to both sides), s\] is a compound sentence and is composed of s2 &quot;-f (c)~(c)~,'~o&quot; (to hold both ends of something) and s3 &quot;Ji~:)~J'l~l l,T-)3 ~ ~13 L 6 &quot; (to apply force to both sides) and two sentence is simultaneous. Sl therefore satisfies Characteristic 2 and S1 D $2 and S1 D $3. Therefore, 5&quot; D 5'2 and S D $3. Because 82 and 83 are simple sentences, the kernel sentences of 82 and 83 are HEDs. When the definition sentence is simple, its kernel sentence is HED.</Paragraph> <Paragraph position="25"> If we decide the proper meaning of the definition verb and the proper correspondence from cases of v e to cases of v d correctly, we conclude</Paragraph> <Paragraph position="27"> We can get a hierarchical relation between v e and v 't as follows from (4), wv~ \[vdeg(,~,v):~ N~(~)^ V%,~)\].</Paragraph> </Section> <Section position="2" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 3.2 Necessary Condition and Heuris- tic </SectionTitle> <Paragraph position="0"> In this paragraph we supposed that an entry verb v C/ has HED.</Paragraph> <Paragraph position="1"> What we call the selectional restriction has been used to narrow down candidates fro' syntactic structnre in the syntactic processing. It is the restriction about the semantic category of a noun phrase which a certain verb can take as a certain case. The semantic category has been called the semantic marker or semantic prim~ itive, libr example, semantic categories of the subjective noun phrase and the objective noun phrase for the verb &quot;fikC/~&quot;(drink) must be 'animal' and 'liquid' respectively. We use this inforo mation to semiautomatically select the proper meaning of v d and the proper correspondence from cases of v ~ to cases of v d. The information is mentioned in the Japanese dictionary we used for the experiment of extraction.</Paragraph> <Paragraph position="2"> The restriction that if a verb vk c~m take a noun phrase with a e~e e the semantic category of the noun phrase is D is expressed logically as follows,</Paragraph> <Paragraph position="4"> where xi is the argument corresponding to the case c, and k is the meaning number of v. We call D in (5) the domain for c of vk. For example, V~a~12\[~tt 1 011, ~'/2) D animal@l) A liquidO?2)\], where 'fi~.O 1 (~h, 712)' means that ~/1 drink ~2. If the semantic category of a nolm n is D, WIN(x) ~ D(~)\]. (6) We call D in (6) the domain for n.</Paragraph> <Paragraph position="5"> If the k-th meaning is proper as v ~ in the definition sentence of v ~ and the correspondence from i-th case of v ~ to j-th ca~e of v~ is correct, then the following formula holds,</Paragraph> <Paragraph position="7"> Assumption 1 We assume ~xV(zc) is true for each verb v and BxN(x) is true for each noun n.</Paragraph> <Paragraph position="8"> We conclude</Paragraph> <Paragraph position="10"> We establish (8) as the necessary condition in which the correspondence is valid. We check (8) with BxN(x) (Assumption 1) and the relation between domain predicates.</Paragraph> <Paragraph position="11"> Necessary Condition If the k-th meaning is proper as v d in the definition sentence of v ~ and the eom'aspondence from i-th case of v ~ to j-th case of v~. is correct, then</Paragraph> <Paragraph position="13"> where D ~ is the domain for i-th case of v ~ and D ~ is one forj-th case ofv~ and the noun ofj-th case of v~ in the definition sentence is n and the domain for n is D '~.</Paragraph> <Paragraph position="14"> The meaning of an entry verb v ~ is defined by using the definition verb v d. Then, the less the number of the variables appearing either only in v ~ or only in v d ( i.e. (size of tuple y) + (size of tuple z) in the formula (4)), the more v ~ restricts the meaning of vL An editor of a dictionary would select such a definition verb.</Paragraph> <Paragraph position="15"> We therefore establish the following heuristic.</Paragraph> <Paragraph position="16"> Heuristic The less the number of the variables appearing either only in v ~ or only in v d, the more we have chance of correct selection for meaning of v '~ and the correspondence of the variables.</Paragraph> </Section> <Section position="3" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 3.3 Example of Extraction </SectionTitle> <Paragraph position="0"> In this paragraph the method how to extract the hierarchical relation on verbs will be introduced. We suppose following definitions about &quot;~-PS &quot;5&quot; and &quot;~9&quot;.</Paragraph> <Paragraph position="2"> experience a strong feeling of fondness) (ghfi, g)~ck~-J-'5. (to have some property or equipment) (r)means that &quot;~T .5 1&quot; is used with the form of &quot;npl ~ np2 ~ ~ &quot;~ &quot;5&quot; and the semantic category of npl and np2 must have 'human'. We get the following knowledge about domain of words. 'all_entities' expresses the set of all entities. We suppose the following relation between domain predicates, its kernel sentence &quot;~,~ C/5 ~k ~-) &quot; is HED. We narrow down candidates for the meaning of the definition verb &quot;~o&quot; on parsing by selectional restriction. Meanings of &quot;i~:o&quot; that satisfy selectional restriction are II and II1. Since we can</Paragraph> <Paragraph position="4"> from Assumption I and the relation between domain predicate, the correspondence from the first case of &quot;'~-~ 6 1&quot; to the first case of &quot;~ 3&quot;satisfies the necessary condition described in paragraph 3.2. Since we can infer</Paragraph> <Paragraph position="6"> the correspondence from the first case of &quot;'Z!PS 70 1&quot; to the second case of &quot;~o a&quot;does not satisfy the necessary condition. After all, for &quot;~ ~)2&quot; and &quot;~'~'-)a&quot;, partial one-to-one correspondences which satisfy the necessary condition are</Paragraph> </Section> </Section> <Section position="5" start_page="0" end_page="0" type="metho"> <SectionTitle> ~o2 : a.{}, </SectionTitle> <Paragraph position="0"> b.{< 1,1 >}, c.{< 1,2 >}, d.{< 2,1>}, e.{< 2,2 >}, f.{< 1,1 >,< 2,2 >}, .q. {< 1,2 >,< 2,1 >}, ~'oa: h.{}, i. {< 1,1>}, j.{< ~,1 >}, For example, the correspondence g means that the first case of &quot;N:-J,5 1&quot; corresponds to the second case of &quot;~.&quot;02&quot; and the second case of &quot;~-PS & 1&quot; corresponds to the first case of &quot;N~ ~D 2&quot;-Because the number of the variables which appear either&quot; only in the entry verb or bl the definition verb for the correspondence g is 1 and one for the correspondence i is 2, the pair of &quot;~o2&quot; and the correspondence g is prior to the pair of &quot;~o3&quot; and the correspondence i by the heuristic. The pair of &quot;~o~&quot; and the correspondence f and the pair of &quot;~'9 2 and the correspondence g are given the highest priority by the heuristic after all.</Paragraph> <Paragraph position="1"> it is decided by a operator that the second meaning of ~ and tile correspondence f are proper, and we get W~z\[~ ~)- 70 1(xl, z2) :9</Paragraph> </Section> <Section position="6" start_page="0" end_page="0" type="metho"> <SectionTitle> 4 Experiment of Extraction </SectionTitle> <Paragraph position="0"> We have experimented on extracting the hierarchical relation using the machine-readable dictionary IPAL (IPA : Information-technology Promotion Agency, Japan ; IPAL : 1PA Lexicon of the Japanese language for computers). 861 verbs and 3379 meanings are contained in this dictionary. The definition sentence of an entry verb and the pattern of cases for the entry verb and the domain for each of the cases of the entry verb are given in this dictionary (see Appendix).</Paragraph> <Paragraph position="1"> And we can also get the domain for a noun from this dictionary.</Paragraph> <Paragraph position="2"> We made a lexical functional grammar which outputs the logical fornl of HED as a feature.</Paragraph> <Paragraph position="3"> We parsed the definition sentences and got 1709 HEDs whose main predicate verb are given as an entry verb in this dictionary with this gramman. We have extracted the hierarchical relations on verbs from 1288 IIEDs. The average number of candidates which are given the highest priority by the heuristic described in paragraph 3.2 is 4.6 and there is the correct solution in 4.6 candidates at tile rate of 70.4%. The number of meanings of verbs in the highest layer in the hierarchy is 288, and the average level in the hierarchy is 2.7. Maybe this value is so little.</Paragraph> <Paragraph position="4"> We think in this point since IPAL is a basic verh dictionary its entry verbs are in a comparatively high ordinate in hierarchy of all verbs.</Paragraph> </Section> class="xml-element"></Paper>