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<Paper uid="C80-1061">
  <Title>ON COMPUTATIONAL SENTENCE GENERATION FROM LOGICAL FORM</Title>
  <Section position="3" start_page="0" end_page="0" type="metho">
    <SectionTitle>
EVERY MEETING WILL BE HELD IN THE
</SectionTitle>
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  </Section>
  <Section position="4" start_page="0" end_page="0" type="metho">
    <SectionTitle>
WHO TAKES PART AT THE MEETING WHICH
TAKES PLACE IN THE COUNTRY &amp;quot;JAPAN&amp;quot;
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    <Paragraph position="0"> 4. Semiotic interpretation as sentence generation basis  Let us proceed to consider the devices for sentence generation from the underlying logical structure. Essentially the generation process will be based on the semiotic interpretation,called by Scholz and Hasenjaeger, of the predicates and functions used in the logical structure. Some of them are listed as follows:</Paragraph>
    <Paragraph position="2"> will be held in city x2  takeplacecountry(xl,x2) =def meeting xl takes place in country x2 makejourneycity(xl,x2) =def person xl makes a journey to city x2 Functions: city(x).eq.y =def the name of city x is y conference(x).eq.y =def the name of meeting x is y pezson(x).eq.y =def the name of person x is y  The semiotic interpretation strings are the building basis for surface sentences. In this respect the semiotic interpretation of predicate may be comparable with the underlying string in the generation tree or phrase-marker which is assumed both in the theory of Chomsky and in the theory of Montague as well. If we look at its actual form more closely, the strings given as semiotic interpretations differ in one essential point from the underlying strings adopted in the school of generative grammar. The underlying string in the deep structure for grammatical transformation contains no variable as used in the logic. On the ground of this essential difference we can make no direct comparison between our approach and that of generative semantics.</Paragraph>
    <Paragraph position="3"> At the disposal of semiotic interpretations of predicates and functions, we could already in principle implement a program to generate somehow quasi natural language sentences from the given logical structures. All what we need to do is to follow the type of reading the logical formula which we have been taught at the class room. We have been taught, for example, to read the following logical structure /true/=.all.x2(.ex.x3(city(x3).eq.</Paragraph>
    <Paragraph position="4"> &amp;quot;tokyo'.and.takeplacecity(x2,x3))) as: for every meeting x2 it holds: there is a city x3,for which it hold: the name of city x3 is &amp;quot;tokyo&amp;quot; and meeting x2 will be held in city x3 This might be considered as a quasi natural language sentence formulation. It has above all the advantage of being universal to the extent that it can be applied to every kind of logical structures. And actually a program has worked in this style (Habel,Schmidt,Schweppe 1977). However,this kind of formulation is not the usual surface sentence and it is also not so intelligible as it could. We need therefore to find out an alternative which might give us a simple and natural formulation . For eample, the logical form given above has the meaning which can be expressed simply as: &amp;quot;Every meeting will be held in the city &amp;quot;Tokyo&amp;quot; &amp;quot; It contains no formal logical quantifiers and no free or bounded variables. We describe below some main methods and principles which we have used to achieve the generation of such surface sentences computationally.</Paragraph>
    <Paragraph position="5"> 5. Quantification order and derivational constraint The problem of quantifiers constitutes one of major obstacles in the computational sentence generation from logical structures. As is well known, the order of different quantifiers has an influence on the meanil~g of the expression whether it is in the case of natural language or it is in the case of predi--407- null cate logic. Thus, Peirce has already pointed out that the sentences &amp;quot;some woman is adored by whatever spaniard may exist&amp;quot; and &amp;quot;whatever spaniard my exist adores some woman&amp;quot; have quite different meanings. Hintikka and Lakoff have made the same observation in their analysis of natural language (but it seems that Chomsky has overlooked this fact in his formulation of Passive-transformation).This phenomenon that the order in which universal and particular quantifier occur is material for the meaning is even more obvious in the language of predicate logic. Let us consider as example the predicate null personvisitcity(x,y) with the assigned semiotic interpretation: null person x visits city y The two logical expressions</Paragraph>
    <Paragraph position="7"> which differs from each other just in the order of quantification means quite differently. In the process of sentence generation from logical structure we can thus not simply take the semiotic interpretation string and substitute for its variables the corresponding types of quantifiers. In other words, the operation of &amp;quot;quantifier-lowering&amp;quot;, as Lakoff has called it, can not be applied in all cases without pertinent differentiation.</Paragraph>
    <Paragraph position="8"> In our example, it can be applied in the first case and yields the correct sentence: null &amp;quot;every person visits some city &amp;quot; However,its direct application would lead rather to incorrect sentence in respect to the secand logical form. It has rather the meaning &amp;quot;some city will be visited by every person &amp;quot; The regularity for the possibility of substitution can be perceived if we look at the semiotic interpretation string and consider the patterns of the follow- null It is then obvious that only in cases, while the order of logical quantifiers is in the same sequence in which the corresponding variables occur in the given semiotic interpretation, the operation of quantifier-lowering can be directly carried out. And it yields correct sentences. In other cases such as in (II ),it is without measures not possible.</Paragraph>
    <Paragraph position="9"> This kind of regularity has been also observed by Lakoff in his discussion of the notion of derivational ;it occurs in the transformational derivation of surface sentences from the underlying deep structures. Without going into the details of his final modifications,the derivational constraint means roughly like this: if one quantifier commands another in underlying structure, then that quantifier must be leftmost in surface structure. He uses the derivational constraint as a means to rule out certain kind of transformational generation of incorrect surface sentences. Our aim is ,however, not to block out but to obtain correct and meaningful surface sentences from meaningful logical structures. We thus try to find out means so that the condition of derivational constraint can always,or at least to a large part, be fulfilled. For this purpose we introduce the notion of the associated forms of the semiotic interpretation of the given predicate. We add for example to the original semiotic interpretation &amp;quot;person x visits city y&amp;quot; its associated form like (5) &amp;quot;city y will be visited by person x&amp;quot; (6).</Paragraph>
    <Paragraph position="10"> It will be simply stored. In dependence on the orders of quantifiers the corresponding semiotic interpretation string will be selected. By this additional means, correct sentences could then be computationally generated from the logical patters mentioned in (II).</Paragraph>
    <Paragraph position="11"> The same problem occurs with the treatment of logical structures underlying Wh-questions (which, who, etc.,). In our conception and in accordance also with the theory of Hintikka,the interrogative operators has the quantification nature. They subject thus to the same derivational constraints. We use thus the associated semiotic interpretation strings in the required cases. By this means, we can generate computationally from the logical structures</Paragraph>
    <Paragraph position="13"> the following interrogative sentences respectively: &amp;quot;Who visits every city&amp;quot; , &amp;quot;Which cities will be visited by every person&amp;quot; It is of interest to note that with this device the topic of interrogative sentences has been treated and solved for the simple cases at the same time. In general, the device of associated forms of the semiotic interpretation,which from the linguistical viewpoint relate to each other transformationally, will be extensively used. Among others, it will be applied in the treatment of the relative sentences. In other words,associated form like &amp;quot;who makes a journey to city y &amp;quot; will be stored together with the given interpreted predicate; and this associated for~ ~ill be used eventually for relative sentence formation.We return to this problem below.</Paragraph>
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