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<Paper uid="C80-1061">
  <Title>ON COMPUTATIONAL SENTENCE GENERATION FROM LOGICAL FORM</Title>
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6. Referential property of variable,
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    <Paragraph position="0"> relative sentence generation and and property of connectivity In computational sentence generation from the underlying logical structure we make an extensive use of the reference nature of the variables. Variables have been called by Quine as pronouns of logic and mathematics. The referential character will be used by us as a kind of red thread in building up the composed sentences. This feature shows clearly in generating sentences with relative clauses. Let us consider as example the logical structure  person(xl)=.ex.x2((.ex.x4(takeplacecountry(x2,x4).and.country(x4).eq. null &amp;quot;japan')).and. (takepart(xl,x2))) The variable xl in the interrogative operator, namely person(xl), indicates the topic of the question concerned.</Paragraph>
    <Paragraph position="1"> This topic is in general specified by the composition of predicates and functions in a certain way which is expressed by the logical matrix. The generation of the corresponding interrogative sentence means to express verbally this composition of predicates and functions after the given prescription in matrix.</Paragraph>
    <Paragraph position="2"> In making use of the referential property of variavles, it is seen that the topic will be characterized at first by the predicate takepart(xl,x2) On this ground its associated form of semiotic interpretation, namely &amp;quot;who takes part at meeting x2&amp;quot; will be used as the main building component of the question sentence to be generated. By means of the variable, we can find that this predicate takepart(xl,x2) is connected directly with the predicate takeplacecountry(x2,x4) .</Paragraph>
    <Paragraph position="3"> In other words, the variable x2 contained in the predicate takepart(xl,x2) is in its turn specified by the predicate takeplacecountry(x2,x4). We use thus in consideration of its modification character the corresponding associated form of semiotic interpretation, namely &amp;quot;which takes place in country x4&amp;quot; to build up the relative clause. In the same way, we find that the variable x4 contained in the predicate takeplacecountry(x2,x4) is referred by the name function country(x4) , whose function value indicates the name Japan. This constant will be thus inserted at the place x4. The termination of these connecting and inserting processes lead then to the generation of the sentence null &amp;quot;Who takes part at the meeting which takes place in the country &amp;quot;Japan'&amp;quot; In connection with the referential feature of variables it is of interest to note that all the logical structures which we have used in our question-answering system shows a remarkable property which we have called the property of connectivity. A logical structure is called to have the property of connectivity, if in the case where it contains more than one predicate or function each of its predicates ~d functions shares some argument with others,i.e, has common variables with other functions or predicates.</Paragraph>
    <Paragraph position="4"> It is on the ground of the property of this connectivity that we can even let the program processing under certain circumstances be driven by variables, such as explained just above. On the contrary, let us consider the following logical structure: /true/=.ex.x1(.ex.x2(.ex.x3(city(x3) .eq. &amp;quot;tokyo'.or.takepart(xl,x2)))) Since the function city(x3) and the predicate takepart(xl,x2) do not share any common argument, this logical form  --409-does not have the defined property of connectivity. Its corresponding surface sentence can therefore not be computed by the process driven by variables* Instead, a different procedure must be applied. At present stage, we let, however, such types of sentences out of our consideration.</Paragraph>
    <Paragraph position="5"> The usefulness of variables is not exhausted in relative sentence generation. In general, we intend to use it to differentiate the varied patterns of the logical forms concerned. And as a result of this differentiation, sentences of varied patterns will be generated. Let us consider the following simple logical form: person(xl)=.ex.x2(takepart(xl,x2).and.</Paragraph>
    <Paragraph position="6"> givelectureconf(xl,x2)) For such pattern, no attempt to generate relative sentence will be made. Instead, it tries to express the surface sentence as follows: &amp;quot;Who takes part at some meeting and gives a lecture at this meeting &amp;quot; Our program is thus in trying to discern as much of logical patterns as possible. It works after them.</Paragraph>
    <Paragraph position="7"> 7. Categorical and hypothetical sentences, idea of Leibniz and Frege In our computational sentence generation we have made use of an old idea, which goes back at least to an observation made by Leibniz in his famous nouveau essais sur l~ntendement humain. In the classical logic, one is customed namely to divide the judgements or assertional indicative sentences into three major types: categorical,hypothetical and disjunctive null Leibniz has remarked that in some cases an actual hypothetical judgement can be expressed in a categorial form. This regularity is discussed also by Frege on the relation between auxiliary sentences (Beis~tze) and conditional sentences (Bedingungss~tze)in his essay 0ber Sinn und Bedeutung. According to Frege the cinditional or hypothetical sentence &amp;quot;Wenn eine Zahl kleiner als I und gr~Ber also ist, so ist auch ihr Quadrat kleiner als I und gr6Ber als O &amp;quot; can be expressed in a categorial form: &amp;quot;Das Quadrat einer Zahl, die kleiner als I and gr~Ber also ist, ist kleiner als I und gr~Ber also &amp;quot; In our system design, we have adopted this old conception. From the underlying logical implication structure its surface sentence will not be generated in hypothetical, but rather in categorial form.' This approach has its practical and stylistic advantages. It can be seen in consideration of the following logical form: /true/=.all.xl (.ex.x2((.ex.x3 ( makejourneycity(xl ,x3) .and.city(x3) * eq. &amp;quot;tokyo&amp;quot; ) ) . imp. (takepart (xl ,x2) ) ) ) . In following this line of thought,the corresponding surface sentence will be generated by the system as follows: &amp;quot;Everybody who makes a journey to the city'~okyo&amp;quot; takes part at some meeting &amp;quot; It is natural and simple. For its generation we need no more additional methods than the ones which have been at our disposal:the quantifier-lowering and formation of relative sentence. The only thing which we must take care of is to choose the semiotic interpretation string of the conclusion rather than that of antecedent as the main building component. Otherwise, the meaning would be distorted.</Paragraph>
    <Paragraph position="8"> The usefulness of this conception of Leibniz and Frege consists for our purpose, above all, in the fact that it can be even extended to the treatment of logical structures for interrogative sentences. Without using this idea,the surface sentences to be computationally generated would have a cumbersome look. This feature may appear clearly,if we try to deal with the following simple logical structure: conference(x2)=.all.xl ((.ex.x3( makejourneycity(xl,x3).and.city(x3) .eq.'tokyo')).imp. (takepart(xl,x2))) It is a logical form underlying an interrogative sentence; it contains the logical form mentioned just above almost as component. In combination of this Leibniz-Frege idea with the other principles like referential property of variables, topic handling and formation of relative sentence which we have described above the system yields then without other detour the interrogative sentence: &amp;quot;Which meetings will be visited by everyone who makes a journey to the city &amp;quot;Tokyo&amp;quot; &amp;quot;  --410-8. General remark and discussion We have above described some main conceptions and principles upon which we have built up the program. The system works essentially after logical patterns, after certain features of logical structures such as connectivity, the occurence of implication sign and so on. It is thus properties-oriented and not syntax-driven. It is needless to say that our program can not deal with all kinds of logical structures. This is also not our original aim, besides the fact that,as Chomsky makes remark about the nature of deep structures, not all logical structure can underly or have a meaningful surface sentence. From the right beginning we have confined ourself to just a specified set of logical structures used as a formal query language. It is remarkable that for such a set of logical formscertain regularities and patterns can be generally established and be used to generate meaningful surface sentences computationally. The progress will depend to a large extent on the careful observation of logical patterns and insightful linguistic analyses. null</Paragraph>
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