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<Paper uid="C80-1061">
  <Title>ON COMPUTATIONAL SENTENCE GENERATION FROM LOGICAL FORM</Title>
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ON COMPUTATIONAL SENTENCE GENERATION FROM LOGICAL FORM
Juen-tin Wang
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    <Paragraph position="0"> Institut fur Angewandte Informatik, TU Berlin Summary.</Paragraph>
    <Paragraph position="1"> This paper describes some computational and linguistical mechanisms in our program written in SIMULA to generate natural language sentences from their underlying logical structures in an extended predicate logic. After the presentation of the augumented logical formalism to deal with illocutionary acts,we explain then the basic devices used in the generation process:semiotic interpretation,orders of quantifications or derivational constraints,the referential property of variables and the Leibniz-Frege idea. Examples from system output will be given.</Paragraph>
    <Paragraph position="2"> 1.Introduction Logical form is one ot the most used notions in philosophy,logi c and linguistics. It goes back at least to Aristoteles in his linguistical and logical analysis of natural language sentences.</Paragraph>
    <Paragraph position="3"> This direct reference to the immediate sentence form which has been characteristic for the logic of syllogism remains unchanged throughout the whole period of scholastic logic until the development of the formal predicate logic. Since then,this logical formalism, with or without variation and modification, has been widely used in the linguistic philosophy to analyse and study the natural language. And it is then the resulted representations in logical formalism which will be taken as the logical form of the analyzed natural language sentences. This changed notion of logical form can be found everywhere in the tractatus of Carnap,Quine,Geach,Hintikka and many others. And this notion of logical form will be now used universally. In recent times, a lot of logically minded linguits like Lakoff, Harman,Keenan and Karttunen have even attempted to put logical form into the relationship with the notion of deep structure in connection with Chomsky~ theory of generative grammar. They hold the view that the semantical representation of natural language sentences can be obtained from the formal logical structures and that these semantical representations can be adapted as a basis for sysntactical generation of natural language sentences.</Paragraph>
    <Paragraph position="4"> However,this school of generative grammar has not given any constructive demonstration of their assertions.</Paragraph>
    <Paragraph position="5"> In this paper we do not concern with the question whether this theory,the so-called generative semantics ,will yield a true grammar theory or a genuine theory of the semantics of natural language. We are rather motivated by real needs.</Paragraph>
    <Paragraph position="6"> We have already at our disposal a question-answering data base system which uses essentially the language of predicate logic as the formal query language. We need to know how to express these logical forms in natural language sentences. And Since we have to do with a question-answering system, we need not only to treat logical forms underlying indicative sentences but,more important, the logical structures which have been used by the system as the representa- , tions for interrogative sentences. In the following we present at first the extended logical formalism. We describe then the conceptions and principles being used in implementation. The program is written in SIMULA.</Paragraph>
    <Paragraph position="7"> 2.Logical formalism as semantical representation of natural language sentences null The logical formalism which we have used to represent the sentence structure of a natural language is in its essence a many-sorted language of predicate logic.</Paragraph>
    <Paragraph position="8"> In the conception of representation we have adopted some ideas from the speech act theory of Austin and Searle.According to this theory, the utterance of any sentences in a natural language is characteristically performing at least three distinct kinds of acts:(1) the uttering of words,(2) referring and predicating, (3) stating, questioning, commanding, promising,etc. The notion of referring and predicating should be thus detached from the notions of such speech acts as asserting,questioning, commanding,etc. , since the same reference and predication can occur in the performance of different complete speech acts. In taking account of this distinction between proposition and illocutionary act we make one addition to the usual logical formalism. We let the pro--405-- null positional part be represented by the usual logical expression. In addition, we have an auxiliary component to represent the different illocutionary acts. This additional component will be connected with the left end of the logical expression by a convention sign &amp;quot; = &amp;quot;, which,by the way, should not be read as &amp;quot;equal&amp;quot;. A detailed description of this extended logical formalism 'is given in Habel,Schmidt and Schweppe (1977). Some examples can be given as follows: Assertions:</Paragraph>
    <Paragraph position="10"> The illocutionary indicators like &amp;quot;conference(x2)&amp;quot;, which is itself a name function, can be compared with the designator of Woods(1968) in his query language formalism. In general, several such illocutionary indicators can be allowed at the same time; they could then lead to the representation of multiple questions as discussed by Hintikka. Here,however, we leave the question open, whether this proposed logical formalism as a representation symbolism is complete and adequate for natural language. For example, we do not consi~ der whether WHY- and HOW-question can also be treated in the same framework.</Paragraph>
    <Paragraph position="11"> It is obvous that this proposal for the semantical representation of natural language sentences does not follow Chomsky &amp;quot;s theory, according to which interrogative sentences should be derived from non-interrogative ones by the application of optional transformations.</Paragraph>
    <Paragraph position="12"> This approach has rather some affinity with the suggestion of Ajdukiewicz(1928) who has described the logical structure of a question as consisting of sentential matrix(a sentence with one or more of its components replaced by variables) preceded by an interrogative operator &amp;quot;for what x&amp;quot; (or &amp;quot;for what x,y ,z,...&amp;quot; ,if the matrix has more than one free variable). In such cases, we can take illocutionary indicators as interrogative operators in the sense of Ajdukiewicz.</Paragraph>
    <Paragraph position="13"> The proposed way of giving semantical representations both to indicative and question sentences seems to have some advantages. Above all, it enable us to deal with question sentences directly without using the somehow artificial method to paraphrase them as indicative sentences or spistemic statements, as suggested by Hintikka. Any way, the suggested kind of semantical representation of question sentences receives a quite natural set-theoretical interpretation. For example, the form (2) used for request corresponds to the meaning of the set expression:</Paragraph>
    <Paragraph position="15"> In such cases, the interrogative operators function as quantifiers; they bind free variables and thus transform conditions exhibited in sentential matrix into complete closed forms.</Paragraph>
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