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<Paper uid="C80-1031">
  <Title>MODEL THEORETIC SEMANTICS FOR MANY-PURPOSE LANGUAGES AND LANGUAGE HIERARCHIES</Title>
  <Section position="1" start_page="0" end_page="215" type="metho">
    <SectionTitle>
MODEL THEORETIC SEMANTICS FOR MANY-PURPOSE
LANGUAGES AND LANGUAGE HIERARCHIES
</SectionTitle>
    <Paragraph position="0"> H.Andr6ka ~, T.Gergely ~, I.N6meti ~  ~n Research Institute for Applied Computer Science, Budapest, H-1536, P.O.Box 227.</Paragraph>
    <Paragraph position="1"> Summary Model theoretic semantics (MTS) has a special attitude to describe semantics, to characterize both artificial and natural languages by pure mathematical tools and some of the basic properties of this attitude are disscussed. The arsenal of MTS equipped here with such tools allowing the investigation at such a level of complexity that approximates the real situations. These tools are developed within the frame of category theory.</Paragraph>
    <Paragraph position="2"> i. The challan~e of formal ha ndlin@ of semantics For long times, natural language has been regarded as some very soft, amorphous, and whimsical phenomenon. Although theoretical considerations showed that this may not be so, the very fact that actual linguistic methodology was quite soft and intuitive seemed to confirm the conviction that language cannot be treated very rigorously. It is clear, however, that the more explicit and transparent framework we use for handling a very complex phenomenon, the more can learn about what its complexity really consists of. It has been the use of more or less mathematical-minded methods improving the situation in recent decades.</Paragraph>
    <Paragraph position="3"> A very important first step in the direction of establishing such a framework has been generative grammar. USing the theory of formal languages it gave a fairly abstract picture of what syntax {s, and it has also proved to be an extremely powerful tool in analysing admittedly very subtle syntactic phenomena and, what is even more, in discovering formerly unnoticed interconnections. null Whatever revealing the results of generative grammar should be with respect to syntax, however, it cannot be regarded as paradigmatic if one is interested in a semantics-oriented model of language. Generative grammarians never put the question of what semantics is and what role it plays in language at the same theoretical level they reached with syntax.</Paragraph>
    <Paragraph position="4"> It is reasonable to require that any treatment of semantics be adequate to rigorously formalized methods used for syntax. For this we should use formalism not as abbreviation but as basic tool of investigation, e.g. relating exact mathematical objects to components of language. Moreover we aim to characterize language through analysing the corresponding mathematical methods. An appropriate approach can be borrowed from mathematical logic. This results the so called model theore~c semantics (MTS). MTS is an attitude to investigate natural language from the point of view of semantics. This attitude provides the investigation of natural language on an abstract level.</Paragraph>
    <Paragraph position="5"> Namely, it answers the question in the most abstract sense what language is and what its basic components are. The basic properties of the MTS's attitude are analysed in \[31.</Paragraph>
    <Paragraph position="6"> 2. What is MTS? Language can be analysed only through analysing language carriers.</Paragraph>
    <Paragraph position="7"> From the different possible functions, the language possesses, we find the cognitive one the most significant and this answers our question above. Considering a language carrying system /whether it be human or a machine or else/ the cognitive function is realized while the language is used to describe objects and events of the environment under cognition. Characterising language we abstract from the cognitive process itself and from the internal  organization of the system. Our mere concern is the outcome of the cognitive process, that is, descriptive texts and their relation to the environment which they refer to. MTS attitude demands an ideal external observer (EO) who is to model the system (S) and the system's environment world (W). EO forms models of S, of W and of the S-W relation.</Paragraph>
    <Paragraph position="8"> In order that EO should be able to form the intended models, he must possess the following kinds of knowledge about the sample situation (and EO being an ideal observer, we assume he really does): (i) EO knows the aspect and the level at which S may perceive and describe the environment; in other words, EO knows S's sensitivity.</Paragraph>
    <Paragraph position="9"> (ii) EO knows those fundamental aspects of W that S may describe.</Paragraph>
    <Paragraph position="10"> (i)-(ii) together ensure that EO models W adequately with respect to S. (iii)EO knows that S is finite whereas W is both infinite and infinitely complex.</Paragraph>
    <Paragraph position="11"> (iv) EO knows that S's actual environment is accidental. The knowledge S may obtain at each stage of its cognition is compatible with infinitely many possible worlds. The S-W relation is therefore uncertain: the texts of S always correspond to infinitely many environments, rather than a unique one.</Paragraph>
    <Paragraph position="12"> On the basis of (i)-(iv) EO forms the following models: The model of S will just be a system producting texts (more precisely, the material bodies of texts, whatever they should be). In case EO happens to be a mathematician,Model (S) will be a formal grammar capable of generating the texts of the language.</Paragraph>
    <Paragraph position="13"> The model of W is a metalinguistic description of the world, adequate to S' s sensitivity. For purely theoretical purposes, EO only has to take into account that S has some fixed though arbitrary sensitivity, determining the possible character of the objects and phenomena of W S may describe. When modelling some concrete language, S's sensitivity is also fixed though no longer arbitraryly . In case EO happens to be a mathematician, Model (W) will be a mathematical object. Because of the uncertainty of the S-W relation,Model(W) is a class of models of infinitely many possible worlds.</Paragraph>
    <Paragraph position="14"> The model of the S-W relation is some correspondance between elements of texts and things in the world-models. In case EO happens to be a mathematician, Model(S-W) can be a class of relations or functions.</Paragraph>
    <Paragraph position="15"> We have reached the point where we may define language as it appears at this level of abstraction. By an abstraot language La we mean a triple &lt;Model (S), Model (W~, Model (S-W)&gt;. Furthermore, we call Model (S) the syntax of LA, and Model (W) and Model (S-W) together the semantics of L A. We emphasize that all these models are formed by an ideal external observer and are described in his own language.</Paragraph>
    <Paragraph position="16"> The aboves illustrated by the following figure.</Paragraph>
    <Paragraph position="18"> In the case of classical mathematical logic first of all a similarity type t is fixed (t is a function that renders a natural number, the arity, to each relation and function symbols of the basic alphabet, i.e. of the signature}. The set F t of all possible formulas generated from the alphabet with logical connectives in the usual way corresponds to Model(S). The class M~ of all possible t-type relation sPSructures (models) corresponds to Model(W). The so called validity relation h% t x to Model Thu~ a t-type classical first order language L t is the triple &lt;Ft,Mt,l=&gt;.</Paragraph>
    <Paragraph position="19"> 3. MTS in more complex situations A very simple, we may say, an idealized situation has been considered above. Namely with respect to S it was supposed that its cognition goes on at a fixed level and aspect of analysis, i.e. with a fixed sensitivity. We call this type of cognition homogeneous cognition.</Paragraph>
    <Paragraph position="20">  However MTS attitude enables us to characterize natural language not only in the above simplicity but in the complexity that approximates more realistic cases.</Paragraph>
    <Paragraph position="21"> Indeed a system S can desribe the same objects and events of W from different aspects and at different levels cf detailing. Moreover beyond the great spectrum of sensitivity different environment worlds can be the object of cognition. Cognition in this situation is said to be heterogeneous cognition. The situation to be described from the point of view of EO is as follows.</Paragraph>
    <Paragraph position="23"> The natural language itself virtually seems to enable us to speak about very different kinds of environment at very different levels from very different aspects.</Paragraph>
    <Paragraph position="24"> Thus in this light natural language appears as an extremely rich many-purpose language.</Paragraph>
    <Paragraph position="25"> Beyond the surface natural language consits of such parts which themselves are languages as well (cf. with the subdevision of natural language into a set of dialects or sociolects). These parts, the sublanguages, are historically formed from others. With the growth of the observable environment the corresponding knowledge also widens. The latter needs new language elements so as to be described. Therefore some words change their meanings, new concepts appear which emerge into new sublanguages.</Paragraph>
    <Paragraph position="26"> E.g. the word &amp;quot;tree&amp;quot; has quite a different meaning for a woodman, for a biologist, for a painter, for a child, for a linguist, for a mathematician, etc. The different meanings are con~ nected with different sublanguages which are but different sociolects in this case.</Paragraph>
    <Paragraph position="27"> However the sublanguages are not independen t . They are in a very complex connection, e.g. one may extract lexical morphological or other kinds of connections on the base of which one or other hierarchy of sublanguages can be sorted out. Such a hierarchy provides a possible &amp;quot;selection&amp;quot; for the natural language. Thus a hierarchy of languages consists of the constituent languages together with the relation considered between them.</Paragraph>
    <Paragraph position="28"> Note that one can find a detailed survey of different approaches to sub-languages in \[6\], where another approach has arisen to analyse sublanguages which are called there subsystems of languages.</Paragraph>
    <Paragraph position="29"> How natural language as a many purpose one can be investigated with MTS attitude.</Paragraph>
    <Paragraph position="30"> First of all a so called disjunctive approach can be applied for, according to which EO subdivides the language into such parts each of which can be modelled as a homogeneous one, i.e. as a language that corresponds to a unique and fixed sensitivity.</Paragraph>
    <Paragraph position="31"> Now it is supposed that S has several languages rather than a single one. So Model (S} should consist of a conglomerate of sublanguages. However if the sublanguages were independent then EO could model S as a conglomerate of subsystems. But this is not the case because among most of the sublanguages there are some transition possibilities e.g. translation, interpretation.</Paragraph>
    <Paragraph position="32"> The MTS attitude possesses tools (developed within the frame of mathematical logic) by the use of which the homogeneous cases can be described. So a conglomerate of languages can also be described by these tools but only as a conglomerate of independent languages.</Paragraph>
    <Paragraph position="33"> What about the connection between two languages? Mathematical logic provides tools only for the case when the languages have the same signature, i.e. when their alphabet is the same. In this case the notion of homomorphism is powerful enough to describe the connection between the languages. But such a case is of not much interest to linguists. null Perhaps it is more interesting to analyse the connection between languages of different type (e.g. between a tl-type and t~-type first order classical languagesl.</Paragraph>
    <Paragraph position="34"> Let us see e.g. translation.</Paragraph>
    <Paragraph position="35"> Having two different languages say, English and Russlan, translating a text from one into the other first of all we require not a direct correspondence  between the words, but a connection between the corresponding &amp;quot;world conceptions&amp;quot; of the languages and only then is it resonable to establish the connection between the syntactical elements. In MTS this means that for the translation we have to i) represent the &amp;quot;world conception&amp;quot; of the languages in question. A &amp;quot;world conception&amp;quot; is but a set of sentences (knowledge) that determines a subclass of Model(W); ii) establish the connection between the corresponding sub-classes of models, i.e. between the &amp;quot;world conceptions&amp;quot;; iii) establish the connection among the corresponding syntactical elements.</Paragraph>
    <Paragraph position="36"> But up to now MTS has not been in possession of tools to satisfy the above requirements (i)-(iii).</Paragraph>
    <Paragraph position="37"> Note that in mathematical logic a set of sentences determines a theory. A theory T determines a subclass Mod (T) of models, namely those models where each sentence of T is valid. (Thus a theory T induces a new language &lt;Ft,Mod(T) , I = &gt;.) Thus first of all a connection between the corresponding theories is required for the translation. However translation between any two languages may not always exist. E.g. let us have two languages physics and biology and we want to establish connection between them. For this we should analyse the connection between the corresponding knowledges.However this analysis, as usual, cannot be established directly. A mediator theory is needed. The mediator is an interdisciplinary theory, e.g. the language of general system theory (see e.g. \[2\]). By the use of the mediator a new language with a new kind of knowledge arizes from the input languages, namely biophysics.</Paragraph>
    <Paragraph position="38"> Our aim is the extension of the MTS attitude to analyse the semantics of many-purpose languages and language hierarchies. We develop such tools (wlthin the frame of mathematical logic) by the use of which EO can model a language carrying system not only in a homogeneous situation, but in a heterogeneous one too, the complexity of which approximates the real cases.</Paragraph>
    <Paragraph position="39"> Here we only outline the basic idea providing the basic notions, since the bounds of this paper do not allow us to give a detailed description of the tools This can be found in \[i\].</Paragraph>
    <Paragraph position="40"> Although the first order classical languages do not seem to be adequate for linguistics, it still provides basis for any MTS research. Therefore we introduce the necessary tools of the analysis of the hierarchies of classical first order languages. These tools can be extended for the analysis of different kinds of languages making use of the experience provided by the analysis of the classical case.</Paragraph>
  </Section>
  <Section position="2" start_page="215" end_page="217" type="metho">
    <SectionTitle>
4. Basic notions
</SectionTitle>
    <Paragraph position="0"> Definition I. (similarity type) A similarity type t is a pair t=&lt;H,t'&gt; such that &amp;quot;t' is a function, t' : Dom t'~N where N is the set of natural numbers and O~N, and H ~_ Dom (t').</Paragraph>
    <Paragraph position="1"> Let &lt;r,n&gt;Et' (i.e. let t'(r) = n). If r6H then r is said to be an n-1 -ary function symbol, if r~H then r is said to be an n-ary relation symbol.(r) Let ~ be an ordinal. F~ denotes the set of all t-type formulas containing variable symbols from a set of variables of cardinality a. Thus a t-type first order language is &lt;F?,M., t = &gt; . If Ax - F. and 9CF then ~x I: ~ means . ~ .</Paragraph>
    <Paragraph position="2"> that 9 is a semantical consequence of  Thus in the case of a given theory T C_ contains all the formulas which are compatible with T. Moreover C determines what can be described aT all about the models by the use of theory T. Note that to CT a Boole algebra can be corresponded where O and 1 correspond to &amp;quot;false&amp;quot; and &amp;quot;true&amp;quot; respectively and the operators correspond to the logical connectives. Let us consider the following</Paragraph>
    <Section position="1" start_page="216" end_page="217" type="sub_section">
      <SectionTitle>
Example
</SectionTitle>
      <Paragraph position="0"> Let t = &lt;~,{&lt;R,i&gt;}&gt; be the simularity type and T = &lt;0,F\[&gt; be a theory. (Note that this theory is axiomless.) We write x instead of Xo, Rx instead of R(x) and ~ instead of 9 / ~. The concept</Paragraph>
      <Paragraph position="2"> where we use the following notations: c=HxRxAHx~Rx , d=VxRxVVx~Rx , e=Rx-VxRx , f=~Rx~VxnRx , g=RxAHx~Rx , h=nRxA~xRx , i=9xRx~(RxAHx~Rx), j=\]x~Rx-(~RxAgxRx). The vertexes marker by ~are the fixpoints of the operation ~Xo.</Paragraph>
      <Paragraph position="3"> The formulas of the above C= tell all T that can be said about the t-type models in the classical first order language of a signature of a single unary relation symbol when the theory is atomless. (r) Now we define how a theory can be interpreted by an other one.</Paragraph>
      <Paragraph position="4"> Definition 4. (interpretation) Let T = &lt;Ax~,F~ &gt; and T0=&lt;Axa,F k &gt; be theories in ~ variables. Let = m:F. e ~F~ .</Paragraph>
      <Paragraph position="5"> The=\[ri~e &lt;T~,m,T~&gt; is said to be an interpretation going from T~ into Ta (or an interpretation of T~ in T~) iff the following conditions hold:</Paragraph>
      <Paragraph position="7"> We shall often say that m is an interpretation but in these cases we actually mean &lt;T~,m,T2&gt;. (r) Let m,n be two interpretations of TI in Ta.</Paragraph>
      <Paragraph position="8"> The interpretations &lt;TI,m,T2&gt;, &lt;T1,n,Ta&gt; are defined to be semantically equivalent, in symbols m~n, iff the following condition holds: I= \[m(~)*-~n(~)\] for all ~F~ Axa Let &lt;TI,m,T~&gt; be an interpretation. We define the equivalence class m~ of m (or mo~e precisely &lt;TI,m,T2&gt;/~) to be: m/~ = {&lt;TI,n,T2&gt; : nmm}.</Paragraph>
      <Paragraph position="9"> Now we are ready to define the connection between two theories TI and T2.</Paragraph>
      <Paragraph position="10"> Definition 5. (theory morphism) By a theory morphism u:T1-T2 going from T~ into T2 we understand an equivalence class of interpretations of TI in Ta,i.e. is a theory morphism ~:TI~T2 iff v= =m/~ for some interpretation &lt;TI,m,T2&gt;.(r) The following definition provides a tool to represent theory morphisms Definition 6. (presentation of theory morphisms ) a &gt;be Let T =&lt;AxI,F9 &gt; and Tp=&lt;Axa,Fta two theories in ~la variaSles.</Paragraph>
      <Paragraph position="11">  (i) By a presentation of interpretations from TI to T2 we understand a mapping p : t ~-~F~ .</Paragraph>
      <Paragraph position="12"> (ii) The interpretation &lt;TI,m,T2&gt; satisfies the presentation p:t~ -~ F~2 ' iff for every &lt;r,n&gt;Et~ the followlng conditions hold: a/ If rEHI then m(r(xo ..... Xn_2) =</Paragraph>
      <Paragraph position="14"> =p(r,n).</Paragraph>
      <Paragraph position="15"> We define the theory morphisms v to satisfy the presentation p if &lt;TI,m,T2&gt; satisfies p for some &lt;TI,m,T2&gt;6~. (r) Proposition I.</Paragraph>
      <Paragraph position="16"> Let TI=&lt;AxI,F9 &gt; and T2=&lt;Axa,F9 &gt; be , 1 t..~ ~ ~2 two theorles. ~et p:tl F~ be a presentation of interpretatio~ from TI to Ta. Then there is at most one theory morphism which satisfies p. (r) Category theory provides the adequate mathematical frame within which theories and theory morphisms can be considered. From now on we use the basic notions of category theory in the usual sense (see e.g. \[4\] or \[5\]).</Paragraph>
      <Paragraph position="17"> First of all we show how the category interesting for us looks like.  MorTHa~{&lt;TI,v,T2&gt;: V is a theory morphism ~:TI T2,TI~E0bT~.</Paragraph>
      <Paragraph position="18"> Let v:TI~T2 and w:Ta--Ts be two theory morphisms. We define the composition wov:T1~Ts to be the unique theory morphism for which there exists mE~ and new such that w0u=(n0m)/~ , where the function (n0m)-F a ~F a is defined * t I ta  by (nom)(~)=n(m(~)) for all ~6F~ I (iii) Let T=&lt;Ax,F~&gt; be a theory. The identity function Idea is defined ~t to be IdF~{&lt;~,~&gt;:~6F~\].</Paragraph>
      <Paragraph position="19"> The identity morphism Id~ on T is defined to be IdT~(IdF~)/~ (r) Proposition 2.</Paragraph>
      <Paragraph position="20"> TH a is a category with objects Ob/H a, morphisms MorTH a, composition v0v for any v,96MorlH a and identity morphisms Id T for all T~ObTH a. (r) 5. The main property of TH a The heterogeneuous situation,where the language carrying system uses not only one language to describe the environment world can be described by EO as the category TH ~. Note that TH ~ contains all possible hierarchies, because the connection between any two constituents is but an element of MorTH a. The mathematical object TH a provides the usage of the apparatus of category theory to analyse the properties of language hierarchies. Moreover this frame allows us to establish connection between any two theories even if there is not any kind of direct relation between them. In the latter case a &amp;quot;resultant&amp;quot; theory should be constructed which has direct connection with original ones and the power of expression of which joins that of the original ones. This &amp;quot;resultant&amp;quot; theory mediates between the original directly unconnected theories.</Paragraph>
      <Paragraph position="21"> Note that the construction of a resultant theory to some given unconnected theories is one of.the most important tasks of the General System Theory (see e.g. \[2\]).</Paragraph>
      <Paragraph position="22"> The following theorem claims the completeness of IH a (in the sense of \[4\] or \[5\]). This notion corresponds (in category theory) to the above expected property.</Paragraph>
      <Paragraph position="23"> Theorem 3.</Paragraph>
      <Paragraph position="24"> (i) The category TH ~ of all theories is complete and cocomplete.</Paragraph>
      <Paragraph position="25"> (ii) There is an effective procedure to construct the limits and colimits of the effectively given diagrams in TH ~ . @ Now we enlight the notions used in the above theorem.</Paragraph>
      <Paragraph position="26"> A diagram D in TH a is a directed graph whose arrows are labelled by morphisms u:Ti~T j of Mor/H a and the nodes by the corresponding objects  (where T0,TI ,T2EObIH a ~I , v26MorlH a ) are diagrams.</Paragraph>
      <Paragraph position="27"> Here the identity morphisms IdT 3_ (i=O,i,2) are omitted for clarity. We indicate the identity morphisms only if they are needed. (r) Definition 8. ( cone, lim~ t, co limit ) A cone over a diagram D is a family {a. :T-T.-T. is object of D} of morphisms 1 i&amp;quot; 1 . from a single ob3ect T such that T6ObTH ~, for any i e. CMorIH a and for any morphisms T.!~T. of D aj=aio~ in TH a ~jiT. \] (i.e. T~I 3 commutes).</Paragraph>
      <Paragraph position="28"> a i ~-~T i The l~mit of a diagram D in TH ~ is a cone {a. :T~T. :T. is object of D\] over D such thalt fop anly other cone {Si:R~Ti:Ti is object of D\] over D there is a unlque morphism v:R~T such that Bi=~oa i * The colimit of D is defined exectly as above but all the arrows are reversed. (r) Definition 9. (complete, cocomplete) A category K is said to be complete and cocomplete if for every diagram D in K both the limit and the colimit of D exist in K. (r) By aboves we see that Theorem 3 says that every diagram in IH a has both limit and colimit in TH a. I.e. in the category TH a of all theories all possible limits and colimits exist (and can be constructed).</Paragraph>
      <Paragraph position="29"> Now let us see some Ex~amp l e s Let T-~&lt;~,F~o&gt;, TI~&lt;AxI,FtI&gt;, where</Paragraph>
      <Paragraph position="31"> Let ~:To~TI and ~:To-TI be two theory morphisms such that for some mEv and n6~ we have</Paragraph>
      <Paragraph position="33"> We have to prove rom=don, i.e. we have to show (Xo+X1=Xl)/~Ta=(Xo'X1=Xo)/~T2, i.e. that Ax2 ~ (Xo+X1=X1*-~Xo'X1=Xo).</Paragraph>
      <Paragraph position="34"> Suppose Xo+X~=Xl. Then xo'x~=; =Xo'(Xo+Xl)=Xo, by (Xo'(Xo+Xl)=Xo)6Ax2.</Paragraph>
      <Paragraph position="35"> We obtain Ax2 1 = (Xo'X~=Xo-Xo+X~=X~) similarly.</Paragraph>
      <Paragraph position="36"> 2./ Suppose 0'or = 6'o~. We have to show ~op = p~ and ~o6 = 6' for some theory morphism ~.</Paragraph>
      <Paragraph position="37"> Let r'~p' and d'E6'.</Paragraph>
      <Paragraph position="39"> We have to show that p determines a theory morphism ~:T2-T2 '. I.e. we have to show that (V~EAx2) Ax2' \]= p(~).</Paragraph>
      <Paragraph position="40"> Notation: r'(+) ~-S, d'(/) = (r) , We know that Ax'l={Xo@Xo=Xo,(Xo@Xl)@x2 =</Paragraph>
      <Paragraph position="42"> We have to show Ax2' I = Xo@(Xo@Xl)=Xo.</Paragraph>
      <Paragraph position="43"> xo@(Xo@Xl ) = (XoGXo)Sxl =Xo@Xl and therefore Xo(r)(Xo@Xl)=Xo. Similarly for the other elements of Ax2. (r) Proof of B: The proof is based on the fact that Th(Ax21=Th(Ax1@{Xo+X1=Xo*-~Xo+Xl=Xl}). @ Many further interesting features of TH a could be detected had we no limits of our paper.</Paragraph>
    </Section>
  </Section>
  <Section position="3" start_page="217" end_page="217" type="metho">
    <SectionTitle>
6. Instead of conclusion
</SectionTitle>
    <Paragraph position="0"> In aboves MTS attitude has been equipped with new tools which might allow the investigation of both natural and artificial languages at such a level of complexity that approximates the real situations. We believe that these open up new perspectives for MTS in the investigation of both computational and theoretical linguistics. E.g. MTS may provide a description in each case where the connection between two or more sublanguages play a significant role. We think that this is the case in the semantical investigation of certain types of humor as well, where humor might appear by unusual interpretations of texts. This can be described by establishing the connection between the corresponding theories that represent knowledge, i.e.</Paragraph>
    <Paragraph position="1"> presupositions. The following jokes reflect the afore mentioned type: l.&amp;quot;Why didn't you come to the last meeting?&amp;quot; &amp;quot;Had I known it was the last I would have come.&amp;quot; 2.Two men were discussing a third.</Paragraph>
    <Paragraph position="2"> &amp;quot;He thinks he is a wit&amp;quot; said one of them.</Paragraph>
    <Paragraph position="3"> &amp;quot;Yes&amp;quot;, replied the other, &amp;quot;but he is only half right&amp;quot;</Paragraph>
  </Section>
class="xml-element"></Paper>