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<Paper uid="C86-1081">
  <Title>A LOGICAL FORMALISM FOR THE REPRESENTATION OF DETERMINERS f</Title>
  <Section position="3" start_page="0" end_page="344" type="metho">
    <SectionTitle>
REPRESENTATION FORMALISM
</SectionTitle>
    <Paragraph position="0"> Ct~ main goals in designing the representation formalism that will be used in the following sections were: I ) To maintain a close relationship between the pieces of informstion that are intuitively present in the input sentence and the predicates appearing in its interpretation.</Paragraph>
    <Paragraph position="1"> 2) To make explicit the distinction between surface objects and semantic entities: words on one side and concepts, individuals, classes etc. on the other.</Paragraph>
    <Paragraph position="2"> 3) To maintain a co~itional analysis of language, where the starting point is provided by the dependency tree built by the rule~bassd syntactic cogent of the FIDO system \[Le~no,  4) To devise a set of predicates allowing an easy translation between the obtained representation and the corresponding operations cn a Knowledge Base.</Paragraph>
    <Paragraph position="3"> A first example concerns a very simple sentence: I) Bob loves Lucy.</Paragraph>
    <Paragraph position="4"> The representation is (lower case strings refer to variables; upper case ones to constants or predicates):</Paragraph>
    <Paragraph position="6"> This can be read as: there are three internal entities (x,y,z); the speaken (S) is referring to the first of them by using the word BOB, to the second with TO LOVE, to the third with LUCY; the agent of y is x, its obiect is z. Fig.1 depicts, in terms of nodes and arcs, the proposed representation. REF predicates are meant to indicate the mapping between words and internal nodes. Consider now ex.2: 2) The boy loves a girl The representation reported below disregards the information con ~ tents gathered from the determiners:</Paragraph>
    <Paragraph position="8"> The representation is analogous to the previous one. On the other hand, some problems arise in this case; they concern the com~uni~ eative impact of ex.2, and which were not evident in the previous exan~)le. If we say &amp;quot;Bob loves Lucy&amp;quot;, we assume that whoever hears this sentence knows both Bob and Lucy, so that he is able to reconstruct the right semantic interpretation, and to identify the specific individuals to whom the speaker is referring. But how can the hearer convey such kind of informmtion when explicit names are not available? And, on the opposite side, how can the speaker tell the hearer that he is not referring to any specific individual, but he wants to mention a general property of the class? We believe that the discriminating information is carried by determiners. If we take them into account, we should state that ex.2 expresses something as: &amp;quot;BOY (this word should suffice for yca to identify whom I'm talking about) LOVES GIRL (this word is not specific enough to allow you to identify the correct referent)&amp;quot; or, if we think of a knowledge base represented as a semantic net ~ work: &amp;quot;Dear hearer, you should find a node satisfying the 'BOY' description (and if ysu consider the context, this can be done unambiguously), then yca should create a new node of type 'GIRL' and connect them via a nede which is an 'ACT~OF 'LOVE' &amp;quot;  We 'can give now the complete representation of ex.2:</Paragraph>
    <Paragraph position="10"> that is: &amp;quot;The .~)eaker is referring to entity x by ~eans of the ~rd BOY, he assumes that x is identifiable to himself and that the description used (BOY) enables the hearer to refer to the same entity; there Ls also an act of loving (y) and another entity (z) what\] he is referring to by means of the word GIRL; z is identifiable to himself, but the word GIRL will not enable the hearer to refer to the same entity he is thinking about. Finally, x is the agent of y and z is the object of y&amp;quot;.</Paragraph>
    <Paragraph position="11"> Actually, 2r' does not correspond exactly to sentence 2. In fact Ex.2 is mrbiguous whilst 2r' is not. The source of ambiguity is the NP &amp;quot;a girl&amp;quot;. In the previous discussions we. assumed that the speaker knows the girl loved by &amp;quot;the boy&amp;quot;, but this is not necessarily true. Tne &amp;quot;specific&amp;quot; reading is given in 2r' by the presence of the predicate IDENTIFIABLE(S,S,z). Now, how can we account for the inherent ambiguity of the indefinite determiner? Simply droppi~ from its sei&amp;nntics the &amp;quot;IDENTIFIABLE&amp;quot; prcdicate: it will be added in case the context provides m~fficient clues to infer the &amp;quot;specific&amp;quot; interpretation, or its negation (&amp;quot;not IDEN = TIFIABLE&amp;quot;) will be added in case some evidence about a &amp;quot;generic&amp;quot; interpretetion is available. No predicate is added (and the sen ~tence remains a~bi\[~ous, as it actually is) if no disambign~ating criterium is provided by the context.</Paragraph>
    <Paragraph position="12"> the approach exemplified above will be de~.~ribed in the next section, covering the definite and Jndef\]nite determiners. The predicates used are listed below, together with an explanation of their intuitive meaning.</Paragraph>
    <Paragraph position="13"> REF(x,y,z): Individual x is able to refer to eatity y by by means of expression z.</Paragraph>
    <Paragraph position="14"> ENABLESAMERI.Im(x,y,z): Ir~\]ividual x assures that individual y is able to identify, by i~eans of expression z, the s~me entity which he refers to.</Paragraph>
    <Paragraph position="15"> IDENTIFIABLE(x,y,z): Individual x assumes that individual y is able to identify (or that y knows) entity z.</Paragraph>
    <Paragraph position="16"> Sl~2(x): Entity x is a set composed of at least t~c elements.</Paragraph>
    <Paragraph position="17"> ARBITRARY(x,z) : Any member of the class x identified by be expression z necessarily satisfies the property expressed by the pro ~ position in which z occurs.</Paragraph>
  </Section>
  <Section position="4" start_page="344" end_page="346" type="metho">
    <SectionTitle>
REPRFSFNPSATION CF DEI~ERMINERS
</SectionTitle>
    <Paragraph position="0"> We wi\] 1 de~.ribe ~ne representations we have adopted for determiners, fell.owing the classification introduced in \[Croft 85\], which we. report here (note, however, that the ARBITRARY predicate introduced above does not correspond to 'arbitrary' in Croft's c\]assification, only to its 'not defeasible' subclass):  Table I lists the various representations we have adopted, b)t us consider first the definite determiners (we are not going to discuss what Enoft refers to as 'perceptually available'-referent determiners, i.e. de~mstratives like 'this' and 'that').</Paragraph>
    <Paragraph position="1"> Tne representation for 'the' reported in table I can be para&amp;quot; phrased as: &amp;quot;there exists an entity that the speaker is able to refer to by ma~s of the expression following the determiner; the speaker asam~s that that expression will enable the hearer to refer to the ~me entity; the speaker is ~le to identiDI the referred entity&amp;quot;. An example is provided by</Paragraph>
    <Paragraph position="3"> It ~st be noted that it is not written anywhere that the entity x has to be m~ individual. In principle, it could be a generic entity (i.e. an 'intensional' node of a semantic not), thus fulfilling the role of 'prototype individual' \[Grosz, Jo~qni, ~in~ stein 83\].</Paragraph>
    <Paragraph position="4"> A few ~rds now to discuss plurals. For example:</Paragraph>
    <Paragraph position="6"> The enly difference is the presence of the predicate SET2(x), ~hich states that the entity x is a set. We use the r~ SEF2 to evidentiate that it refers to the pretheoretical notion of set as 'a group' ca~posed by mere than ore element.</Paragraph>
    <Paragraph position="7"> As regards indefinite determiners, the representations given in Table I can be paraphrased as: &amp;quot;There is an entity that the speaker is able to refer to by means of the expression following the determiner; the speaker cannot assume that that expression will enable the hearer to refer to the seme entity&amp;quot;. Let us consider first the 'specific' meaning of the determiner 'a':</Paragraph>
    <Paragraph position="9"> (note that the speaker assumes that the use of the lexeme 'room' enables the he~'er to identify the specific room he is thinking about). This interpretation is the simplest one, since it directly encodes the basic m~ning of' the indefinite determiner, i.e. the reference to an unspecified entity.</Paragraph>
    <Paragraph position="10"> A first problem is how to get the 'generic' rreaning f~ii this representation (epistemic and intensio~l interpretations will be analyzcwl afterw~lrds, since they do not appear as subjnots of sentences). In: 6) Un onso va in letargo in inverno (A bear hibernates in winter) you could probably perceive a ~r~@tning such as: &amp;quot;If yea randar6y pick an iedividtml bear, then yea will see that it hibernates in winter; of course, the bear y~l will select will probably rmt be the same bear I am thinking of, but it still hibernates in winter&amp;quot;. Notice that this paraphrase (as we aassme it is) does not i\[~oly the existence of a 'prototypieal' bear to khich the general property of 'hibernating in winter' &lt;'~ihould apply: we are referring to an arbitrary element of the class we are talking about, although ~.~ are not saying that no exceptions exist. It is this non~identlfiability of the element for which the property is predicated that allows the he;men to obtain the state general result.</Paragraph>
    <Paragraph position="11"> But now, what is the difference between ex.5 and ex.6? In the first ease (specific interpretation), the speaker is referring to a particular individt~al, ~hereas in the second one he is not. We. can state that in the specific interpretation IDE~\['IFIABLE(S,S,x), whereas in the generic interpretation 'not ID\[~I'IFIARLE(S,S,x)'. Of course, in both eases the presence of ' not ENABLESA~REF(S,H,EXP) ' should allow to infer that 'not IDE~'IFIABLE(S,H,x) ' , that is, to the speaker's knowledge, x is not identifiable by the hearer by ire~mns of the expression EXP used. Note that this does not mean that the hearer will not be able to identify x, but only t~at the speaker is not willing to asssme so (s~m examples will be provided afterwards). The representation we get for ex.6 is:  Note that the representation includes the R~,' predicate, which will be actually built up on the basis of the expression following the determiner,. This has been done in order to provide a means of unifying the variable x occurring in the other predicates with the one appearing in the representation of the relmining NP.</Paragraph>
    <Paragraph position="13"> It could be argued that there is no reason why in the analysis of definite determiners we allowed the 'expression' following the determiner to refer to an intensional object, whereas in the inde~ finite case we do not. However, lar~uage works just because we assume (sometimes incorrectly) that a given lexeme refers to the same concept for the whole comr~nity of language users. This means that ~e cannot accept a reading where 'not ENABLNSAFEREF(S,H,EXP)' occurs and where EXP is intended to refer to a generic concept.</Paragraph>
    <Paragraph position="14"> In order to discuss the other two interpretations of indefinite determiners, we need to refer to their use in eases different from the subject of the sentence, or, more precisely, in sententlal contexts where there is another partecipant, different f~em the speaker, who has an 'active' role. In these cases, the representa ~ tion m~st account for the existence of a referentiality predicate attributed to someone different from the speaker and the hearer.</Paragraph>
    <Paragraph position="15"> The first well known example is provided by a 'desire' verb, that  is 'to want': 7) John wants to nmrry a Norwegian Some different meanings can be characterized by the hearer's different replies : 7a) No, Ingrid isn't a Norwegian.</Paragraph>
    <Paragraph position="16"> 7b) Who is she? 7c) How does he think he can find one?  In the first case, the speaker is using the word 'Nor~ngian' to refer to John's future wife, bat the speaker does net agree on that word (*). In the second case, the hearer assumes that the speaker is referring to a specific girl whom he does net knew. In the third case, he assumes the speaker is not referring to any par ticu\]ar Norwegian.</Paragraph>
    <Paragraph position="17"> In all cases there is a common core in the representation of the initial sentence; it is:</Paragraph>
    <Paragraph position="19"> To this basic interpretation, scme different predicates are added for each different case: 7ar) IDE~FfIFIABLE(S,S,w) for the standard &amp;quot;specific&amp;quot; interpretation of the indefinite determine~; IDENTIFIABLE(H,H,w) &amp; not REF(H,w,NDRWEGIAN) to state the hearer's disagreement.</Paragraph>
    <Paragraph position="21"> But now ~e have the possibility to characterize two subcases of c: in the first one (ci) S does not know the Norwegian that John wants to m~rry, but John does know her; in the second ease (c2) the identification is generic fer both of them:</Paragraph>
    <Paragraph position="23"> The last determiner (in Croft's analysis) is &amp;quot;any&amp;quot;. Its represen ~ tation is reported in table I, but lack of space prevents us from discussing it (mereover, not all students agree on its status of determiner ~ vs. quantifier ~ and no Italian lexeme has a meaning exactly equivalent to &amp;quot;any&amp;quot;).</Paragraph>
    <Paragraph position="24"> We list below the rules m~re strictly concerned with the operational inter1~retation of the predicates associated with deter ~ miners:  ly right. Fer instance, the speaker could reply &amp;quot;She was born in O~Io&amp;quot;, and the hearer &amp;quot;~t last year she got the U.S. citizen ~ ship&amp;quot;.</Paragraph>
    <Paragraph position="26"> then ereatenode(exp,x), r~rk(x, 'GENERIC~BEFgASIBLE ' ) A few words on the functions used in the acticn part of the rules: locatenode looks first for individual referents; if none is available it considers generic nodes.</Paragraph>
    <Paragraph position="27"> createnede builds a new instance of the most specific available concept identified by exp.</Paragraph>
    <Paragraph position="28"> iooateset works exactly as looatenode, but the node that it looks for nust represent a set.</Paragraph>
    <Paragraph position="29"> Tnese rules are not complete, as they do not take into account ~istemic and Intensional Indefinite: in fact, both the represen ~ tations of these interpretations nust include the hypothetical knowledge of another individual and, as we said before, we did not treat belief contexts.</Paragraph>
  </Section>
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