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<Paper uid="C02-1061">
  <Title>Antonymy and Conceptual Vectors</Title>
  <Section position="4" start_page="0" end_page="0" type="metho">
    <SectionTitle>
2 Conceptual Vectors
</SectionTitle>
    <Paragraph position="0"> We represent thematic aspects of textual segments (documents, paragraph, syntagms, etc) by conceptual vectors. Vectors have been used in information retrieval for long (SM83) and for meaning representation by the LSI model (DDL+90) from latent semantic analysis (LSA) studies in psycholinguistics. In computational linguistics, (Cha90) proposes a formalism for the projection of the linguistic notion of semantic eld in a vectorial space, from which our model is inspired. From a set of elementary concepts, it is possible to build vectors (conceptual vectors) and to associate them to lexical items2. The hypothesis3 that considers a set of concepts as a generator to language has been long described in (Rog52). Polysemic words combine di erent vectors corresponding  to di erent meanings. This vector approach is based on known mathematical properties, it is thus possible to undertake well founded formal manipulations attached to reasonable linguistic interpretations. Concepts are de ned from a thesaurus (in our prototype applied to French, we have chosen (Lar92) where 873 concepts are identi ed). To be consistent with the thesaurus hypothesis, we consider that this set constitutes a generator family for the words and their meanings. This familly is probably not free (no proper vectorial base) and as such, any word would project its meaning on it according to the following principle. Let be C a nite set of n concepts, a conceptual vector V is a linear combinaison of elements ci ofC. For a meaning A, a vector V(A) is the description (in extension) of activations of all concepts of C. For example, the di erent meanings of ,door- could be projected on the following concepts (the CON-CEPT[intensity] are ordered by decreasing values): V(,door-) = (OPENING[0.8], BARRIER[0.7], LIMIT[0.65], PROXIMITY [0.6], EXTERIOR[0.4], IN-TERIOR[0.39], . . .</Paragraph>
    <Paragraph position="1"> In practice, the largerCis, the ner the meaning descriptions are. In return, the computing is less easy: for dense vectors4, the enumeration of activated concepts is long and di cult to evaluate. We prefer to select the thematically closest terms, i.e., the neighbourhood. For instance, the closest terms ordered by increasing distance to ,door- are: V(,door-)=,portal-, ,portiere-, ,opening-, ,gate-, ,barrier-,. . .</Paragraph>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
2.1 Angular Distance
</SectionTitle>
      <Paragraph position="0"> Let us de ne Sim(A;B) as one of the similarity measures between two vectors A et B, often used in information retrieval (Mor99). We can express this function as: Sim(A;B) = cos( dA;B) = A BkAk kBk with \ &amp;quot; as the scalar product. We suppose here that vector components are positive or null. Then, we de ne an angular distance DA between two vectors A and B as DA(A;B) = arccos(Sim(A;B)). Intuitively, this function constitutes an evaluation of the thematic proximity and measures the angle between the two vectors. We would generally consider that, for a distance DA(A;B) 4 4Dense vectors are those which have very few null coordinates. In practice, by construction, all vectors are dense.</Paragraph>
      <Paragraph position="1"> (45 degrees) A and B are thematically close and share many concepts. For DA(A;B) 4 , the thematic proximity between A and B would be considered as loose. Around 2 , they have no relation. DA is a real distance function. It veri es the properties of re exivity, symmetry and triangular inequality. We have, for example, the following angles(values are in radian and degrees). null</Paragraph>
      <Paragraph position="3"> The rst one has a straightforward interpretation, as a ,tit- cannot be closer to anything else than itself. The second and the third are not very surprising since a ,tit- is a kind of ,sparrowwhich is a kind of ,bird-. A ,tit- has not much in common with a ,train-, which explains a large angle between them. One can wonder why there is 32 degrees angle between ,tit- and ,insect-, which makes them rather close. If we scrutinise the de nition of ,tit- from which its vector is computed (Insectivourous passerine bird with colorful feather.) perhaps the interpretation of these values seems clearer. In e ect, the thematic is by no way an ontological distance.</Paragraph>
    </Section>
    <Section position="2" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
2.2 Conceptual Vectors Construction.
</SectionTitle>
      <Paragraph position="0"> The conceptual vector construction is based on de nitions from di erent sources (dictionaries, synonym lists, manual indexations, etc). De nitions are parsed and the corresponding conceptual vector is computed. This analysis method shapes, from existing conceptual vectors and de nitions, new vectors. It requires a bootstrap with a kernel composed of pre-computed vectors. This reduced set of initial vectors is manually indexed for the most frequent or di cult terms. It constitutes a relevant lexical items basis on which the learning can start and rely.</Paragraph>
      <Paragraph position="1"> One way to build an coherent learning system is to take care of the semantic relations between items. Then, after some ne and cyclic computation, we obtain a relevant conceptual vector basis. At the moment of writing this article, our system counts more than 71000 items for French and more than 288000 vectors, in which 2000 items are concerned by antonymy. These items are either de ned through negative sentences, or because antonyms are directly in the dictionnary. Example of a negative de nition: ,non-existence-: property of what does not exist.</Paragraph>
      <Paragraph position="2"> Example of a de nition stating antonym: ,love-: antonyms: ,disgust-, ,aversion-.</Paragraph>
    </Section>
  </Section>
  <Section position="5" start_page="0" end_page="0" type="metho">
    <SectionTitle>
3 De nition and Characterisation of
Antonymy
</SectionTitle>
    <Paragraph position="0"> We propose a de nition of antonymy compatible with the vectorial model used. Two lexical items are in antonymy relation if there is a symmetry between their semantic components relatively to an axis. For us, antonym construction depends on the type of the medium that supports symmetry. For a term, either we can have several kinds of antonyms if several possibilities for symmetry exist, or we cannot have an obvious one if a medium for symmetry is not to be found. We can distinguish di erent sorts of media: (i) a property that shows scalar values (hot and cold which are symmetrical values of temperature), (ii) the true-false relevance or application of a property (e.g. existence/nonexistence) (iii) cultural symmetry or opposition (e.g. sun/moon).From the point of view of lexical functions, if we compare synonymy and antonymy, we can say that synonymy is the research of resemblance with the test of substitution (x is synonym of y if x may replace y), antonymy is the research of the symmetry, that comes down to investigating the existence and nature of the symmetry medium. We have identi ed three types of symmetry by relying on (Lyo77), (Pal76) and (Mue97). Each symmetry type characterises one particular type of antonymy. In this paper, for the sake of clarity and precision, we expose only the complementary antonymy. The same method is used for the other types of antonymy, only the list of antonymous concepts are di erent.</Paragraph>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
3.1 Complementary Antonymy
</SectionTitle>
      <Paragraph position="0"> The complementary antonyms are couples like event/unevent, presence/absence.</Paragraph>
      <Paragraph position="1"> he is present ) he is not absent he is absent ) he is not present he is not absent ) he is present he is not present ) he is absent In logical terms, we would have:</Paragraph>
      <Paragraph position="3"> This corresponds to the exclusive disjunction relation. In this frame, the assertion of one of the terms implies the negation of the other.</Paragraph>
      <Paragraph position="4"> Complementary antonymy presents two kinds of symmetry, (i) a value symmetry in a boolean system, as in the examples above and (ii) a symmetry about the application of a property (black is the absence of color, so it is \opposed&amp;quot; to all other colors or color combinaisons).</Paragraph>
    </Section>
  </Section>
  <Section position="6" start_page="0" end_page="0" type="metho">
    <SectionTitle>
4 Antonymy Functions
</SectionTitle>
    <Paragraph position="0"/>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
4.1 Principles and De nitions.
</SectionTitle>
      <Paragraph position="0"> The aim of our work is to create a function that would improve the learning system by simulating antonymy. In the following, we will be mainly interested in antonym generation, which gives a good satisfaction clue for these functions.</Paragraph>
      <Paragraph position="1"> We present a function which, for a given lexical item, gives the n closest antonyms as the neighbourhood function V provides the n closest items of a vector. In order to know which particular meaning of the word we want to oppose, we have to assess by what context meaning has to be constrained. However, context is not always su cient to give a symmetry axis for antonymy. Let us consider the item ,father-.</Paragraph>
      <Paragraph position="2"> In the ,family- context, it can be opposite to ,mother- or to ,children- being therefore ambiguous because,mother-and,children-are by no way similar items. It should be useful, when context cannot be used as a symmetry axis, to re ne the context with a conceptual vector which is considered as the referent. In our example, we should take as referent , liation-, and thus the antonym would be ,children- or the specialised similar terms (e.g. ,sons- , ,daughters-) ,marriageor ,masculine- and thus the antonym would be ,mother-.</Paragraph>
      <Paragraph position="3"> The function AntiLexS returns the n closest antonyms of the word A in the context de ned by C and in reference to the word R.</Paragraph>
      <Paragraph position="5"> The partial function AntiLexR has been dened to take care of the fact that in most cases, context is enough to determine a symmetry axis.</Paragraph>
      <Paragraph position="6"> AntiLexB is de ned to determine a symmetry axis rather than a context. In practice, we have AntiLexB = AntiLexR. The last function is the absolute antonymy function. For polysemic words, its usage is delicate because only one word de nes at the same time three things: the word we oppose, the context and the referent.</Paragraph>
      <Paragraph position="7"> This increases the probability to get unsatisfactory results. However, given usage habits, we should admit that, practically, this function will be the most used. It's sequence process is presented in picture 1. We note Anti(A,C) the  antonymy function at the vector level. Here, A is the vector we want to oppose and C the context vector.</Paragraph>
      <Paragraph position="8"> Items without antonyms: it is the case of material objects like car, bottle, boat, etc. The question that raises is about the continuity the antonymy functions in the vector space. When symmetry is at stake, then xed points or plans are always present. We consider the case of these objects, and in general, non opposable terms, as belonging to the xed space of the symmetry. This allows to redirect the question of antonymy to the opposable properties of the concerned object. For instance, if we want to compute the antonym of a ,motorcycle-, which is a ROAD TRANSPORT, its opposable properties being NOISY and FAST, we consider its category (i.e. ROAD TRANSPORT) as a xed point, and we will look for a road transport (SILEN-CIOUS and SLOW ), something like a ,bicycle- or an ,electric car-. With this method, thanks to the xed points of symmetry, opposed \ideas&amp;quot; or antonyms, not obvious to the reader, could be discovered.</Paragraph>
    </Section>
    <Section position="2" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
4.2 Antonym vectors of concept lists
</SectionTitle>
      <Paragraph position="0"> Anti functions are context-dependent and cannot be free of concepts organisation. They need to identify for every concept and for every kind of antonymy, a vector considered as the opposite. We had to build a list of triples hconcept;context;vectori. This list is called antonym vectors of concept list (AVC).</Paragraph>
      <Paragraph position="1">  The Antonym Vectors of Concepts list is manually built only for the conceptual vectors of the generating set. For any concept we can have the antonym vectors such as:</Paragraph>
      <Paragraph position="3"> As items, concepts can have, according to the context, a di erent opposite vector even if they are not polysemic. For instance, DE-STRUCTION can have for antonyms PRESERVA-TION, CONSTRUCTION, REPARATION or PROTEC-TION. So, we have de ned for each concept, one conceptual vector which allows the selection of the best antonym according to the situation.</Paragraph>
      <Paragraph position="4"> For example, the concept EXISTENCE has the vector NON-EXISTENCE for antonym for any context. The concept DISORDER has the vector of ORDER for antonym in a context constituted by the vectors of ORDER DISORDER5 and has CLAS-SIFICATION in a context constituted by CLASSI-</Paragraph>
    </Section>
  </Section>
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