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<Paper uid="W06-1805">
  <Title>Adjective based inference</Title>
  <Section position="3" start_page="0" end_page="0" type="metho">
    <SectionTitle>
2 A fine grained classification for
adjectives
</SectionTitle>
    <Paragraph position="0"> As mentioned above, we propose a classification of adjectives based on their lexical, their model theoretic and their morpho-derivational properties.</Paragraph>
    <Paragraph position="1"> To facilitate the link with compositional semantics (the construction of a meaning representation for sentences containing adjectives), we also take into account syntactic properties such as the predicative/attributive or the static/dynamic distinction. We now detail each of these properties. The over-all categorisation system is given in Figure 1.</Paragraph>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
2.1 Model theoretic properties
</SectionTitle>
      <Paragraph position="0"> The main criteria for classification are given by (Kamp, 1975; Kamp and Partee, 1995) semantic classification of adjectives which is based on whether it is possible to infer from the Adj+N combination the Adj or the N denotation.</Paragraph>
      <Paragraph position="1"> Intersective adjectives (e.g., red) licence the following inference inference patterns: A + N j= A A + N j= N For instance, if X is a red car then X is a car and X is red Subsective adjectives (e.g., big) licence the following inference pattern: A + N j= N For instance, if X is a big mouse, then X is a mouse but it is not necessarily true X is big Privative adjectives licence the inference pattern: A + N j= :N For instance, if X is a fake gun then X is not a gun Plain non-subsective adjectives (e.g., alledged) do not licence any inference For instance, if X is an alleged murderer then it is unknown whether X is a murderer or not</Paragraph>
    </Section>
    <Section position="2" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
2.2 Lexical semantics
</SectionTitle>
      <Paragraph position="0"> From the lexical semantics literature, we take one additional classification criterion namely antonymy. As described in (Cruse, 1986), this term covers different kinds of opposite polarity relations between adjectives namly, binary opposition, contraries and multiple oppositions.</Paragraph>
      <Paragraph position="1"> Binary oppositions covers pairs such as wet/dry which license the following inference pattern:</Paragraph>
      <Paragraph position="3"> Contraries are pairs such as long/short where the implication is unidirectional:</Paragraph>
      <Paragraph position="5"> and in particular: long j= :short^:long 6j= short short j= :long ^:short 6j= long Multiple oppositions involve a finite set of adjectives (e.g., linguistic/economic/mathematical/... ) which are pairwise mutually exclusive. For a set of opposed adjectives A1 : : : An, the following axioms schemas will be licensed: 8i; j s:t: 1 i; j and i 6= j Ai j= :Aj and :Ai 6j= Aj  We also take into account related forms that is, whether there exists a verb (Va) or a noun that is semantically related to the adjectives being considered. Moreover, for nominalizations we distinguish whether the morphologically related noun is an event noun (Ne), a noun denoting a theta role of the related verb (N ) or a non-event noun (Na). As we shall see, this permits capturing entailment relations between sentences containing morphoderivational variants such as for instance :  (2) a. John is asleep (Adj ! Va) j= John sleeps b. John is absent (Adj ! N ) j= John is the absentee c. John is deeply asleep (Adj ! Ne) j= John's sleep is deep  To better support the syntax/semantic interface, we refine the adjectives classes distinguishable on the basis of the above criteria with the following syntactic ones taken from (Quirk et al., 1985). Attributiveness/Predicativeness. English adjectives can be divided in adjectives which can be used only predicatively (such as alone), adjectives which can be used only attributively (such as mechanical in mechanical enginner) and adjectives which can be used in both constructions such as red.</Paragraph>
      <Paragraph position="6"> Modifiability by very. We distinguish between adjectives such as nice which can be modified by very (i.e. very nice) and adjectives such as alleged which cannot (*very alleged).</Paragraph>
      <Paragraph position="7"> Gradability. We distinguish between adjectives such as big which express gradable properties and have comparative and superlative forms (bigger, biggest) and adjectives such as rectangular which don't (*more rectangular).</Paragraph>
      <Paragraph position="8"> Staticity/Dynamicity. Dynamic adjectives can be used in imperative constructions and in the progressive form (Be reasonable, He is being reasonable), static adjectives cannot (*Be short, He is being short).</Paragraph>
    </Section>
  </Section>
  <Section position="4" start_page="0" end_page="0" type="metho">
    <SectionTitle>
3 Semantic Classes and textual
</SectionTitle>
    <Paragraph position="0"> entailment recognition In order to build our classification, we have analysed a set of about 300 english adjectives each of which was manually mapped to the WordNet synset correspondent to the more frequent meaning of the adjective. In some case, when an adjective presents polysemic forms which belong to different semantic classes more than one form has been considered. For example, for the adjective civil we consider two senses/forms civil1 (synonym of polite, as in civil man) and civil2 (as in civil engineer) which belong to different semantic classes, the first being intersective and the second subsective. As Figure 1 shows, the proposed classification includes 15 adjective classes, each with distinct syntactic and semantic properties.</Paragraph>
    <Paragraph position="1"> To account for these differences, we define for each class a set of axiom schemas capturing the model theoretic, lexical semantics and morpho-derivational properties of that class. Lexical semantics and morpho-derivational information are derived from WordNet. For example, the axioms describing antonymy are obtained by extracting from WordNet the antonyms of a particular adjective and then by considering the direction of the entailment relevant for the class the adjective belongs to: asleep wake vs. polite &lt;rude Morpho-derivational information are derived from WordNet by extracting the derivationally related forms for the given adjective and then iterating the extraction on nouns and verbs in order to obtain information about their antonyms and hyponyms.</Paragraph>
    <Paragraph position="2"> For scalar adjective like tall, WordNet contains also a relation is a value of which offers a pointer to the noun concept the adjective is a value of. Moreover, WordNet links the noun concept to a list of attributes which describe the scalar prop-erty it represents. For example, the adjective tall is a value of fstature,heightg and attributes offstature,heightg are tall and short.</Paragraph>
    <Paragraph position="3"> Based on some basic syntactic patterns, we then show that these axioms predict the observed textual entailment patterns for that class.</Paragraph>
    <Paragraph position="4"> Before we illustrate this approach by means of some example, we first show how we capture logical entailment between NL semantic representations in a description logic setting.</Paragraph>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
3.1 Using description logic to check
</SectionTitle>
      <Paragraph position="0"> entailment between NL sentences As argued in (Gardent and Jacquey, 2003), description logic (DL) is an intuitive framework within which to perform lexical reasoning: it is efficient (basic versions of description logics are decidable), it is tailored to reason about complex taxonomies (taxonomies of descriptions) and it is equipped with powerful, freely available automated provers (such as RACER, (Volker Haarslev, 2001)). For these reasons, we are here exploring a DL encoding of the entailment recognition task for the set of examples we are considering.The particular language we assume has the following syntax. C; D ! Aj&gt;j?j:A j C u D j C t D j 8R:C j 9R:C The semantics of this language is given below with the domain of interpretation and I the interpretation function which assigns to every atomic con-</Paragraph>
      <Paragraph position="2"> Now one basic problem with using DL to check entailment between NL expressions, is that DL formulae are &amp;quot;directional&amp;quot; in that they refer to a given set of individuals. For instance the sentence The boat is floating might be represented by either of the two formulae given in 3 but these two formulae do not stand in an entailment relation (since they refer to different kind of objects namely floating event of a boat in 3a and boats that float in 3b).  (3) a. float u9theme.boat b. boat u9theme 1.float To remedy this shortcoming, we introduce the notion of a rotation. Given a DL formula which only contains conjunction (disjunction is translated in DL as different formulas) = ui=1;n Eventi uj=1;m 9Rj.Typej a rotation of this formula is defined as: 1.</Paragraph>
      <Paragraph position="3"> 2. 8j 2 f1; :::; mg :</Paragraph>
      <Paragraph position="5"> corresponds to the following n Rotations each of which describe the same situation from the point of view of a particular type  So for example, the sentence Mary knows that John is the inventor of the radio will be represented as a predicate logic formula</Paragraph>
      <Paragraph position="7"> the denotation of this PL formula corresponds to the set of individuals fx1; x2; x3g[fe1; e2g. The corresponding DL representation will be the underspecified representation know u9 agent.mary u9 topic.( invent u9agent.john u9 patient.radio) null the denotation of which corresponds to the set fe1g and all its rotations which permit to access the other sets of individuals asserted in the sentence. Thus for example, the set fx1g which describes the individual Mary can be accessed through the following rotation: Rotation1: mary u9 agent 1.(know u9 topic.( invent u9agent.john u9 patient.radio)) Finally, we say that an arbitrary formula/representation 1 implies the formula</Paragraph>
    </Section>
    <Section position="2" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
3.2 Example class axioms and derivations
</SectionTitle>
      <Paragraph position="0"> We now illustrate our approach by looking at two classes in more detail namely, class 1 and class 8.</Paragraph>
      <Paragraph position="1">  Syntactically, Class 1 contains adjectives like adrift,afloat,aground which can only be used predicatively, are non gradable and cannot be modified by very. Semantically, they behave like intersective adjectives which enter in multiple opposition relations with other adjectives. They are furthermore morphologically derived from verbs and can be nominalized. To reflect these semantic properties we use the following axioms.</Paragraph>
      <Paragraph position="2"> Model theoretic semantics. Adjectives of class 1 are intersective adjective. They will thus licence the correponding inference patterns namely:  A + N j= A (2) A + N j= N (3) Lexical semantics. Adjectives of class 1 enter in multiple opposition relations. Hence For instance: afloat j= : aground ^: afloat 6j= aground aground j= : afloat ^: aground 6j= afloat sunken j= : afloat ^: afloat 6j= sunken afloat j= : sunken ^: sunken 6j= afloat  Morpho-derivational semantics. Adjectives in Class 1 can be related to both nouns and verbs. Thus, for example the adjective afloat in WordNet is related to the noun floating which is related to the verb float, by assuming that the semantics assigned to the verb float is float(e), theme(e,a), the adjective afloat is assigned the following semantics: null afloat 9 Theme 1.float This is encoded in the following axiom schemas:  MDR 1. Adj1 &lt;: Adj2 If Adj1 = Anto(Adj2) e.g., afloat &lt;: sunken MDR 2. Adj1 9 Theme 1.V1 If Adj1 is related to V1 e.g.,afloat 9 Theme 1.float MDR 3. V1 &lt;: V2 If V1 = Anto(V2) e.g., float &lt;: sink MDR 4. N1 V1 If Adj1 is related to an evt denoting N1 e.g., floating float MDR 5. N1 &lt;: N2 If N1 is an antonym of N2 e.g., floating &lt;: sinking MDR 6. N11 9 Theme 1.V1 If Adj1 is related to a  noun N11 denoting the theme role of the verb V1 e.g., floater 9 Theme 1.float We make the following assumptions about the syntax/semantic interface that is, about the semantic representations associated with given sentence patterns.</Paragraph>
      <Paragraph position="3">  SCR 1. NP toBe Adj ADJ u NP SCR 2. NP toBe clearly Adj ADJ u NP SCR 3. Ni[+event] of NP is clear</Paragraph>
      <Paragraph position="5"> Given the above axiom schemas and semantic constructions rules, the following inference patterns can be handled:  1. ADJ1 + N j= N Ex. This boat is afloat. j= This is a boat. 2. ADJ1 + N j= ADJ1 Ex. This boat is afloat. j= This is afloat. 3. ADJ1 + N 6j= : N Ex. The boat is afloat. 6j= This not a boat. 4. ADJ1 + N j= : ADJ2 u N Ex. The boat is afloat. j= The boat is not sunken. 5. : ADJ1 + N 6j= ADJ2 u N Ex. The boat is not afloat. 6j= The boat is sunken. 6. ADJ1 + N j= N u9theme 1:V 1 Ex. The boat is afloat. j= The boat is the floater. 7. ADJ1 + N j= V1 u9theme.N Ex. The boat is afloat. j= The boat is floating. 8. ADJ1 + N j= N1 u9theme.N Ex. This boat is clearly afloat. j= The floating of the boat is clear.</Paragraph>
      <Paragraph position="6"> 9. ADJ1 + N j= N u9theme 1.N1 Ex. This boat is clearly afloat. j= The floating of the boat is clear (or the boat is the floating object). 10. : (ADJ1 + N) j= : (V1 u9theme.N) 6j= : N Ex. This is not a floating boat. 6j= This is not a boat. 11. : (ADJ1 + N) 6j= : Adj1 Ex. This is not a floating boat. 6j= This is not afloat. 12. : (ADJ1 + N) 6j= : V1 Ex. This is not a floating boat. 6j= This is not floating. 13. : (ADJ1 + N) 6j= : N1 Ex. This is not a floating boat. 6j= This is not a floating. 14. : (ADJ1 + N) 6j= :9 theme 1.V1 Ex. This is not a floating boat. 6j= This is not the floater. 15. : (ADJ1 + N) 6j= :9 theme.N Ex. This is not a floating boat. 6j= This is not a floating.  In the inference patterns 10 to 15, the negation of the adjective-noun compound : (ADJ1 + N) is syntactically blocked, as the adjectives in this class are used predicative only, however the equivalent representation V1 u9theme.N can be used to motivate the inferences.</Paragraph>
      <Paragraph position="7"> The following show in more detail how the first three of the above (non) entailments are recognised. null  (4) a. The boat is afloat.</Paragraph>
      <Paragraph position="8"> b. j= The boat is floating.</Paragraph>
      <Paragraph position="9">  (6) a. The boat is afloat.</Paragraph>
      <Paragraph position="10"> b. j= The boat is not sinking.</Paragraph>
      <Paragraph position="11">  big,fast,tall,deep which can be used attributively and predicatively, are gradable, can be modified by very. Semantically, they are classified as subsective adjectives and their antonyms are contraries. They are morphologically related to nouns which describe the particular property denoted by the adjectives and to nouns of which they are attributes.</Paragraph>
      <Paragraph position="12"> Model theoretic semantics. Adjectives of class 8 are subsective adjective. They will thus licence the correponding inference patterns namely: A + N 6j= A (4) A + N j= N (5) Lexical semantics. The Adjectives of class 8 enter in contrary opposition relations. Hence, the following axioms schemas will be licensed:  Morpho-derivational semantics. Adjectives in Class 8 can be related to nouns but not to verbs. Moreover, such adjectives are mapped in WordNet to noun concepts through two different links: derivationallyrelated to and is a value of. For example, the adjective tall in WordNet is derivationally related to the noun tallness and is a value of the concept noun height. The adjectives in this class describe gradable properties so that their semantics corresponds to: has-property(Related Noun u9has-measure.Top) in which the role has-measure account for the value of the scalar property described by the adjective, which remain underspecified (Top) if the adjective is used without a reference to the value of measure. When the value of the measure is specified, for example by combining the adjective with a noun, as for example in This is a tall man, then the noun is assigned as a value of the measure role: man u9has-property.(tallness u9has-measure.man) which translate This is tall as a man.</Paragraph>
      <Paragraph position="13"> This is encoded in the following axiom schemas:  scalar attribute with value less then Adj11 (hyponymy is not defined for adjectives) Ex. giant &lt; tall For the moment, we don't account for the semantics of comparatives forms of adjectives but we will do that in the feature, by also introducing a representation for scales as described in (Kennedy, 2005).</Paragraph>
      <Paragraph position="14"> We make the following assumptions about the semantic representations associated with basic sentence patterns.</Paragraph>
    </Section>
  </Section>
  <Section position="5" start_page="0" end_page="0" type="metho">
    <SectionTitle>
4 Implementation
</SectionTitle>
    <Paragraph position="0"> For each of the 15 classes, we have specified a set of axioms schemas, some basic semantic construction rules and a set of inference patterns which could be deduced to follow from both of these.</Paragraph>
    <Paragraph position="1"> The axioms schemas were implemented in Description Logic using RACER and for each inference pattern identified, the corresponding Description Logic query was checked to verify that the proposed axioms and semantic construction rules did indeed correctly predict the deduced inference patterns.</Paragraph>
  </Section>
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