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<Paper uid="P06-2105">
  <Title>Sydney, July 2006. c(c)2006 Association for Computational Linguistics A Logic-based Semantic Approach to Recognizing Textual Entailment</Title>
  <Section position="4" start_page="0" end_page="819" type="intro">
    <SectionTitle>
2 Cogex - A Logic Prover for NLP
</SectionTitle>
    <Paragraph position="0"> Our system uses COGEX (Moldovan et al., 2003), a natural language prover originating from OT-TER (McCune, 1994). Once its set of support is loaded with a1 and the negated hypothesis (a2 a0 ) and its usable list with the axioms needed to gener- null ate inferences, COGEX begins to search for proofs. To every inference, an appropriate weight is assigned depending on the axiom used for its derivation. If a refutation is found, the proof is complete; if a refutation cannot be found, then predicate arguments are relaxed. When argument relaxation fails to produce a refutation, entire predicates are dropped from the negated hypothesis until a refutation is found.</Paragraph>
    <Section position="1" start_page="819" end_page="819" type="sub_section">
      <SectionTitle>
2.1 Proof scoring algorithm
</SectionTitle>
      <Paragraph position="0"> Once a proof by contradiction is found, its score is computed by starting with an initial perfect score and deducting points for each axiom utilized in the proof, every relaxed argument, and dropped predicate. The computed score is a measure of the kinds of axioms used in the proof and the significance of the dropped arguments and predicates. If we assume that both text fragments are existential, then</Paragraph>
      <Paragraph position="2"> ple read) and penalizing a pair whose a0 contains predicates that cannot be inferred is a correct way to ensure entailment (Some people read a2a0 Some smart people read). But, if both a1 and a0 are universally quantified, then the groups mentioned in a0 must be a subset of the ones from a1 (All people read a0 All smart people read and All smart people read a2a0 All people read). Thus, the scoring module adds back the points for the modifiers dropped from a0 and subtracts points for a1 's modifiers not present in a0 . The remaining two cases are summarized in Table 1.</Paragraph>
      <Paragraph position="3"> Because a3 a1a5a4 a0a7a6 pairs with longer sentences can potentially drop more predicates and receive a lower score, COGEX normalizes the proof scores by dividing the assessed penalty by the maximum assessable penalty (all the predicates from a0 are dropped). If this final proof score is above a threshold learned on the development data, then the pair is labeled as positive entailment.</Paragraph>
    </Section>
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