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<Paper uid="P90-1028">
  <Title>ALGORITHMS FOR GENERATION IN LAMBEK THEOREM PROVING</Title>
  <Section position="6" start_page="224" end_page="224" type="evalu">
    <SectionTitle>
5 CONCLUDING
REMARKS
</SectionTitle>
    <Paragraph position="0"> Implementation The algorithms and calculi presented here have been implemented with the use of modified versions of the categorial calculi interpreter described in Moortgat (1988).</Paragraph>
    <Paragraph position="1"> Conclusion Efl\]cient, bidirectional use of categorial calculi is possible if extensions are made with respect to the calculus, and if s combined bottom-up/top-down algorithm is used for generation. Analysis and generation take place within the same processing architecture, with the same linguistics descriptions, be it with the use of different algorithms. LTP thus serves as a natural candidate for a uniform architecture of parsing and generation.</Paragraph>
    <Paragraph position="2"> Semantic non-monotonieity A constraint on grammar formalisms that can be dealt with in current generation systems is semantic monotonicity (Shieber, 1988; but cf. Shieber et al., 1989). The algorithm in Calder et al. (1989) requires an even stricter constaint. Firstly, in van der Linden and Minnen (submitted) we describe how the addition of a unification-based semantics to the calculus described here enables processing of non-monotonic phenomena such as non-compositional verb particles and idioms. Identity semantics (cf. Calder et al. p. 235) should be no problem in this respect. Secondly, unary rules and type-raising (ibid.) are part of the L-calculus, and are neither fundamental problems.</Paragraph>
    <Paragraph position="3"> Inverse E-reduction A problem that exists for all generation systems that include some form of ~-semantics is that generation necessitates the inverse operation of~-reduction. Although we have implemented algorithms for inverse E-reduction, these are not computationally tractable, e A way out could be the inclusion of a unification based semantics. 7 SBunt (1987) states that an expression with n constants results in 2 n - 1 possible inverse ~-reductlons.</Paragraph>
    <Paragraph position="4"> 7As proposed in van der Linden and Minnen (submitted) for the calculus in (2). 225</Paragraph>
  </Section>
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