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<Paper uid="P01-1047">
  <Title>Alain.Lecomte@upmf-grenoble.fr</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
2 The grammatical architecture
</SectionTitle>
    <Paragraph position="0"> The general picture of these logical grammars is as follows. A lexicon maps words (or, more generally, items) onto a logical formula, called the (syntactic) type of the word. Types are defined from syntactic of formal features a0 (which are propositional variables from the logical viewpoint): null a1 categorial features (categories) involved in merge: BASE a2a4a3a6a5a8a7a10a9a11a7a10a12a13a7a15a14a11a7a17a16a18a7a20a19a20a19a20a19a22a21 a1 functional features involved in move: FUN a2a4a3 a23a18a7 a24a13a7 a25a27a26a18a7a20a19a20a19a20a19a28a21 The connectives in the logic for constructing formulae are the Lambek implications (or slashes)  a7a31a30 together with the commutative product of linear logic a32 . 1 Once an array of items has been selected, a sentence (or any phrase) is a deduction of IP (or of the phrasal category) under the assumptions provided by the syntactic types of the involved items. This first step works exactly as Lambek grammars, except that the logic and the formulae are richer.</Paragraph>
    <Paragraph position="1"> Now, in order to compute word order, we proceed by labeling each formula in the proof. These labels, that are called phonological and semantic features in the transformational tradition, are computed from the proofs and consist of two parts that can be superimposed: a phonological label, denoted by a30a34a33a36a35a38a37a6a39a40a30 , and a semantic label2 denoted by a41a42a33a36a35a38a37a6a39a40a43 -- the super-imposition of both 1The logical system also contains a commutative implication, a44a6a45 , and a non commutative product a46 but they do not appear in the lexicon, and because of the subformula property, they are not needed for the proofs we use.</Paragraph>
    <Paragraph position="2"> 2We prefer semantic label to logical form not to confuse logical forms with the logical formulae present at each node of the proof.</Paragraph>
    <Paragraph position="3"> label being denoted by a33a36a35a38a37a6a39 . The reason for having such a double labeling, is that, as usual in minimalism, semantic and phonological features can move separately. It should be observed that the labels are not some extraneous information; indeed the whole information is encoded in the proof, and the labeling is just a way to extract the phonological form and the logical form from the proof.</Paragraph>
    <Paragraph position="4"> We rather use chains or copy theory than movements and traces: once a label or one aspect (semantic or phonological) has been met it should be ignored when it is met again. For instance a label</Paragraph>
    <Paragraph position="6"> a54a66a56a27a37a59a58 corresponds to a semantic label a41 a47a49a48a51a50a52a48 a37a67a43a68a41a55a54a66a56a27a37a59a58a69a43a70a41a63a61a63a35a38a64 a48 a43 and to the phonological form a30 a47a49a48a20a50a10a48 a37a57a30a71a30a38a61a63a35a34a64 a48a72a65 a30a73a30a74a54a66a56a27a37a59a58a69a30 .</Paragraph>
  </Section>
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