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<Paper uid="C73-1007">
  <Title>S --&gt; NP VP VP -+ TV NP NP --&gt; PN NP-+ Adj N</Title>
  <Section position="18" start_page="91" end_page="91" type="concl">
    <SectionTitle>
ON LOGICAL FORMULATION OF THE COMPUTATION PROCESS 99
</SectionTitle>
    <Paragraph position="0"> Thus, we may have semantic projection rule like SIN (3)^ N (x) =.f (x-y)=f (3) (f (x)).</Paragraph>
    <Paragraph position="1"> One of its instances is as follows: s/N ( 1 ep4,, n (John) =.f (John-steees)=f (sleees) 0 r (john)). In combination with the logical formulae (5.4)-(5.8), such rules enable one to derive logically the meaning of the sentence like John steeps, which can be represented as v, (sleefs) (vx (John)). And this representation would correspond to the usual so-called logical form: SLEEP(j). The set of projection rules thus obtained specifies in connection with those semantic rules like (5.4)-(5.8), which constitute the dictionary component, the evaluation function f recursively. This kind of formulation of semantic rules stands very near to our intuition, that on the basis of the syntactic structure and on the knowledge of the meanings of the constituting words we can understand the meaning of an expression.</Paragraph>
    <Paragraph position="2"> The semantic projection rule stated above has a nice homogeneous feature in specifying semantic evaluation function. This holds actually for all grammars using the notion of functor which combines one or more phrases as its arguments to form a new phrase. The meaning of the composed phrase can be then always considered as the result of the operation of the meaning of the functor with the meanings of its arguments. According to H. B. CURRY (1961), what Harris and Chomsky call transformations are also functors. From this point of view, we can then state the semantic projection rule for a given transformation rule in the same way as described above.</Paragraph>
  </Section>
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