By Valerie Adams
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Additional resources for An Introduction to Modern English Word Formation
As we said, the Lambek calculus is the logic for merging two expressions into a new one; dually the Dual Lambek calculus is the logic for merging contexts into a new one. Hence, we will call the new relation Mergec. (63) If c3 Œ B, then c3 Œ A ÿ (A ¼ B), since B Ĉ A ÿ (A ¼ B); then, by definition of ÿ, for all contexts c1, c2 if Mergec(c1, c2, c3), viz. c3 is the context resulting by the merge of the contexts c1 and c2, then c1 Œ A or c2 Œ A ¼ B . A context c2 belongs to a co-function category A ¼ B if there are two contexts c1 and c3 such that Mergec(c1, c2, c3), c1 ∉A and c3 Œ B.
S3 ³ s4 (92) s6 s6 s1 Ĉ s3 If Alex [thinks [everyone left]] Alex [thinks [dp left]] In the second reading of the sentence, the syntactic and semantic domain of thinks coincides: it takes scope over the structure it c-commands/dominates, hence also on the quantifier. Proof theoretically this means that its s-value (s1) is linked to the goal formula (s6), and its s-argument (s2) is reached by the quantifier s-argument (s4). The application of the function thinks to the expression everyone left reduces the problem of verifying that the full structure is of category s6 to two simpler problems: verifying that [everyone left] is s2 and the subject dp1 composed with the verb phrase category dp1\s1 is of category s6.
56) sval1 Ĉ sgoal OP1: sval1/sarg1 OP2: sval2/sarg2 sval2 Ĉ sgoal sval2 Ĉ sarg1 OP2: sval2/sarg2 s Ĉ sarg2 dp2. dp1 OP1: sval1/sarg1 sval1 Ĉ sarg2 s Ĉ sarg1 dp2. dp1 The trees are consistent with the standard idea that the later a quantifier is introduced in the semantic structure the wider its scope. In Section 4, we discuss the formal properties that characterize the function sval/sarg and its connection with the dp component as well as the composition relation holding between it and the structure over which it takes scope.
An Introduction to Modern English Word Formation by Valerie Adams
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