A Lesniewskian Version Of Montague Grammar
نویسنده
چکیده
We shall be concerned in this paper with the logical analysis of natural language on the basis of Lesniewski's ontology, which is a logical system without type-distinction between individuals and monadic predicates. This, it is believed, is also one of the features of natural language, and use will be made of this feature for developing a fragment of n atnral language. I Introduction According to Montague every simple sentence of natural language is of the form Np + Vp = (Det + N) + Vp, and, as emphasized by Barwise-Cooper [1] Det + N constitutes a generalized quantifier to be applied to Vp or verb phrase as one-place predicate. (For Montague grammar consult among others Montague[10], Cresswell [3] and Jirku [6]<) Thus, simple sentences suck as: .1 the man walks, .2 every man walks, • 3 some (a) men (man) walk(s) .4 (at least) two men walk, • 5 (at least) three men walk, are respectively,of the following logical forms: 1.11 (kPkQP1x man) walk, 1.21 (~P~Q~x(P x O Q x) man) walk, 1.31 (XP%Q3x(P x A Q x) man) walk, 1.~l (kPkQBxBy(P x ^ P y A P x A Q y A xz~ y) man) Walk, 1.51 (kPkQBx~y3z(P x A Q y ~ Q x A Q y A P z ~ Q z A x~y A y~z A z~x).man) walk, where QIxP x is the Russellian-type definite description to be defined as ~x(P x ~ Q x) A ~x~ty(P x A P Y.~ X~ry) , with the scope restricted to Q. By means of k-con,~ersion, for example," from 1.11 and 1.21 we respectively obtain: walk ix man x, and Vx(man x O walk x), so that Det + N now becomes in both cases a generalized quantifier.
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