Vorlesungen ueber numerisches Rechnen by Runge C.

By Runge C.

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Eliminating redundancy is secondary in the sense that it does not really constrain rule formulation: it just removes one formulation of equal power with another that is maintained. Less redundancy may help state some generalizations in a simpler way or make them more transparent because their effects are not spread over two components, but it does not have the impact of constraining rule formulation by considerations of necessity. For instance, Chomsky (1995) argues that the level of D-Structure should be eliminated because the information it provides for interpretation is recoverable from LF.

To see that this is not cyclic, take f (n) = 2n and calculate f r (n) = [n/2], f (n) = [(n + 1)/2]. where [x] denotes the greatest integer ≤ x. The free pregroup F (A) generated by a poset A is defined like the free protogroup of Section 1, only now there is an additional case in the definition of α ≤ β, to be called an expansion: Case 3. αi = γδ, αi+1 = γa(n) a(n−1) δ. It is easily verified that F (A) is a pregroup with the expected universal property. A generalized expansion has the form γδ ≤ γa(n) b(n−1) δ, where n is odd and a ≤ b in A or n is even and b ≤ a in A.

Symposia Applied Mathematics 12 (1961), 56–67. 26 J. Lambek C. Dexter, The second Inspector Morse omnibus, Pan Books, London 1994. K. Doˇsen and P. Schroeder-Heister (eds), Substructural logics, Oxford University Press, Oxford 1993. G. Gazdar, E. Klein, G. Pullum and I. Sag, Generalized phrase structure grammar, Harvard University Press, Cambridge Mass. 1985. -Y. Girard, Linear Logic, J. Theoretical Computer Science 50 (1987), 1–102. N. Grishin, On a generalization of the Ajdukiewicz-Lambek system, in: Studies in nonclassical logics and formal systems, Nauka, Moscow 1983, 315-343.

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