Induction hypothesis

There is at least one node s in G - Sn directly connected to n s must be an ancestor of n. If any other node in G - Sn were directly connected to n, then two ancestors of n would be directly connected to n, a contradiction of the fact that G is tree-like. Essentially G is formed by block composition from G - Sn and Sn. Form G by removing all of Sn from G and replacing the connection from s to n by an exit out of G. Then G is clearly a single entry tree-like subgraph with dg, dg - 1 and hence by the induction hypothesis G is a block. Similarly, is a single entry tree-like flow diagram. Form S ... 

There are three subcases to consider. First suppose that e is not a branch node. Then e is directly connected to exactly one node n. Clearly e chain dominates n and G = (e) U S(n,d). The subscheme corresponding to e is well-structured and e is not in S(n,d) which is line-like by Lemma 4.12. Thus P is the block composition of the subschemes corresponding to e and to S(n,d). By the induction hypothesis S(n,d) corresponds to a well-structured subgraph, and so P is well-structured. 

If 7 0, then, by the inductive hypothesis, we have a finite list Wi, Wk of distinct irreducible representation such that... 

The fourth equality follows from Equations 8.11 and 8.10, while the fifth uses the inductive hypothesis. 

First note that al s are free and finitely generated and that by construction and because of the inductive hypothesis d5+1 d = 0 for all i2n-l. 

In the Myth of Inductive Hypothesis Generation Karl Popper (2) states that the belief that we can start with pure observations alone without anything in the nature of a theory is absurd. As he illustrated by the story of the man who dedicated his life to natural science, wrote down everything he could observe and gave his... 

Ling, G. N. (1962). A Physical Theory of the Living State The Association-Induction Hypothesis. Blaisdell, Waltham, MA. 

Ling, G. N. (1979). The polarized multilayer theory of cell water according to the association-induction hypothesis. In Cell-Associated Water (Drost-Hansen, W Clegg, J. S., eds.), pp. 261-269, Academic Press, New York. 

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