[Smt-talk] Classical Form and Recursion

[Thomas Noll]

At closer inspection I need to discard this idea:

> I wonder wether in the study of reasoning, iteration could be a  
> concatenation of deductions along the same rule, while (primitive)  
> recursion could be a concatenation of abductions along the same rule.

Recursion - as a mode of access to some object - requires an  
instantiation of other objects which are accessed in the same/ 
analogous way. Each intermediate instance is incomplete in the sense  
that the missing component has to be accessed as another object in  
this chain. However, the nature of incompleteness differs  
dramatically from the incomplete knowledge in abduction. In abduction  
(hypothesis ) it is a lack of evidence, rather than a lack of access  
to some object. In deduction or abduction we may keep or "burn" the  
intermediate premises, when we draw chains of conclusions. But in  
recursion we need all intermediate instances at once.
best wishes
Thomas

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Thomas Noll
http://flp.cs.tu-berlin.de/~noll
noll at cs.tu-berlin.de
Escola Superior de Musica de Catalunya, Barcelona
Departament de Teoria i Composició
Tel (priv.):   +34 93 268 75 19
Tel (mobil): +34 66 368 12 02

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