Steve K wrote:Denis, further down the page is the TM definition. It is unclear what you think is undefined. Everything that needs to be defined is defined.
Steve K wrote:Tri-angular matrix definition:
nxn
Each row contains at least one truth
The top entry of each column is in conflict with each item below it.
For row i, items i+2 and greater are empty. This can be translated, in Booleans, as False.
Same remarks as for the PM's
[Two lines deleted. They were the result of a careless reading on my part.]
[Added:]
To repeat and extend one of my previous posts:
the definition is not given in factual terms, but in terms of weak and strong inference sets. The way these inference sets are related to facts on the grid is undefined. E.g. do these strong inference sets allow ALSs?
I'ven't yet received any answer to this question.
What is clear is that PMs and TMs, like AICs, are tools to combine "weak" and "strong" inferences.
In the case of AICs, "strong links" have received successively several interpretations in terms of factual patterns (bilocation, + bivalue, + ALSs). In the philosophy of AICs, one insists on the trivial alternance between "weak" and "strong" inferences and considers the nature of the patterns allowing "strong links" as secondary. Unfortunately, the 3 patterns mentioned above correspond to wildly different complexities and neglecting this amounts to cheating with a major aspect of chains.
PMs, TMs and AICs are general logical means of combining truth values. Unless the basic building blocks corresponding to these truth values are defined, PMs, TMs and AICs do not specify patterns on a grid. In this sense, yes, I repeat it, PMs and TMs are largely undefined. (And the same could be said of AICs if usage hadn't established bilocation + bivalue + ALSs as the supports for "strong links").
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