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MatPlus.Net Forum General For the theoreticians
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(1) Posted by Hauke Reddmann [Monday, Oct 31, 2022 15:20]

For the theoreticians

Is there an algorithm that takes the description
of a theme and replaces words (white<>black,
mate<>defense,open<>close etc.) such that the
new description always makes sense?
I.e. an antiform algorithm?

For example. Mari.
White has apparently two mating moves, but he may
not close the line Black just opened.
The new one, call it Iram for now:
Black has apparently two defense moves, but he must
open the line that White just closed.
(What is the standard name of this theme?)

(You'll see the snag as soon as you have three
thematic lines. In a Mari, White would have
two mating moves. In an Iram, Black still has
one defense. Maybe "must/may not" was the one
flip too many?)
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(2) Posted by seetharaman kalyan [Monday, Oct 31, 2022 22:33]

Inverse of Mari theme seems to be:
White should close a line which black has not closed. (apparently simple battery play)
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(3) Posted by Andrew Buchanan [Tuesday, Nov 1, 2022 03:50]

“Anti-“ definitions are notoriously troublesome, because in which dimensions does one decide to take the opposite?

Hauke’s suggestion is more specific, so I strongly suggest avoiding the term “anti-“ in this context. I suspect however that the foundation is not solid since a text description might take different forms.

As a theoretical endeavour, it might be interesting to explore a graphical language for these things, building on the innovative diagrams in James Quah’s excellent new book “Triple Grimshaw and Beyond”. One can then define in graphical terms the transforms sought.

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(4) Posted by Anders Thulin [Tuesday, Nov 1, 2022 07:58]

Probably no direct algorithm. A possible way would be to a) transform the textual description to a formal language, perhaps on the line of Dawson's effect notation used in his "Systematic Terminology", and b) in that notation flip elements that have opposites (binary or N-ary), singly or in groups, and c) transfer back to text. Step a would be the difficult part, while b and c seem easier.

As only the simplest of Dawson's themes had a single 'flippable', it seems likely that step b will produce multiple expressions, from which then one or more have to be manually selected, either in notation or as reverse-translated text. (Unless all/some 'positive' effects were flipped into 'negative' in one go, and vice versa, for example.)

I have a vague memory of having seen a short article (? or just a note) do something like that: take one standard pin theme, explore the flippables, identify one or two 'unknown but possibly interesting' themes resulting from 'flipping', and explore possible forms for them. (I don't think Dawson's 'language' was used, though, so he probably didn't write it, but I can't think of anyone else who would. Probably from the early 1960s, or perhaps around the time "Systematic Terminology" appeared in B.C.M. I'll try to dig it up.)

(@Andrew: Thanks for the pointer to Quah's book -- it will be interesting to compare the formal approach with Dawson.)
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(5) Posted by Hauke Reddmann [Tuesday, Nov 1, 2022 10:45]

Indeed, if one scans the Degener book for "anti" the definitions are...antisystematic :-)

I'm very interested in your dig-ups!

(The "verbal equivalence" problem I don't see as that hard. A "sensible" algorithm
should give the same result even for different verbal descriptions.)
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MatPlus.Net Forum General For the theoreticians