[Retros] Ortho-reconstructions

[Guus Rol]

The relevance of a seemingly complicated concept like "premature
termination" may not be clear until it is placed in the broader context
which I will try to present here. The "premature terminations" are to be
viewed as the TRY subset of the "conventional terminations" which in turn
belong to the set of "all chess terminations".

Mate, stalemate, dead reckoning, repetition draws and 50M draws may be
viewed as postional properties reflecting the state of the position / game.
Where it is uncertain that a position is a draw or mate, the illusion may
arise that draws or mates can be "game state variables". Closer inspection
reveals that these "variables" are only derivatives of the "primary game
state variables" e.p. right, castling right, positional repetition, 50M
series. The uncertainty in "prmary game state varibles" is handled by the
retro conventions and not the FIDE laws. Draws and mates can therefore be
viewed as "secondary game state variables" at best.

Questions raised in the past by Andrew Buchanan are hereby answered. Since
the conventions provide default game state values for every unknown
property, all situations reflecting "possible terminations" are
automatically resolved (a) by the application of FIDE laws and (b) by
further reduction through the retro conventions. I do know of one exception
in orthodox chess but its discussion merely provides us with a sneak preview
of fairyland where such issues are more common.

Examples: (1) A.possible mate with possible e.p. right, is simply mate (2) A
possibly dead position which is alive with castling rights, is alive.

Surprising observations can be made from "reflex chess". Since the mating
move is automatic, all considerations regarding "game termination"  move one
step backward from the mating position. Obviously, one can't be expected to
make an e.p. move in order to mate unless the e.p. right is provable. And
possible castling is mandatory when it produces mate. Reversely, had the
FIDE laws provided the right to castle when in check, it would equally apply
to a "possible mating position". The comparison demonstrates the natural
alignment of termination considerations with those in different stages of
the game.

On the highest logical plane, the role of  "game termination" is that of
"interrogator" of a "quantum game state". Like castling or an e.p. move it
demands the resolution of certain dual state items which are
therefore demanded to manifest. The special power of termination in this
encounter is that non-termination may be just as state revealing as
termination. Any doubts, revisit R309 Probleemblad.

On a final note, the proper axiomization of retro-logics in fairy types
depends on a sensible implementation of supplementary retro-conventions and
their interactions with game termination. Without carrying decent concepts
from orthodox chess, no hope exists that this will ever be achieved.

Guus Rol
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