[Retros] The basics of the relationsship between laws and conventions

[Guus Rol]

Dear retro-friends,

In the past weeks I have reacted on several posts related mostly to 3R. Now
this is kind of a random subject to plunge into the retro-field and not
easy to handle as an isolated item. It is part of a larger structure of
concepts I developed many years ago. You can find the results of that
research in Probleemblad since 2007 starting with R309. Not many problems,
but all the essentials to demonstrate the scope and power of this approach.

In this post I go back to the very beginning of that research which is the
understanding of the retro-active subject - everything retro that is not
purely analytical but contains uncenrtainty - through its conepts and
structure. Nothing in this analysis is based on opinion. Everything is
either fact or inevitable. That is probably not true for everything in my
theory but it is for this part.

*The first environment to define is the one where the FIDE laws operate. It
is filled by the set of all (partial) games played according to the FIDE
laws. There are operations such as moves and there are positions and
players and others things. We cal this set the Game-set.*

*The second environment is the one of chess diagrams. Every diagram
represents billions of proof games leading from PAS to the diagram. We call
it DGC, the Diagram Game Cluster. All DGCs together form a superset of the
previous set and we name it the DGC-set. There are no FIDE rules defined
for the DGCs, no moves and no other charateristics associated with games.*

And there are chess problems. Most problems like #3 are formulated by
diagram. Formally you cannot solve any problem since there are no 'playing'
rules for game clusters, but one may assume - as a necessity - that FIDE
intended that you can reduce the DGC to an arbitrary game in the Game-set.
As long as it doen't matter which game you take!

*Here complexity starts. In retro-active problems the solution may change
with the game you pick from the DGC and therefore FIDE laws cannot decide.
They were only made to decide moves in known states and not for unknown
histories. Here - as a necessity - something is needed to reduce the DGC
to games where FIDE rules can apply. And these are "the conventions".
Whatever personal opinion you may have about the conventions, it is clear
that there are no other concepts or items anywhere in chess that are
capable of performing this task. And so, this is what conventions do, as a
bare minimum necessity: The conventions reduce a DGC to a game or
games that can be handled by the FIDE laws. It does not mean that
everything is decided all at once, it only decides what must be decided in
view of an intended action.*

Examples: (1) you wish to play e.p.; the e.p. conventions evaluates it and
hands back 0 games where e.p. is allowed. The request is denied (2) you
wish to play e.p. but this time under Petrovic a posteri logic. The
convention and logic allow it (provisionally, you must prove somrthing
later) and hand back all games where e.p. is legal. The move is then
executed by FIDE law (3) you do not castle and think you can get away with
it; the convention on castling detects however that you play reflex chess
and must mate by castling which is the preferred assumption. It returns 0
games without castling rights and your request to 'not castle' is thereby
rejected.

In a mathematical sense we have a very simple set - superset combination
here which basically represents the whole retro-active spectrum. The
functions for the DGC-set are "selections" - queries in database language -
designed to deliver games that can be handled by the Game-set functions
such as "moving". Many posts I read show that the authors (con)fuse the
functions performed on both sets. There exists no FIDE law - DR, mate ,
stalemate, 3R - that requires that a conditions is true or false for "all
games", only for "all moves in a game". The decision on which games can
only be delivered through the conventions.

The impact of these very simple principles is fantastic. It uplifts the
status of the conventions to stellar heights. Not only are they equals to
the FIDE laws, they preprocess all input for the FIDE laws, they have a
domain all of their own where FIDE laws cannot possibly enter. And finally,
they are required for any fairy type which pretends to support the
retro-field. Provided that these fairies introduce new retro-active
attributes which is quite often the case..

Does this resolve issues such as DR and 3R, or dynamic castling evalautions
in relation to 3R? Not quite, but you may be able to see that it takes us
quite a long way in the right direction. I hope to show that some other
time.

Best wishes, Guus Rol.
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