[Retros] The basics of the relations​hip between Laws and Convention​s

[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 only a detail in a larger
structure of concepts I developed many years ago. You can find the
composition 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 my new approach.

In the present post I go back to the very beginning of that research which
is the understanding of the retro-active subject - defined as 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 identify is the one where the FIDE laws operate.
It is filled by the collection of all (partial) games playable under the
FIDE laws. There are operations such as moves and there are positions and
players and others things. We call this set the Game-set.*

*The second environment is the one of all chess diagrams. Every diagram
represents billions of proof games leading from PAS to the diagram. We call
it the 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 presented 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 to handle
uncertainties. 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 retro-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 your
wish 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 rejected.
Reflex chess is an excellent way to test retro-active-theories as it turns
passive attributes such as "not castling" into active ones.

In the mathematical context we see a very simple set - superset combination
here which represents the most fundamental objects in the retro-active
domain. The functions for the DGC-set are "selections" - queries in
database language - designed to deliver games that can be handled by the
FIDE Game-set functions such as "playing a move". 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 or otherwise - that requires
that a conditions is true or false for "all games", only for "all moves in
a game". The decision on "which games" are involved can only be delivered
through conventions.

The impact of these very simple concepts is immense. They uplift 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 and they have a domain
all of their own where FIDE laws cannot possibly enter. And finally, they
set demands for any fairy type which pretends to support the retro-field.
Conventions must be defined for all the fairy related retro-active
attributes or there is no place to go..

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
some way in the right direction. I expect to show that in another post..For
the moment, these paragraph outline a new approach to the understanding of
the retro field based on a workable information model with considerable
capability to tackle both the orthodox and the fairy domain. Which is
something I will present examples of in upcoming posts.

Best wishes, Guus Rol
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