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Representation of Knowledge for Chess Endgames Towards a Self-Improving System
This thesis describes an investigation of the problems involved in representing knowledge within the task area of elementary Chess endgames. Two major criteria are taken for the choice of a model of & the chessplayer's knowledge : firstly, that algorithms constructed using the model should be natural from the viewpoint of a chessplayer and commensurate with his, view of the complexity of the task, and secondly that the algorithms should be capable of refinement in the light of experience in a manner which preserves the previous property.
Elementary chess endgames are studied as a field in which programs based on tree-searching and traditional evaluation functions have achieved poor results and where tree-searching seems to play little or no part for people. It is therefore possible to examine problems of knowledge representation and program refinement largely independently of the tree-searching paradigm.
A long term aim of the research is to develop a representation suitable as the basis for a fully automatic system of algorithm refinement, whilst maintaining the criteria given above.
A model is proposed and algorithms are given for two endgames, King and Rook against King (KRK) and King and Pawn against King (KPK) using this model. It is argued that both algorithms are reasonably natural and compact representations and experiments in refining these algorithms are described in detail. In both cases, the process of refinement is shown to be a reasonably straightforward one (for people) and one which maintains the properties of naturalness and compactness. The possibility of automating this process is considered
Validation of machine-oriented strategies in chess endgames
This thesis is concerned with the validation of chess endgame
strategies. It is also concerned with the synthesis of strategies
that can be validated. A strategy for a given player is the
specification of the move to be made by that player from any
position that may occur. This move may be dependent on the
previous moves of both sides. A strategy is said to be correct if
following the strategy always leads to an outcome of at least the
same game theoretic value as the starting position. We are not concerned with proving the correctness of programs
that implement the strategies under consideration. We shall be
working with knowledge-based programs which produce playing
strategies, and assume that their concrete implementations (in
POP2, PROLOG etc.) are correct. The synthesis approach taken attempts to use the large body
of heuristic knowledge and theory, accumulated over the centuries by chessmasters, to find playing strategies. Our concern here is
to produce structures for representing a chessmaster's knowledge
wnich can be analysed within a game theoretic model. The validation approach taken is that a theory of the domain
in the form of the game theoretic model of chess provides an objective measure of the
strategy followed by a program. Our concern here is to analyse the
structures created in the synthesis phase. This is an instance of
a general problem, that of quantifying the performance of
computing systems. In general to quantify the performance of a
system we need,- A theory of the domain.
- A specification of the problem to be solved.
- Algorithms and/or domain-specific knowledge to be
applied to solve the problem
Human and Machine Representations of Knowledge
Four ex1st1ng Knowledge-representations for the computat1on
of s1m1lar functions 1n a chess endgame were 1mplemented on the
same computer 1n the same language. They are compared w1th
respect to effic1ency regard1ng time-space requirements.
Three of these programs were then paraphrased 1nto English
and all four were studied for their feasibility as 'open book'
advice texts for the human beginner in chess. A formally verified
set of rules was also tested for its suitability as an advice
text. The possible effectiveness of these advice texts in
'closed book' form is considered.
The above experiments comprise a case study of a phenomenon
known as the "human window". This phenomenon mot1vated an
analysis of four documented instances of mismatch between human
and machine representations. These are:
Three Mile Island
II Air Traffic Control,
III NORAD Mil1tary Computer System,
IV The Hoogoven Royal Dutch Steel automation failur