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Pattern-Based Representation of Chess End-Game Knowledge

Students of computer chess aim at an operational theory of Master skill—operational in the sense that it can be run on the machine. In one form of the aspiration Masters must be defeated across the board under full tournament conditions, so far achieved only for 'blitz' chess but not for play under standard time control (see SIGART Newsletter No. 62, 1977). Another form of the 'Master skill' aspiration aims at correct play for defined subsets of chess. It is not known whether 'strong mastery' in this sense is attainable for the complete game or whether chess is 'hard' in the sense of Knuth (1976). We can, however, start with elementary endings such as King and Queen versus King (denoted KQK), KRK, KBBK, KBNK and KPK, and seek to extend mastery backwards a step at a time into the game's increasingly complex hinterland. Work at Edinburgh follows the second approach, seen as a means for studying forms of knowledge representation in relation to three desiderata: (a) forms more powerful than present programming languages for specifying strategies, (b) forms more suitable for proofs of correctness of strategies and (c) forms more convenient for automatic optimisation of strategies ('machine learning'). None of the above listed end-games contains anything problematical from a Master's point of view and computer programs embodying correct strategies have been written for all of them. In reviewing this work Bramer (1977) remarks that the task, not of playing such end-games correctly, but of expressing in program form the knowledge required for correct play, has turned out to be surprisingly and disproportionately hard. For his own implementations of KRK and KPK Bramer uses pattern-based models of a general kind now accepted as indispensable to the extension of machine mastery into more complex chess subdomains. Such exercises as KRK and KPK can be done (with some difficulty) without special programming tools; but it needs only a small step in the direction of greater complexity to bring us into territory where the use of such tools become critical. In this paper we describe pattern descriptional aids to strategy building in two areas more complex than KRK, KPK, KQK and the rest; namely (a) pawns-only positions and (b) the defence of king and knight against king and rook.