A Set of APL Functions to Play New Eleusis

II SET OF APL FUNCITONS TO PLAY NEW ELEU.SIS

~uchael J. A. Berry

T. P. Sharp, Associates 148 State Street, Boston, MA 02109

T 'IHE GAI-lE

New Eleusis is a game, invented by Robert Abbott, which has been used to simulate hypothetico-deductive reasoning.[3]

Players of New Eleusis attempt to find the "secret rule" which governs the play of cards. ~is rule, which is made up by a player refered to AS "God," may be anything at all so long as it nepends only on attributes of the cards themselves. The scoring of the game punishes a God who makes up rules which are too difficult for any of the players to discover. Players experiment by playing cards which are then either accepted or rejected by Ood.

TI 'mE OHGANIZATION OF INFORMATION

nne of APL's greatest strengths is its ability t~ deal with rectangular arrays as easily as scalars. With the introduction of nested arrays, this power is enhanced by the ability to enclose or "scalarize" any APL array so that it may itself be an element of a larger array. The Eleusis workspace uses these new nested arrays to great Advantage.

nne example is the prediction matrix. This matrix contains a row for each rule under consideration, and a column for each position on the mainline including 20 or 30 columns representing positions at which no cards have yet been played. Each element of the array is an enclosed vector of all cards which would be permissible at that position according to a particular rule. Any card in the intersection of a column of the matrix is allowed by all the rules. When the rule list has reached its final state, these are the cards which the program acting as prophet would approve. By comparing rows and ~olumns of the prediction matrix with the vectors representing the cards accepted and rejected at a position, the p~ram can detennine whether an imlividual rule is consistent with the results of past experiments.

'l'he rules themselves are numerically encoded A translation pr~ram renders these rules into ll:raJliiHtlcal l~nv,lish for comnunication with the human players.

Til TI-lE ME'IHODOLOOY

The Eleusis workspace contains 50 or 60 APL functions. Each of these is a single purpose ~ule which can be fitted together with other modules to build a complex system.

~e program works by applying a collection of "screen functions" each of which is blind to all hut one aspect of the cards, and then looking for patterns in the results. ·The part of the problem requiring the most intelligence is recognizing which rules are not likely to be correct because they do not correspond to human styles of thinking. ~is is done by employing a number of functions which wieght the rules by "common sense." r'or instance, 1t was pointed out by Dietterich[2] that nost rules invented by human Gods have symmetry. Once the program has a set of possible rules it tests them by playing cards which seem likely to eliminate the largest number of unlikely rules. When all the remaining rules meet the "reasonability" criteria and even long strings of rards can be played successfully by following them, t.he program declares itself to be a prophet. The nrogram can play against itself, or against one or more other players.

Complete program listings are available from the author.

1. Abbott, Robert The New Eleusis Rox 1175, GPO, New York, NY 10001 1977
2. Dietterich, Thomas G. The Methodology of Knowledge Layers for Inducing Descriptions of .Sequentially Ordered Events llniversity of Illinois Thesis IIUIU<DCS-R-80-1-24 198o
3. Gorman, r-tichael E. How Communication and Confirmatory .Strategies Affect the ".Search for Truth." Doctoral Dissertation, University of New Hampshire 1981