We were led to this comparison by the observation that the computer model is weaker in three important ways: search depth is not unbounded, structures matching variables cannot be compared, and structures matching variables cannot be moved. Thus, every recursively enumerable language is generated by a transformational grammar with limited search depth, without equality comparisons of variables, and without moving structures corresponding to variables. On the other hand, both mathematical models allow unbounded depth of analysis; both allow equality comparisons of variables, although the Ginsburg-Partee model.compares
The work on automatic chess therefore started when men, such as the musician-chess player Philidor (1749), formulated general principles of play. Then the decision of whether to regard that position, 7r, as an endpoint, when analysing a position, no, depends on the following considerations: (a) The depth (i.e., the number of moves ahead) of the position From the point of view of strict logic, chess is a game of pure skill, but it is a physical impossibility to avoid some degree of chance. Closely allied to the problem of selecting endpoints on an analysis tree, is the selection of which moves to discard without analysis. This problem is discussed in Appendix H. Hence, from the point of view of the Borel-von Neumann theory of games, chess is'trivial' (see Appendix A).
What is needed is a discipline which will study semantic message-connection in a way analogous to that in which metamathematics studies mathematical connection, and to that in which mathematical linguistics now studies syntactic connection. Research Used as Data for the Construction of T (a) Conceptual Dictionary for English The uses of the main words and phrases of English are mapped on to a classificatory system of about 750 descriptors, or heads, these heads being streamlined from Roget's Thesaurus. For Instance, a single card covers Disappoint, Disappointed, Disappointing, Disappointment. The two connectives, / ("slash") and: ("colon") and a word-order rule are used as in T to replace R.H. Richens' three subscripts, and every two pairs of elements are bracketted together, two bracketted pairs of elements counting as a single pair for the purpose of forming 2nd order brackets.