Logic of English grammar

The logic of English grammar is being investigated by a process of approximative logical synthesis. Beginning with a kernel language which is an alphabetically spelled form of symbolic logic with English-like vocabulary, English-like extensions are constructed simulating selected features of English grammar. For each extended language, an algorithm is given which would permit a computer to make a left-to-right, word-by-word scan of an input sequence, to transform it by stages (as long as the sequence is found to be a well-formed formula of the extended language) into a sentence in the logical grammar of the kernel (or into a logical symbolization if desired). The algorithm thus constitutes simultaneously (1) a recognition grammar of the extended language, i.e., not just formation rules or productions, but a decision method for sentencehood, and (2) a portion of its transformation rules (defining a consequence relation). To date, languages have been constructed simulating the English determiners, (e.g., “every”, “any”, “no”, “a”) and the system of groupers (“either”, “both”, “if”) with precedence-ordered connectives (e.g., “and”, “and furthermore”, “or”, “or else”) by which English achieves the effect of parentheses. Work soon to be reported extends the analysis to relative, general and indefinite pronouns. It is expected that the algorithms will be embodied in computer programs within the year for purposes of comparison with results of human parsers.

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