The Recursive Unsolvability of the Decision Problem for the Class of Definite Formulas.

by Robert Di Paola

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A class of formulas of the first-order predicate calculus--the definite formulas--have recently been proposed as formal representations of "reasonable" questions to be processed by an actual data retrieval system known as the Relational Data File (see RM-5428-PR). It is shown in this study that the decision problem for the class of definite formulas is recursively unsolvable. Hence there is no algorithm that can be used to decide whether or not a given formula is definite. 12 pp. Ref

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