The Relational Data File and the Decision Problem for Classes of Proper Formulas

by Robert Di Paola

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In connection with Rand's Relational Data File (RDF), the class of proper formulas has been proposed as comprising those formalizations of questions to be processed by the RDF that are especially suitable for machine processing (see R-511 and RM-5428). The subclasses of proper formulas depend on the identity of the logical primitives employed. Different sets of primitives give rise to different classes of proper formulas. In this report it is shown that the decision problem is solvable for (1) the class of proper prenex formulas (on any set of primitives), (2) the class of proper formulas on negation, disjunction, and existential quantification, (3) the class of proper formulas on negation, implication, and existential quantification, and (4) the class of proper formulas on negation, disjunction, implication, and existential quantification. Thus, for each of these classes there is a mechanical decision procedure that determines if an arbitrary formula (on the relevant set of primitives) is a member of the class.

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