Robert A. Di Paola

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A class of formulas of the first-order predicate calculus, the definite formulas has recently been proposed as the formal representation of the “reasonable” questions to put to a computer in the context of an actual data retrieval system, the Relational Data File of Levien and Maron. It is shown here that the decision problem for the class of(More)
Successive modifications of Church's definition of a random sequence are considered in terms of their relative position in the Ritchie hierarchy of Kalmar elementary functions. A general result is derived governing the classification of Church random sequences in subrecursive hierarchies which include the elementary functions, such as the Grzegorczyk and(More)
In connection with the development of an actual question-answering system, the Relational Data File of The Rand Corporation, a class of formulas of the predicate calculus, the definite formulas of Kuhns, was proposed as the class of symbolic representations of the “reasonable” questions to put to this retrieval system. Roughly speaking, the(More)
The Relational Data File (RDF) of The Rand Corporation is among the most developed of question-answering systems. The "information language" of this system is an applied predicate calculus. The atomic units of information are binary relational sentences. The system has an inference-making capacity.As part of the actual construction and implementation of the(More)
It is proved that there is a single unary formula F of Peano arithmetic PA and a fixed infinite set S of fixed points ^ of F in PA with the following property. Let T be any recursively enumerable, 2"-sound extension of PA. Then (i) almost all $ in & are undecidable in T, and (ii) for all such ¡j> and all equivalence relations E satisfying reasonable(More)