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Testing singly quantified tautologies

Published online by Cambridge University Press:  12 March 2014

Gerald Standley
Gerald Standley*
Affiliation:
University of Florida
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Extract

An effective method for testing arguments consisting of singly quantified expressions has recourse to Parry's trapezoid symbolism.1 The procedure entails representing in that symbolism each premise of the argument and the negation of the conclusion. Variables are disregarded. After clearing away any negated quantifiers, the universal statements, including a denied existential conclusion, are first set down and their conjunction (KU) derived. Existential statements, including a denied universal conclusion, are then listed. The argument is valid if and only if some contradiction appears, whether as some premise empty of lines, as a KU empty of lines, or as some existential statement having no lines in common with the KU.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 3 , 02 September 1966 , pp. 478 - 480
Copyright
Copyright © Association for Symbolic Logic 1996

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References

1 This Journal, Vol. 19 no. 3, Sept. 1954, A new symbolism for the prepositional calculus, by William Tuthill Parry, and Ideographic computation in the propositional calculus, by the present author.

2 A conjunction (only) of unnegated existential expressions will be separated into two or more statements (Cf. example below). A conjunction (only) of unnegated universal expressions will ultimately be conjoined in the KU, so that how they are listed is immaterial. A conjunction (only) of unnegated ‘mixed’ expressions will have its existential components separately listed.