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W. A. Pogorzelski 《Studia Logica》1962,13(1):129-131
Summary The sentential calculiR, under discussion, are axiomatizable and implication is among their primitive terms. The modus ponens and the rule of substitution
are their primitive rules. ByS
r
is denoted the set of sentences obtained from the formulae of the calculusR by substituting sentences of a given language for all variables. The variablesx, y, z ... represent the elements of the setS
r
, the variablesX, Y, Z ... represent the subsets ofS
R
. The formulacxy designates an implication withx as its antecedent andy as its consequent,cxy is always an element ofS
R
δ(X) means, thatX is closed with respect to the modus ponens rule.A
R
designates the class of allS
R
-substitutions of the axioms of the sentential calculusR. 相似文献
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W. A. Pogorzelski 《Studia Logica》1964,15(1):179
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W. A. Pogorzelski 《Studia Logica》1964,15(1):188
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We attempt to define the classical propositional logic by use of appropriate derivability conditions called Cn-definitions. The conditions characterize basic properties of propositional connectives. 相似文献
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Allatum est die 28 Augusti 1959 相似文献