On Substitutive Algebra and its Syntax

Karl Menger

A chapter in Selecta Mathematica, 2003, pp 247-270 from Springer

Abstract: Abstract In the calculus of propositions, meaningful expressions in ŁuKASiEwiez’ parentheses-free frontal notation were characterized in 1932 as strings of symbols satisfying certain formal conditions.1) A string made up of references 2) to binary and unitary logical functors (e.g., C for implication, and n for negation) and to propositions or truth-values is well-formed if and only if the number of references to propositions or truth-values exceeds the number of the binary symbols in the entire string without exceeding it in any of its initial segments, and the string terminates in a proposition symbol. This theorem (which clearly also applies to arithmetical expressions written in ŁUKASIEWICZ’ notation) later was generalized 3), has been rediscovered 4), and has found its way into compendia and textbooks 5).

Date: 2003
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DOI: 10.1007/978-3-7091-6045-9_24

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