The formula-controlled logical computer “Stanislaus”
1960; American Mathematical Society; Volume: 14; Issue: 69 Linguagem: Inglês
10.1090/s0025-5718-1960-0135685-3
ISSN1088-6842
Autores Tópico(s)Mathematics, Computing, and Information Processing
ResumoThe evaluation of a formula of propositional calculus is considerably simplified if this formula is written in the parenthesis-free notation of the Warsaw School, [1]. The Warsaw notation may be formulated in the following way: There are symbols for operations, e.g.: N for negation; K for conjunction; A for disjunction; E for equivalence; C for implication; and symbols p, q, r, 8, t for variables. A variable is a formula. A formula preceded by the symbol N is a formula. Two juxtaposed formulas preceded by any one of the symbols, K, A, E, C are a formula. Evaluation of such a formula is done in the following way: Each of the variable symbols p, q, r,... has a value 0 or 1. The operation symbol acts on the value of the one or two formulas governed by it giving the value of the compound formula. It was remarked in 1950 by H. Angstl, [21, that a mechanical evaluation of a formula, written in Warsaw notation without brackets, can be done in the following easy way: Each of the variable symbols is represented by a box with one output, the negation by a box with one input and one output, and the other operation symbols by a box with two inputs and one output. The meaning of a formula in the Warsaw notation is given by Angstl's rule: The first input of each operation symbol is to be connected with the output of the next following symbol, either variable or operation. The symbol N excepted, the second input of each operation symbol is to be connected with the first remaining free output of a symbol going from left to right. This may be demonstrated by an example, which uses Stanislaus present capacity of eleven symbols: the tautology of transitivity of the implication [(p -+ q) & (q -+ r)] -+ (p -r), written in Warsaw notation
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