Generalization of Kalmar’s method for quasi-matrix logic

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Yu. V. Ivlev

Аннотация




Quasi-matrix logic is based on the generalization of the principles of classical logic: bivalency (a proposition take values from the domain {t (truth), f (falsity)}); consistency (a propo- sition can not take on both values); excluded middle (a proposition necessarily takes some of these values); identity (in a com- plex proposition, a system of propositions, an argument the same proposition takes the same value from domain {t, f }); matrix prin- ciple — logical connectives are defined by matrices. As a result of our generalization, we obtain quasi-matrix logic principles: the principle of four-valency (a proposition takes values from domain{tn,tc,fc,fi}) or three-valency (a proposition takes values from domain {n, c, i}); consistency : a proposition can not take more than one value from {tn,tc,fc,fi} or from {n,c,i}; the principle of excluded fifth or fourth; identity (in a complex proposition, a system of propositions, an argument the same proposition takes the same value from domain {tn,tc,fc,fi} or domain {n,c,i}); the quasi-matrix principle (logical terms are interpreted as quasi- functions). Quasi-matrix logic is a logic of factual modalities.




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Y. V. Ivlev. Generalization of Kalmar’s method for quasi-matrix logic // Логические исследования / Logical Investigations. 2018. Т. 19. № 1.
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