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Quasi-matrix Logic
Yu. V. Ivlev

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

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