Generalization of Kalmar’s method for quasi-matrix logic
Ю.В. Ивлев · Logical Investigations · 2013
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 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 takes 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 four-valency (a proposition takes values from domain $\{ t^n; t^c; f^c; f^i\}$ or three-valency (a proposition takes values from domain $\{ n; c; i\}$); consistency: a proposition can not take more than one value from $\{ t^n; t^c; f^c; f^i\}$ 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 $\{ t^n; t^c; f^c; f^i\}$ or domain $\{ n; c; i\}$); the quasi-matrix principle (logical terms are interpreted as quasifunctions). Quasi-matrix logic is a logic of factual modalities.