A COMBINATORIAL ANALOG OF FORMAL SYSTEMS WITH BUILT-IN CONSISTENCY
Vitaliy Valentinovich Tselishchev1,2, Artem Olegovich Kostyakov1,2
1Institute of Philosophy and Law, Siberian Branch of the Russian Academy of Science, 8, Nikolaev st. 630090, Novosibirsk, Russia
2Novosibirsk National Research State University, 2, Pirogov st. 630090, Novosibirsk, Russia
Keywords: комбинаторика, непротиворечивость, дистрибутивная нормальная форма, конституента, разрешимость, вторая теорема Геделя о неполноте, combinatorics, consistency, distributive normal form, constituent, solvability, GГ¶del’s Second Incompleteness Theorem
Abstract
The article deals with the representation of formal systems on the base of the distributive normal form of first-order logic. We show that in such systems, according to the depth of decomposition of the distributive normal form, one may demonstrate consistency combinatorially by means of the system itself which makes it a system with a «built-in» consistency. We draw an analogy with elementary arithmetic formal systems where the Gödel’s Second Incompleteness Theorem is not true. We compare combinatorial syntactic methods of demonstrating the consistency of a formal system and metatheoretical evidence of consistency.
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