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Presentation of Mathematical Induction by Formula of Algebra of Algorithms

Ovsyak V., Ovsyak O., Petrushka J.

Measurement Automation Monitoring

2016

Vol. 62, No. 11

367--370

The analysis of the axiom of mathematical induction, which is given by the formula of mathematical logics is presented in the paper. It has been established that the famous formula of mathematical induction is executed only in case of ordered values of the variable linked by a quantifier. This ordering is not described analytically. Algebra of algorithms is applied for an analytical description of ordering of the variable values. The axiom of mathematical induction is described by the formula of algebra of algorithms.

Some dual logic without tautologies

Górnicka A., Bryll A.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2015

Vol. 20

39--47

On this paper we consider a logic dual to the logic CRA and prove that it does not contain tautologies.

Several Remarks about Three-valued Kleene's Propositional Logic, without Tautologies

Bryll G., Jaworski L.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2003

Vol. 9

11--15

In this article we give, in the syntetic way, diferent formal aproachings to Kleene's propositional logic. In the work [5] S. C. Kleene gives a three-valued sentential calculus characterized by the following matrix:[formula]. The operators of the matrix are given by the formulas:[formula]. The operators have the tables: [tables]. It is easy to see that the set of tautologies is an empty set.