Open AccessNatural Implication and Modus Ponens Principle
Author(s) -
Natalya Tomova
Publication year - 2015
Publication title -
logičeskie issledovaniâ
Language(s) - English
Resource type - Journals
eISSN - 2413-2713
pISSN - 2074-1472
DOI - 10.21146/2074-1472-2015-21-1-138-143
Subject(s) - modus ponens , natural deduction , mathematics , normality , natural (archaeology) , calculus (dental) , epistemology , philosophy , discrete mathematics , inference , statistics , archaeology , dentistry , history , medicine
In [6] the definition of natural implication was introduced. One of the criteria for naturalimplication is the normality of logical matrix [2, p. 134], a condition sufficient for verification of modus ponens. In this paper two definitions of modus ponens are regarded: in the designation-preserving sense and in the tautologousness-preserving sense. These formulations are considered as applied to two-valued and three-valued cases. In two- valued case these formulations are equivalent. But in case of three-valued logic we have another situation: they are not equivalent, but the first formulation entails the second, the reverse is not the case. According to that fact, the definition of natural implication is transformed and truth tables for extended class of natural implications are presented.