Intuitive Idea of Implication vs. Formal Definition: How to Define the Corresponding Degree

Authors

Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

6-2019

Comments

Technical Report: UTEP-CS-19-53

Abstract

Formal implication does not capture the intuitive idea of "if A then B", since in formal implication, every two true statements -- even completely unrelated ones -- imply each other. A more adequate description of intuitive implication happens if we consider how much the use of A can shorten a derivation of B. At first glance, it may seem that the number of bits by which we shorten this derivation is a reasonable degree of implication, but we show that this number is not in good accordance with our intuition, and that a natural formalization of this intuition leads to the need to use, as the desired degree, the ratio between the shortened derivation length and the original length.