New Boolean Multivalued Logic System Simplifying Inferences in Flexible Styles

Abstract

This article, by regarding the relative number of affirmative bits on an arbitrary finite sequence of bits as the truth value, defines a new multivalued logic system such that the set of logic formulae forms a Boolean algebra in contrast to other non-Boolean multivalued logic systems, which we call a Boolean multivalued logic system. This article also, for demonstrating compactly that the Boolean properties (in contrast to other multivalued logic systems) simplify multivalued inferences in flexible styles, shows several intuitively-understandable examples tracing biotic diversity such that, on the proposed logic system, we can easily handle semantic inferences verifying values of all bits of each logic formula, inductive inferences counting the relative numbers of affirmative bits for determination of truth values, and deductive inferences syntactically narrowing ranges of truth values.