On the Reversibility of Inference for Natural Language Propositions Involving Fuzzy Quantifiers and Truth Qualifiers and the Symmetry among the Inference Results

Abstract

In this paper, we talk about reversibility of inference for natural language propositions involving fuzzy quantifiers and truth qualifiers. We find that the reversibility does not hold true only in transforming fuzzy subjects and in the end, the reversibility does not hold true in generalized inference method. And then we talk about symmetry of the inference results. We find that the symmetry exists in the inference results transforming fuzzy subjects between different types of fuzzy quantifiers and that in wide meaning, the symmetry exists in the inference results transforming fuzzy predicates, too.