A Multi-linguistic-Valued Modal Logic

摘要

This paper develops a multi-valued modal logic, in which a logic formula takes a value of truth in linguistic terms. In other words, truth in our logic is regarded as a linguistic variable and its values are linguistic terms, which can be modelled as fuzzy sets. In particular, we define negation and implication on linguistic truth values such that their truth tables accord with those in conventional three-valued logic. Moreover, we also prove the soundness and completeness of our logic.