One New Interpretation of Infinite Valued for Medium Proposition Logic

摘要

Since three-valued model of medium logic (ML) was established, ML has been affirmed one kind of three-valued logic by many scholars. However, for medium proposition logic (MP) being as kernel theory of ML, Pan gave out a model of infinite valued of MP, on which based, proved the theorems of completeness and reliability. Based on this, this paper sets up a new model of infinite valued of MP whose truth valued range is [0, λ)∪(λ,1](λ ∈ (0.5,1)), some properties of the model are investigated, and the theorems of completeness and reliability are proved, also. This new model not only further shows that "medium proposition logic is one kind of three valued logic" is incorrect, but also rightly depicts the medium principle which is basic idea of MP, and offered foundation for MP used in more other fields.