多值逻辑与悖论

Multi-valued Logic and Paradox

悖论是困扰逻辑学的难题,在经典逻辑中往往难以解决,诉诸多值逻辑成为一种重要选择。说谎者悖论、罗素悖论可以在三值逻辑中得到解决,连锁悖论可以在更多值的多值逻辑中得到一定程度的解决。多值逻辑解决连锁悖论时可以把真值解释为概率或逻辑真值,但是概率和逻辑真值存在明显的差异,通过对两种解释的比较可以进一步加深对多值逻辑的理解。多值逻辑在解决悖论的过程中找到了其应用价值,即可以处理含有模糊概念的推理,同时,其合法性也得到了辩护。

Paradox is a disturbing question in logics which is difficult to solve,so resorting to multi-valued logic becomes an important choice. Liar paradox and Russell＇s paradox can be settled in three-valued logic,while chain paradox can be addressed in multi-valued logic to a certain extent and under this circumstance truth can be interpreted as probability and logical truth. It is obvious that probability and logical truth are quite different interpretations. By comparison of the two interpretations,we can understand the truth of multi-valued logic clearly,and find the application and legality of multi-valued logic in solving paradoxes.