Infinite-valued logic

In logic, an infinite-valued logic (or real-valued logic or infinitely-many-valued logic) is a many-valued logic in which truth values comprise a continuous range. Traditionally, in Aristotle's logic, logic other than bivalent logic was abnormal, as the law of the excluded middle precluded more than two possible values (i.e., "true" and "false") for any proposition.^[1] Modern three-valued logic (trivalent logic) allows for an additional possible truth value (i.e., "undecided")^[2] and is an example of finite-valued logic in which truth values are discrete, rather than continuous. Infinite-valued logic comprises continuous fuzzy logic, though fuzzy logic in some of its forms can further encompass finite-valued logic. For example, finite-valued logic can be applied in Boolean-valued modeling,^[3][4] description logics,^[5] and defuzzification^[6][7] of fuzzy logic.