How do many-valued logics differ from ordinary true-or-false logic?

In the context of the philosophy of logic, the primary difference between many-valued logics and classical logic lies in the number of truth-values assigned to propositions.12

• Classical Logic: Operates on a binary system where every well-formed formula is strictly either true or false. This framework is foundational to Boolean algebra, which uses these two values to manipulate propositions through logical connectives.134
• Many-valued Logics: These are formal systems that allow for more than two truth-values, ranging from three to an uncountable number. For example, some systems introduce a third value, such as "indeterminate," to handle cases like future contingents—statements about uncertain future events that may not be currently true or false. Other systems, such as fuzzy logic, utilize a spectrum of values between 0 and 1.135

Because many-valued logics expand the set of possible truth-values, they often result in the failure of classical principles, such as the law of excluded middle, which asserts that every proposition must be either true or false.5