glossary.md
glossary.md
**Fuzzy logic** is a form of [many-valued logic](http://en.wikipedia.org/wiki/many-valued_logic) in which the [truth value](http://en.wikipedia.org/wiki/truth_value)s of variables may be any real number between 0 and 1, considered to be "fuzzy". By contrast, in [Boolean logic](http://en.wikipedia.org/wiki/Boolean_algebra), the truth values of variables may only be the "crisp" values 0 or 1. Fuzzy logic has been employed to handle the concept of partial truth, where the truth value may range between completely true and completely false.
In [logic](http://en.wikipedia.org/wiki/logic) and [mathematics](http://en.wikipedia.org/wiki/mathematics), a **truth value**, sometimes called a **logical value**, is a value indicating the relation of a [proposition](http://en.wikipedia.org/wiki/proposition) to [truth](http://en.wikipedia.org/wiki/truth).
In [logic](http://en.wikipedia.org/wiki/logic), a **many-valued logic** (also **multi-** or **multiple-valued logic**) is a [propositional calculus](http://en.wikipedia.org/wiki/propositional_calculus) in which there are more than two [truth value](http://en.wikipedia.org/wiki/truth_value)s. Traditionally, in [Aristotle](http://en.wikipedia.org/wiki/Aristotle)s [logical calculus](http://en.wikipedia.org/wiki/Term_logic), there were only two possible values (i.e., "true" and "false") for any [proposition](http://en.wikipedia.org/wiki/proposition). Classical [two-valued logic](http://en.wikipedia.org/wiki/two-valued_logic) may be extended to n*-valued logic* for *n* greater than 2. Those most popular in the literature are [three-valued](http://en.wikipedia.org/wiki/Three-valued_logic) (e.g., [Łukasiewiczs](http://en.wikipedia.org/wiki/Jan_Łukasiewicz) and [Kleenes](http://en.wikipedia.org/wiki/Stephen_Cole_Kleene), which accept the values "true", "false", and "unknown"), the [finite-valued](http://en.wikipedia.org/wiki/Finite-valued_logic) ([finitely-many valued](http://en.wikipedia.org/wiki/Finitely-many_valued_logic)) with more than three values, and the [infinite-valued](http://en.wikipedia.org/wiki/Infinite-valued_logic) ([infinitely-many valued](http://en.wikipedia.org/wiki/Infinitely-many_valued_logic)), such as [fuzzy logic](http://en.wikipedia.org/wiki/fuzzy_logic) and [probability logic](http://en.wikipedia.org/wiki/probabilistic_logic).
In [mathematics](http://en.wikipedia.org/wiki/mathematics) and [mathematical logic](http://en.wikipedia.org/wiki/mathematical_logic), **Boolean algebra** is the branch of [algebra](http://en.wikipedia.org/wiki/abstract_algebra) in which the values of the [variables](http://en.wikipedia.org/wiki/variable_(mathematics)) are the [truth value](http://en.wikipedia.org/wiki/truth_value)s *true* and *false*, usually denoted 1 and 0 respectively. Instead of [elementary algebra](http://en.wikipedia.org/wiki/elementary_algebra) where the values of the variables are numbers, and the main operations are addition and multiplication, the main operations of Boolean algebra are the [conjunction](http://en.wikipedia.org/wiki/Logical_conjunction) *and* denoted as ∧, the [disjunction](http://en.wikipedia.org/wiki/Logical_disjunction) *or* denoted as ∨, and the [negation](http://en.wikipedia.org/wiki/negation) *not* denoted as ¬. It is thus a formalism for describing logical relations in the same way that ordinary algebra describes numeric relations.