Editing Philosophical logic (section)

=== Many-valued ===
[[Many-valued logic]]s are logics that allow for more than two truth values.<ref name="Gottwald">{{cite web |last1=Gottwald |first1=Siegfried |title=Many-Valued Logic |url=https://plato.stanford.edu/entries/logic-manyvalued/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=11 December 2021 |date=2020}}</ref><ref name="MacMillanNonClassical"/><ref name="Malinowski">{{cite book |last1=Malinowski |first1=Grzegorz |title=A Companion to Philosophical Logic |date=2006 |publisher=John Wiley & Sons, Ltd |isbn=978-0-470-99675-1 |pages=545–561 |url=https://onlinelibrary.wiley.com/doi/10.1002/9780470996751.ch35 |language=en |chapter=Many-Valued Logic|doi=10.1002/9780470996751.ch35 }}</ref> They reject one of the core assumptions of classical logic: the principle of the bivalence of truth. The most simple versions of many-valued logics are three-valued logics: they contain a third truth value. In [[Stephen Cole Kleene]]'s three-valued logic, for example, this third truth value is "undefined".<ref name="Gottwald"/><ref name="Malinowski"/> According to [[Nuel Belnap]]'s four-valued logic, there are four possible truth values: "true", "false", "neither true nor false", and "both true and false". This can be interpreted, for example, as indicating the information one has concerning whether a state obtains: information that it does obtain, information that it does not obtain, no information, and conflicting information.<ref name="Gottwald"/> One of the most extreme forms of many-valued logic is fuzzy logic. It allows truth to arise in any degree between 0 and 1.<ref name="Cintula">{{cite web |last1=Cintula |first1=Petr |last2=Fermüller |first2=Christian G. |last3=Noguera |first3=Carles |title=Fuzzy Logic |url=https://plato.stanford.edu/entries/logic-fuzzy/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=11 December 2021 |date=2021}}</ref><ref name="Gottwald"/><ref name="MacMillanNonClassical"/> 0 corresponds to completely false, 1 corresponds to completely true, and the values in between correspond to truth in some degree, e.g. as a little true or very true.<ref name="Cintula"/><ref name="Gottwald"/> It is often used to deal with vague expressions in natural language. For example, saying that "Petr is young" fits better (i.e. is "more true") if "Petr" refers to a three-year-old than if it refers to a 23-year-old.<ref name="Cintula"/> Many-valued logics with a finite number of truth-values can define their logical connectives using truth tables, just like classical logic. The difference is that these truth tables are more complex since more possible inputs and outputs have to be considered.<ref name="Gottwald"/><ref name="Malinowski"/> In Kleene's three-valued logic, for example, the inputs "true" and "undefined" for the conjunction-operator {{nowrap|"<math>\land</math>"}} result in the output "undefined". The inputs "false" and "undefined", on the other hand, result in "false".<ref>{{cite journal |last1=Malinowski |first1=Grzegorz |title=KLEENE LOGIC AND INFERENCE |journal=Bulletin of the Section of Logic |date=2014 |volume=43 |issue=1/2 |pages=3–52}}</ref><ref name="Malinowski"/>