Editing Philosophical logic (section)

=== Epistemic ===
[[Epistemic logic]] is a form of modal logic applied to the field of [[epistemology]].<ref name="StanfordEpistemic">{{cite web |last1=Rendsvig |first1=Rasmus |last2=Symons |first2=John |title=Epistemic Logic |url=https://plato.stanford.edu/entries/logic-epistemic/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=14 December 2021 |date=2021}}</ref><ref name="BritannicaEpistemic">{{cite web |title=applied logic - Epistemic logic Britannica |url=https://www.britannica.com/topic/applied-logic/Epistemic-logic |website=www.britannica.com |access-date=14 December 2021 |language=en}}</ref><ref name="MacMillanModal"/><ref name="Britannica"/> It aims to capture the logic of [[knowledge]] and [[belief]]. The modal operators expressing knowledge and belief are usually expressed through the symbols {{nowrap|"<math>K</math>"}} and {{nowrap|"<math>B</math>"}}. So if {{nowrap|"<math>W(s)</math>"}} stands for the proposition "Socrates is wise", then {{nowrap|"<math>K W(s)</math>"}} expresses the proposition "the agent knows that Socrates is wise" and {{nowrap|"<math>B W(s)</math>"}} expresses the proposition "the agent believes that Socrates is wise". Axioms governing these operators are then formulated to express various epistemic principles.<ref name="MacMillanModal"/><ref name="StanfordEpistemic"/><ref name="BritannicaEpistemic"/> For example, the axiom schema {{nowrap|"<math>K A \to A</math>"}} expresses that whenever something is known, then it is true. This reflects the idea that one can only know what is true, otherwise it is not knowledge but another mental state.<ref name="MacMillanModal"/><ref name="StanfordEpistemic"/><ref name="BritannicaEpistemic"/> Another epistemic intuition about knowledge concerns the fact that when the agent knows something, they also know that they know it. This can be expressed by the axiom schema {{nowrap|"<math>K A \to KK A</math>"}}.<ref name="MacMillanModal"/><ref name="StanfordEpistemic"/><ref name="BritannicaEpistemic"/> An additional principle linking knowledge and belief states that knowledge implies belief, i.e. {{nowrap|"<math>K A \to B A</math>"}}. Dynamic epistemic logic is a distinct form of epistemic logic that focuses on situations in which changes in belief and knowledge happen.<ref>{{cite web |last1=Baltag |first1=Alexandru |last2=Renne |first2=Bryan |title=Dynamic Epistemic Logic |url=https://plato.stanford.edu/entries/dynamic-epistemic/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=13 December 2021 |date=2016}}</ref>