"Modal logic is a kind of logic used to represent statements about necessity and possibility."
Study of propositions that express modalities, such as necessity and possibility.
"It plays a major role in philosophy and related fields as a tool for understanding concepts such as knowledge, obligation, and causation."
"The formula ◻P can be used to represent the statement that P is known."
"That same formula can represent that P is a moral obligation."
"Modal logic considers the inferences that modal statements give rise to."
"Most epistemic logics treat the formula ◻P → P as a tautology, representing the principle that only true statements can count as knowledge."
"Modal logics are formal systems that include unary operators such as ◊ and ◻, representing possibility and necessity, respectively."
"◊P can be read as 'possibly P.'"
"◻P can be read as 'necessarily P.'"
"◊P is true at a world if P is true at some accessible possible world."
"◻P is true at a world if P is true at every accessible possible world."
"The first modal axiomatic systems were developed by C. I. Lewis in 1912."
"The now-standard relational semantics emerged in the mid twentieth century."
"The standard relational semantics emerged from work by Arthur Prior, Jaakko Hintikka, and Saul Kripke."
"Yes, recent developments include alternative topological semantics such as neighborhood semantics."
"Applications include game theory, moral and legal theory, web design, multiverse-based set theory, and social epistemology."
"Recent developments include alternative topological semantics such as neighborhood semantics."
"Modal logic has applications in web design."
"Modal logic has applications in social epistemology."
"Fields such as game theory, moral and legal theory, web design, multiverse-based set theory, and social epistemology benefit from the applications of the relational semantics."