300px|Diagram of common modal logics Modal logic is a collection of formal systems originally developed and still widely used to represent statements about necessity and possibility. The basic unary (1-place) modal operators are usually written "□" for "Necessarily" and "◇" for "Possibly". In a classical modal logic, each can be expressed by the other with negation . The modal formula can be read  as "if P is necessary, then it is also possible" . This formula is widely regarded as valid when necessity and possibility are understood with respect to knowledge, as in epistemic modal logic .
300px|Diagram of common modal logics Modal logic is a collection of formal systems originally developed and still widely used to represent statements about necessity and possibility. The basic unary (1-place) modal operators are most often interpreted "□" for "Necessarily" and "◇" for "Possibly". In a classical modal logic, each can be expressed in terms of the other and negation in a De Morgan duality: The modal formula can be read using the above interpretation as "if P is necessary, then it is also possible" , which is almost always held to be valid. This interpretation of the modal operators as necessity and possibility is called alethic modal logic. There are modal logics of other modes, such as "□" for "Obligatorily" and "◇" for "Permissibly" in deontic modal logic, where this same formulae means "if P is obligatory, then it is permissible", which is also almost always held to be valid .
R
usually written
most often interpreted
R
by the other with negation .
in terms of the other and negation in a De Morgan duality:
A
using the above interpretation
R
. This formula is widely regarded as valid when
, which is almost always held to be valid. This interpretation of the modal operators as
R
are understood with respect to knowledge, as in epistemic modal logic
is called alethic modal logic. There are modal logics of other modes, such as "□" for "Obligatorily" and "◇" for "Permissibly" in deontic modal logic, where this same formulae means "if P is obligatory, then it is permissible", which is also almost always held to be valid