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a modal is an expression (like ‘necessarily’ or ‘possibly’) that is used to qualify the truth of a judgement. modal logic is, strictly speaking, the study of the deductive behavior of the expressions ‘it is necessary that’ and ‘it is possible that’. however, the term ‘modal logic’ may be used more broadly for a family of related systems. these include logics for belief, for tense and other temporal expressions, for the deontic (moral) expressions such as ‘it is obligatory that’ and ‘it is permitted that’, and many others. an understanding of modal logic is particularly valuable in the formal analysis of philosophical argument, where expressions from the modal family are both common and confusing. narrowly construed, modal logic studies reasoning that involves the use of the expressions ‘necessarily’ and ‘possibly’. however, the term ‘modal logic’ is used more broadly to cover a family of logics with similar rules and a variety of different symbols.
a list describing the best known of these logics follows. modal logic it is necessary that ..
it is possible that ..
deontic logic o it is obligatory that ..
p it is permitted that ..
f it is forbidden that ..
temporal logic g it will always be the case that ..
f it will be the case that ..
h it has always been the case that ..
p it was the case that..
doxastic logic bx x believes that .. | 
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