Basic Modal Logic

<jats:title>Abstract</jats:title> <jats:p>Modal logics are logics of qualified truth.Necessary, obligatory, true after an action (such as running a computer program),known, knowable, believed, provable, from now on, so far, since anduntil are qualifiers with similar formal characteristics. But while they are related, these qualifiers differ markedly from each other.Necessity can have different properties depending on whether physical necessity, logical necessity, or something else is being considered. Even if this has been decided, can we have a sentence whose truth is necessary, without that fact in turn being necessary? Briefly, if some truth is necessary, is it necessarily necessary? What if a sentence is not necessarily true; must that be a necessary truth? In every-day life we are not in the habit of asking such questions, and so may have little feeling for appropriate answers.Known andbelieved differ in a basic principle: what is known must be true, but what is believed need not be. Time can be thought of as discrete or continuous, the future as fixed or not, the past as determined or not, so qualifiers likeuntil can be given varied interpretations. In addition to variations motivated by considerations like these, large numbers of modal logics have been created for purely formal purposes: their mathematical properties are of interest for some reason or other. Clearly there are a great many modal logics and it is impossible to cover them all in even passing detail.</jats:p>