## Modal Logic

**Modal logic** is a type of formal logic primarily developed in the 1960s that extends classical propositional and predicate logic to include operators expressing modality. Modalsâ€”words that express modalitiesâ€”qualify a statement. For example, the statement "John is happy" might be qualified by saying that John is usually happy, in which case the term "usually" is functioning as a modal. The traditional alethic modalities, or modalities of truth, include possibility ("Possibly, p", "It is possible that p"), necessity ("Necessarily, p", "It is necessary that p"), and impossibility ("It is impossible that p"). Other modalities that have been formalized in modal logic include temporal modalities, or modalities of time (notably, "It was the case that p", "It has always been that p", "It will be that p", "It will always be that p"), deontic modalities (notably, "It is obligatory that p", and "It is permissible that p"), epistemic modalities, or modalities of knowledge ("It is known that p") and doxastic modalities, or modalities of belief ("It is believed that p").

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### Some articles on modal logic:

**modal Logic**)

... In

**logic**and philosophy, S5 is one of five systems of

**modal logic**proposed by Clarence Irving Lewis and Cooper Harold Langford in their 1932 book ... It is a normal

**modal logic**, and one of the oldest systems of

**modal logic**of any kind ...

**Modal Logic**- Controversies

...

**Modal logic**has been rejected by many philosophers ... starting with Aristotle seem to have had priority of interest in

**modal logic**over mathematicians.) Nicholas Rescher has argued that Bertrand Russell ... Dejnozka has argued against this view, stating that a

**modal**system which Dejnozka calls MDL is described in Russell's works, although Russell did believe the concept of modality to "co ...

**Modal Logic**

... in this area is considered by some to be an anticipation of

**modal logic**and its treatment of potentiality and time ... Contemporary philosophy regards possibility, as studied by

**modal**metaphysics, to be an aspect of

**modal logic**...

**Modal logic**as a named subject owes much to the writings of the Scholastics, in particular William of Ockham and John Duns Scotus, who reasoned informally in a

**modal**manner, mainly to analyze ...

... The same argument applies to any multi-valued

**logic**L complete with respect to a logical matrix whose all elements have a name in the language of L.) The Kreisel ... In fact, it is admissible in every superintuitionistic

**logic**... The rule is admissible in many

**modal logics**, such as K, D, K4, S4, GL (see this table for names of

**modal logics**) ...

**Modal Logic**

... may have their semantics modified by special verbs or

**modal**particles ... new work on the topic, expanding the kinds of modality treated to include deontic

**logic**and epistemic

**logic**... work of Arthur Prior applied the same formal language to treat temporal

**logic**and paved the way for the marriage of the two subjects ...

### More definitions of "modal logic":

- (
*noun*): The logical study of necessity and possibility.

### Famous quotes containing the word logic:

“The *logic* of worldly success rests on a fallacy: the strange error that our perfection depends on the thoughts and opinions and applause of other men! A weird life it is, indeed, to be living always in somebody else’s imagination, as if that were the only place in which one could at last become real!”

—Thomas Merton (1915–1968)