Modal logic

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Modal logic is a type of formal logic primarily developed in the 1960s that extends classical propositional logic and predicate logic to include operators expressing modality.

Description

Modals -- words that express modalities -- 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.

Traditional alethic modalities

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")
  • Impossibility ("Impossibly, p", "It is impossible that p").

Other modalities

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")
  • Doxastic modalities, or modalities of belief ("It is believed that p")

See also

External links