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Modal Operators

Core Modal Operators

  1. ◇ (diamond): possibility, “could be true”
  2. □ (box): necessity, “must be true” i.e, true in all possible worlds

For example, an atom ‘a’ exists, then □ a means that “a must be true”.

However, it is not possible to infer whether □ a or ◇ a is true or false based on knowing the value of a.

Example (from Graham Priest): a = “I will wake before 7:00 AM” might be true, but its not necessary that this must happen, so □ a is not true.