Which logic is designed to address the problem of referential

Referential opacity occurs in statements involving propositional attitudes like belief, knowledge, necessity, etc., where substitution of identical terms may change truth.

Example:
“John believes that Superman can fly”
Even though Superman = Clark Kent,
“John believes that Clark Kent can fly” may not be true.

Why Classical Logic Fails

• First-order / Predicate logic follows substitution of equals.

• But in such contexts, substitution fails ⇒ cannot handle referential opacity.
  
  Why Modal Logic Works

  • Modal logic introduces operators like:

    • □ (necessarily)

    • ◇ (possibly)

    • Belief/knowledge operators

  • These create intensional contexts, where meaning depends on more than truth value.

  • Hence, it correctly models propositional attitudes.