Mirqāt The Ascent of Logic

Advanced · a field of logic

Modal Logic

Necessity and possibility, made rigorous by Kripke’s possible-worlds semantics, with their kin: temporal, epistemic, and deontic logics.

The problem
How can “necessarily” and “possibly” be made precise enough to reason with, without collapsing into paradox?
The turning point
Kripke semantics: necessity is truth at every accessible world, and the modal systems map onto properties of accessibility.
An open question
What is the right modal logic for knowledge, obligation, and provability, and how do they interact?

The Canon

  • Kripke Semantical Considerations on Modal Logic 1963
  • Lewis Counterfactuals

To study it

  • Chellas Modal Logic: An Introduction
  • Hughes & Cresswell A New Introduction to Modal Logic
  • Blackburn, de Rijke & Venema Modal Logic