---
tag: VC3A2VWXND
kind: concept
name: S5 (modal logic)
aliases: [axiom-s5, logic-s5]
sources:
  - wikipedia: en:12708106@r1375088158
    locator: S5 (modal logic)
    note: adopted
    mention: wikipedia://en/12708106
    sections: [Summary]
same_as:
  wikidata: Q7388341
  wikipedia: S5 (modal logic)
inventory: [D5JKKWKM27]
---

## Summary

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 *Symbolic Logic*. It is a normal modal logic, and one of the oldest systems of modal logic of any kind. It is formed with propositional calculus formulas and [[tautologies|05006AJ7DZ]], and inference apparatus with substitution and [[modus ponens|0Y0MQYST0M]], but extending the syntax with the modal operator *necessarily* $\Box$ and its dual *possibly* $\Diamond$.