Practice question · Put in order
Arrange these modal systems in order of increasing strength, from the weakest constraints on accessibility to the strongest.
- S5, reflexive, symmetric and transitive
- T, with reflexive accessibility
- S4, reflexive and transitive
- K, with no constraint on accessibility
Hints
- Each system adds a constraint to the one before.
- More constraints on accessibility validate more principles.
Show the answer
- K, with no constraint on accessibility
- T, with reflexive accessibility
- S4, reflexive and transitive
- S5, reflexive, symmetric and transitive
Why
Each added constraint validates further principles, so the systems nest. S5 makes accessibility an equivalence relation, which collapses iterated modalities, in S5 a string of boxes and diamonds reduces to its last operator.
Practise Modal Logic: Necessity and Possibility
The app has 5 more questions on this lesson, and keeps your place in the course. Philosophy I is free to start.
More questions on Modal Logic: Necessity and Possibility
- Why must deontic logic reject the principle that whatever is necessary is actually true?
- The possibility operator means that a sentence is probably true.
- Modal logic models necessity across possible worlds rather than degrees of belief. What follows from treating…
- Match each accessibility constraint to the principle it validates.
- Sort each claim by whether it concerns necessity or possibility.