# 2. Basic Modal Propositional Logic

Logical System

10/3/08 10 Software, under construction.

#### K Modal Trees

Close the following trees using S5. Then go to the Rule Set Menu and change the rules to K, then try to close the trees a second time.

Remember that, with K, to remove or instantiate necessity across worlds, you also need access to the world you want to instantiate. So you will need two lines in the tree, one with the form □F for some world, say 1, and an access relation 1r2 and then you can go to F for the world 2. [To make this kind of extension you need to select two lines, click on one then command click on the other.]

a) ∴□F⊃□□F

b) ∴F⊃□◊F

c) ∴ (□A ∧□B)⊃□(A∧B)

d) ∴ (□A∨□B)⊃□(A∨B)

Type your own entries into the next applet. The applets can be configured to run a variety of symbol systems. This particular one is running those of Priest's book, so use these symbols for the logical connectives.

F ∴ F ∧ G ¬ ∧ ∨ ⊃ ≡ ∀ ∃ ∴ □ ◊

You need a list of zero or more premises, separated by commas, then a therefore, and then the conclusion. Use this as a template

P, Q, R ∴ S