$\square\diamond\varphi$ valid in a Model with a single world with no successor

30 Views Asked by At

$\square\varphi$ is valid in model M that has a single world w, and w has no outgoing arcs(it has no successor). $\square\varphi$ is vacuously truth at w.

Would $\square\diamond\varphi$ be also valid in this same Model M that has a single world w, and w has no outgoing arcs(it has no successor)?

1

There are 1 best solutions below

3
On BEST ANSWER

Every formula of the form $\square\psi$ is valid at $w$ (because $w$ has no successors). So, this also holds if $\psi$ happens to be of the form $\diamond\varphi$.