Semantics for ML

Present counter-interpretations to the following:

1. $\neg P\vDash_{\mathbf{K}}\neg\Diamond P$

2. $\Box(P\vee Q)\vDash_{\mathbf{K}}\Box P\vee\Box Q$

3. $\vDash_{\mathbf{K}}\neg\Box(A\wedge\neg A)$

4. $\Box A\vDash_{\mathbf{K}}A$

Present counter-interpretations to the following:

1. $\Box(M\rightarrow O),\Diamond M\vDash_{\mathbf{T}}O$

2. $\Box A\vDash_{\mathbf{T}}\Box\Box A$

Present counter-interpretations to the following:

1. $\Diamond A\vDash_{\mathbf{S4}}\Box\Diamond A$

2. $\Diamond A,\Box(\Diamond A\rightarrow B)\vDash_{\mathbf{S4}}\Box B$