the success and failure of transitivity, again

1.
John is taller than Jack; Jack is taller than Joey.
It follows that John is taller than Joey.


2.
John likes Jack; Jack likes Joey.
But it doesn't follow that John likes Jack.


3.
John thinks that he is taller than Jack; Jack thinks that he is taller than Joey. It doesn't follow that John thinks he is taller than Joey.


4.
John thinks that he is taller than Jack, and John thinks that Jack is taller than Joey. Does John think he is taller than Joey?

a: John
b: Jack
c: Joey

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R1xy: x is taller than y

R1ab, R1bc => R1ac

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R2xy: x likes y

R2ab, R2bc =/=> R2ac

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R3xy: x thinks that x is taller than y

R3ab, R3bc =/=> R3ac

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R4xy: John thinks that x is taller than y (CAN WE DO THIS?)

R4ab, R4bc => R4ac