If the epistemic conditions sufficient for weak rationality already entail common knowledge, the additional eliminations attributed to strong rationality are already implicit in weak rationality's closure conditions.
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Sufficient conditions(used to explain what makes an event happen)
A set of circumstances that guarantee something will happen—if all these conditions are present, the outcome must occur.
Weak rationality(as used in decision theory and epistemology)
A basic standard for making decisions or beliefs that requires you to be logically consistent and avoid obvious contradictions.
common knowledge(Condition for the formation of a joint commitment)
A state in which each party knows the relevant fact, knows that the others know it, and so on — used here as the threshold condition for a joint commitment coming into force.
epistemic conditions
Conditions such as space and time, without which we cannot cognize any object
knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.)
Justified true belief — true belief that has been arrived at through the exercise of deliberative capacities, including comparison of and deliberation among alternatives.