Usually “has preferences” is used to convey that there is some relation (between states?) which is consistent with the actions of the agent. Completeness and transitivity are usually considered additional properties that this relation could have.
Yes. I believe that is consistent with what I said.
“not((necessarily, for each thing) : has [x] → those [x] are such that P_1([x]))” is equivalent to, ” (it is possible that something) has [x], but those [x] are not such that P_1([x])”
not((necessarily, for each thing) : has [x] such that P_2([x]) → those [x] are such that P_1([x])) is equivalent to “(it is possible that something) has [x], such that P_2([x]), but those [x] are not sure that P_1([x])” .
The latter implies the former, as (A and B and C) implies (A and C), and so the latter is stronger, not weaker, than the former.
Usually “has preferences” is used to convey that there is some relation (between states?) which is consistent with the actions of the agent. Completeness and transitivity are usually considered additional properties that this relation could have.
Yes. I believe that is consistent with what I said.
“not((necessarily, for each thing) : has [x] → those [x] are such that P_1([x]))”
is equivalent to, ” (it is possible that something) has [x], but those [x] are not such that P_1([x])”
not((necessarily, for each thing) : has [x] such that P_2([x]) → those [x] are such that P_1([x]))
is equivalent to “(it is possible that something) has [x], such that P_2([x]), but those [x] are not sure that P_1([x])” .
The latter implies the former, as (A and B and C) implies (A and C), and so the latter is stronger, not weaker, than the former.
Right?