Is there a distinction between strong or complete qualitative probability orders which are considered to be strong representation or total probability relations neither of which involve in-com parables events, use the stronger form of Scott axiom (not cases of weak, partial or intermediate agreements) and both of whose representation is considered 'strong '
of type (1)P>=Q iff P(x)>= P(y)
versus type
(2) x=y iff P(x)=P(x)
y>x iff P(y)>Pr(x) and
yB or A=B]iff not AB equiv B=B equiv B=B or BB and not A< B yet not A=B is possible in the second yet
A>= B or AB or A=A where this mutually exclusive to A>B equiv ~B= |
Maybe expain what it is that you have read, can understand better
Additivity in Physics is important when you have interference phenomena.
as
Add quantum waves BEFORE you calculate psi* psi
Add electromagnetic waves BEFORE you find Intensity (E.E) where E is electric field
Add vectors vectorialy before finding net force say
In optics there are all kinds of examples of this
and where = reflects 'equality in rank in the probability',not 'incomparability,' and not necessarily 'logical 'equivalence'and is an equivalence relations.
, but where in both cases, it is generally expected that it =relflectsts numerical identity in probability value in the homo-morphism, although the events A, B may be distinct events. I
and but in (1) its a derived,weakly connected, strict, weak order over the derived :
and
= are primitive, and = are derived,
and in (2) >|=|=B' or it has the same meaning, as in (2),
, axiomatizedby a total negative transitive bi-conditional anti symmetric total probability over B: if A>=B and not A=B
as compared to the less ambiguous representations given by a total bi-conditional anti symmetric order , AC
connected
[not A=B i]ff A>B or AB iiff BA], implies false [A=B B>=C implies A>=C
and over , =B B>C implies A>C
and over =, A>=B B=C implies A>=C
reflexive, A=B or AB and A=C then A>C not just when A>B and A>C; ie no information is lost through B and B=C then AUB>A UC not just >=. I guess the best way to avoid the issue is not really have >=
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