Unconditional or Prior Joint Probabilities
for independent events A and B (coin toss resulting in head or tail):
P(A ^ B) = P(A) * P(B)
P (A V B) = P(A) + P(B)

Conditional Joint Probabilities
for events A and B influencing each other (disease and ache):
P(A ^ B) = P(A|B) * P(B)  = P(B | A) * P(A)
P(A V B) = P(A) + P(B) - P(A ^ B)

Any query may be answered using joint probability table.

If there are v variable in KB with n domain elements for each,
the joint probability table to answer any query is n x n x n x ... v-times = n^v -1
Minus 1, as all probability entries must sum up to 1.

Note: P(A | b, c) is probability of A, so, P(A, D |b, c) = P(A |b,c) * P(D |b,c)
However: P(A |b,c) is NOT P(A |b)* P(A |c)

Global semantics of Prob reasoning is the exhaustive joint probability distribution
table of all variable domains.

Different choice of initial ordering of variables may draw different Bayesian network.

In a Bayesian network node n's conditional probability table will have P rows for P number of its parents.
One column for n=T or n=F will suffice, the other column may be computed.
If n is categorical, with d domains, then how many columns do you need?

OTHER TYPE OF REASONING:

Dempster-Shafer: P(A) + P(~A) <= 1,  1-P(A)-P(~A) is "unknown" 

Fuzzy Logic: "Nate is Tall" may be difficult to formulate in terms of Probabilistic Logic.
Tall(Nate) is not a probability, although between [0, 1]
T(A and B) = min( T(A), T(B))	  		What is P(A and B)?
T(A or B) = max( T(A), T(B))
T(~A) = 1 - T(A)