Table 3.

Permitted intervals for conclusions probabilities for the four conditional inferences on two measures.

p-validity			Coherence
Inference	Min	Max	Min	Max
MP	max{x+y−1,0}	1	xy	1−y+xy
DA	max{x+y−1,0}	1	(1−x)(1−y)	1−x(1−y)
AC	max{x+y−1,0}	1	0	min{y/x,(1−y)/(1−x)}
MT	max{x+y−1,0}	1	max{(1−x−y)/(1−x),(x+y−1)/x}	1

Notes: (1) In each case x = The probability of the major premise, if p then q, and y = the probability of the relevant minor premise, i.e., P(p) for MP, P(not-p) for DA, P(q) for AC, and P(not-q) for MT.

(2) P(if p then q) = P(q|p) is assumed for calculation of the coherence but not p-validity intervals.

(3) For both measures, a “hit” is defined as an estimated conclusion probability which is between the minimum and maximum values shown in the table.