$$\begin{array}{c c c}{{\mathrm{M\,S\;QU}}}&{{,}}\\ {{}}&{{\mathrm{ST\,U\;M}}}\end{array}$$
Fig. shows two conditional constraint trees of which the one on the left side is exact.

STU MNQR)[ ; x is query, while MS QU)[ ; x is not query to the conditional
constraint trees of Fig. 2. Furthermore, STU M)[ ; x is premise-restricted query,
ise-restricted complete query to the conditional constraint trees of Fig. 2.

Figure 2: Two Conditional Constraint Trees

to basic event in have at least one basic event in common is crucial for the deduction

technique of Section 4. It assures that the problem of computing the tight answer to

complete query can be reduced to the problems of computing the tight answer to premiserestricted complete query and the tight answer to strongly conclusion-restricted complete

queries (for example, by all the queries in Section 2.3).

practice. They may be used to characterize the probability of uncertain basic events given

collection of basic events that are known with certainty.

O QRSTU)[ ; x strongly conclusion-restricted query, and QRSTU M)[ ; x prem-

![0_image_0.png](0_image_0.png)

For conditional constraint trees B; KB), conjunctive events C and basic events B we write C B i there exists path G ; G ; : : : ; Gk from basic event G in C to the basic event Gk B such that Gi+1 Gi)[1; 1] KB for all i [1 k 1]. We write B C i for all paths G ; G ; : : : ; Gk from the basic event G B to basic event Gk in C it holds Gi+1 Gi)[1; 1] KB for all i [1 k 1]. That is, the conditions C B and B C immediately entail KB B C)[1; 1] and KB C B)[1; 1], respectively. Note that the restriction u ; v for all B A)[u ; u ], A B)[ ; v KB is just made for technical convenience. The deduction technique of Section can easily be generalized to conditional constraint trees B; KB that satisfy only the restriction u i for all B A)[u ; u ; A B)[ ; v KB (Lukasiewicz, 1996). The restriction that for each query E)[ ; x ], all paths from basic event in E

query. Note that this restriction is trivially satised by all premise- and conclusion-restricted Especially tight answers to conclusion-restricted queries seem to be quite important in

