A common-sense intuition suggests affirmative answers to both queries.

Denote Si = Si−1 ∧ ∆Si, and let the domain D of all terms in Si **be a finite**
set of names of individuals in the community under consideration. Then from expressions (20, 21) we get by induction on i |MOD(Si)| = (2i + 1)2(4i+1 + 2i+1 **+ 2)**|D|−2 and E(Si, Helpf ul(Alex)) = E(Si, Dangerous(Bob**)) = 1** −1 2 i + 1
.

Hence for all i > 0 0.5 < E(Si, Helpf ul(Alex)) = E(Si, Dangerous(Bob)) < 1, lim i→∞
E(Si, Helpf ul(Alex**)) = lim**
i→∞
E(Si, Dangerous(Bob**)) = 1**.

So for all i > 0 Helpf ul(Alex) and Dangerous(Bob**) are typical atoms**
in Si **suggesting beliefs in agreement with the common-sense intuition, and**
the larger i the better this agreement. By Corollary 4.1 (ii), Helpf ul(**Alex**) ∧
Dangerous(Bob**) is consistent with all** Si.

Noteworthy, any approach preferring a minimal model yields **counter-intuitive**
beliefs in this example. Indeed, by definition, a model m is a **minimal model**
of S if there is no model µ of S such that the set of unnegated atoms of µ **is a**
proper subset of the set of unnegated atoms of m. For all i ≥ 0 Si **has a single**
minimal model in which all atoms except P oliceman(Alex) and Criminal(Bob)
are negated suggesting that under all circumstances Alex is **not helpful and Bob** is not dangerous - beliefs that are hardly reasonable.

## 6 Computing Evidence

Recently several algorithms have been developed for counting models (Bayardo et al., 2000; Birnbaum et al., 1999; Gomes et al., 2006; Lozinskii, 1992; Morgado et al., 2006; Sang et al., 2005; Thurley, 2006; Wei et al., 2005) that **can be employed**
for computing evidence. The following algorithm (based on the algorithm CDP (Birnbaum et al., 1999)) has been used in this work for computing evidence of propositional formulas.

Algorithm 6.1 Given S, let V = {v1, v2, . . . , vn} **be a set of all propositional**
variables of S.

1. Apply to S **the Davis-Putnam-Logemann-Loveland procedure (Davis et al.,**
1962). Let P
(k) = {l1, . . . , lk} represent a sequence of truth assignments to literals on a path **from the root of the search tree to a node. If** P
(k)**satisfies** S,
but {l1, . . . , lk−1} **does not, call** P
(k) a satisfying path. Let a **full assignment** be an assignment to all variables of S**. Any full assignment containing a satisfying**
path is a model of S.