6be7d8ee
 Francisco Coelho
Organised text
|
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
|
# Probabilistic ASP
## Weighted Approach
1. **Total Choices.** $N(C = x) = \prod_{a \in x} w_a \prod_{\neg a \in x} (1 - w_a)$.
2. **Stable Models.** $N(S = x | C = c) = \alpha_{x,c}$,
where the set of parameters $\alpha_{x,c}$ is such that:
$$
\begin{cases}
\alpha_{x,c} \geq 0, & \forall c, x\cr
\alpha_{x,c} = 0, & \forall x \not\supseteq c \cr
\sum_{x} \alpha_{x,c} = 1, & \forall c.
\end{cases}
$$
3. **Worlds.** $N(W = x)$
1. If $x$ is a _total choice_: $
N(W = x) = \prod_{a \in x} w_a \prod_{\neg a \in x} (1 - w_a).
$$
|