

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

![0_image_1.png](0_image_1.png)

Figure 3 depicts a sentence in MODS**. As we show later,** MODS **is the most tractable** NNF **subset we**
shall consider (together with OBDD<**). This is not surprising since from the syntax of a sentence in**
MODS**, one can immediately recover the sentence models.**
The languages we have discussed so far are depicted in Figure 4, where arrows denote set inclusion.

Table 1 lists the acronyms of all of these languages, together with their descriptions. Table 2 lists the key language properties discussed in this section, together with a short description of each.

## 3. On The Succinctness Of Compiled Theories

We have discussed more than a dozen subsets of the NNF **language. Some of these subsets are well**
known and have been studied extensively in the computer science literature. Others, such as DNNF
(Darwiche, 2001a, 1999) and d-DNNF **(Darwiche, 2001b), are relatively new. The question now is:**
What subset should one adopt for a particular application? As we argue in this paper, **that depends**