Let’s use $b(x)$ to represent the strength of belief in (plausibility of) proposition $x$.

$$\begin{array}{cc} 0 \leq b(x) \leq 1 & \\ b(x) = 0 & x \mbox{ is definetely not true}\\ b(x) = 1 & x \mbox{ is definetely true}\\ b(x|y) & \mbox{strength of belief that } x \mbox{ is true given that we know } y \mbox{ is true} \end{array}$$

Desiredata:

• Strengths of belief are represented by real numbers.
• Qualitative correspondence with common sense.
• Consistency
  • If a conclusion can be reasoned in several ways, then each way should lead to the same answer.
  • The robot (analyzer) must always take into account all relevant evidence.
  • Equivalent states of knowledge are represented by equivalent plausibility assignments.