 Just as in the case of FOL, in probability theory we are concerned with declarative statements, or propositions, to which degrees of belief are applied; we can thus say that both logicist and probabilistic approaches are symbolic in nature. Both approaches also agree that statements can either be true or false in the world. In building agents, a simplistic logic-based approach requires agents to know the truth-value of all possible statements. This is not realistic, as an agent may not know the truth-value of some proposition \(p\) due to either ignorance, non-determinism in the physical world, or just plain vagueness in the meaning of the statement. More specifically, the fundamental proposition in probability theory is a random variable, which can be conceived of as an aspect of the world whose status is initially unknown to the agent. We usually capitalize the names of random variables, though we reserve \(p,q,r, \ldots\) as such names as well. For example, in a particular murder investigation centered on whether or not Mr. Barolo committed the crime, the random variable \(Guilty\) might be of concern. The detective may be interested as well in whether or not the murder weapon – a particular knife, let us assume – belongs to Barolo. In light of this, we might say that \(\Weapon = \true\) if it does, and \(\Weapon = \false\) if it doesn’t. As a notational convenience, we can write \(weapon\) and \(\lnot weapon\) and for these two cases, respectively; and we can use this convention for other variables of this type. 