Formulas

Formalized contexts as discussed in [McCarthy 1993] will be helpful in expressing self-awareness facts compactly.

Pat is aware of his intention to eat dinner at home.

$$\begin{array}[l]{l} c(Awareness(Pat)): Intend(I, Mod(At(H... ...ess(Pat),Intend(I, Mod(At(Home),Eat(Dinner)))) \\ \end{array}$$ (1)

Here $Awareness(Pat)$ is a certain context. $Eat(Dinner)$ denotes the general act of eating dinner, logically different from eating $Steak7642$.
$Mod(At(Home),Eat(Dinner))$ is what you get when you apply the modifier ``at home'' to the act of eating dinner. I don't have a full writeup of this proposal for handling modifiers like adjectives, adverbs, and modifier clauses. $Intend(I,X)$ says that I intend $X$. The use of $I$ is appropriate within the context of a person's (here Pat's) awareness.

We should extend this to say that Pat will eat dinner at home unless his intention changes. This can be expressed by formulas like

$$\lnot Ab17(Pat,x,s) \land Intends(Pat,Does(Pat,x),s) \rightarrow (\exists s' > s)Occurs(Does(Pat,x),s).$$ (2)

in the notation of [McCarthy 2002].

Here's an example of awareness leading to action.

Pat is driving to his job. Presumably he could get there without much awareness of that fact, since the drive is habitual. However, he becomes aware that he needs cigarettes and that he can stop at Mac's Smoke Shop and get some. Two aspects of his awareness, the driving and the need for cigarettes are involved. That Pat is driving to his job can be expressed with varying degrees of elaboration. Here are some I have considered.

$$\begin{array}[l]{l} Driving(Pat,Job,s) \\ \mbox{} \\ D... ...ation(Job,Action(Drive,Pat))),s) \\ \mbox{}. \\ \end{array}$$ (3)

The last two use a notion like that of an adjective modifying a noun. Here's a simple sentence giving a consequence of Pat's awareness. It uses $Aware$ as a modal operator. This may require repair or it may be ok in a suitably defined context.

$$\begin{array}[l]{l} Aware(Pat,Driving(Job,s),s) \land Awa... ... \\ \rightarrow Occurs(StopAt(CigaretteStore),s). \end{array}$$ (4)

The machine knows that if its battery is low, it will be aware of the fact.

$$\begin{array}[l]{l} Knows(Machine, (\forall s')(LowBattery(s') \rightarrow Aware(LowBattery(s'))),s) \\ \end{array}$$ (5)

The machine knows, perhaps because a sensor is broken, that it will not necessarily be aware of a low battery.

$$\begin{array}[l]{l} Knows(Machine, \lnot (\forall s')(LowBattery(s') \rightarrow Aware(LowBattery(s'))),s) \end{array}$$ (6)

The positive sentence ``I am aware that I am aware ...'' doesn't seem to have much use by itself, but sentences of the form ``If X happens, I will be aware of Y'' should be quite useful.