Peis response

Re: [open-nars] Re: Temporal Feedback
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Let me explain from the beginning, so everyone following this discussion can understand.

By default, the truth-value of a statement in NARS is "eternal", in the sense that it is about all the moments. An example is "robin --> bird". With events, however, the situation is different, since by definition an "event" only happen in a certain interval. The most common way in the current AI systems is to explicitly specify the time interval for each event, but this approach is not taken in NARS, because, roughly speaking, the system does not always have the knowledge, nor is it always meaningful to do so --- what intervals should be given to "Industrial Revolution" or the rain in the past Christmas Eve (yes, rain, not snow!)?

So for each judgment on event, in NARS an occurrenceTime is stored, in terms of the system's internal clock (so it does not depends on any specific outside clock, including the system clock of its hosting hardware). Since this is a purely subjective measurement, it is not used in the interface when communicating with other systems. Instead, it will use three tenses {past, present, future) to vaguely convert this information, and the tense-ccurrenceTime mapping is carried out automatically, according to the current time on the internal clock and a parameter which specifies the width of "now". "Eternal" is taken as a special value of occurrenceTime., and all the other (numerical) values correspond to "tensed" sentences --- not only Judgments, but also Questions. Goals are handled differently, because a goal always needs to be achieved "as soon as possible", so no tense is specified.

In temporal inference, there are the following possible situations with respect to t1 and t2, the occurrenceTime values of the two premises (for single-premise inference, the other one is taken to be "eternal"):

(1) The belief is eternal, while the task is tensed. In this case, the conclusion will get the occurrenceTime of the task, because an eternal belief applies to every moment;

(2) The task is eternal, while the belief is tensed. In this case, the conclusion will be eternal, by generalizing the belief on a moment to the general situation. According to the semantics of NARS, each truth-value provides a piece of evidence for the general statement, so this inference can be taken as a special case of abduction from the belief B<f,c> and G==>B<1,1> to G<f,c/(c+k)> where G is the eternal form of B.

(3) Both premises are tensed. In this case, the truth-value of the belief B<f,c> will be "projected" from its previous OccurrenceTime t1 to the time of the task t2 to become B<f,d*c>, using the discount factor d = 1 - |t1-t2| / (|t0-t1| + |t0-t2|), where t0 is the current time. This formula is cited in https://code.google.com/p/open-nars/wiki/OpenNarsOneDotSix. Here the idea is that if a tensed belief is projected to a different time, its confidence should decrease as a function of the distance, with respect to the current time. Especially, when t1 = t2, d = 1 (no discount); otherwise if t1 or t2 equals t0, d = 0 (no projection).

There is a tricky relationship among the above three cases. Since in principle it is always valid to eternalize a tensed belief, (3) can be replaced by (2) followed by (1). In implementation, we can simply calculate both then keep the larger confidence value.

If the result of eternalization turns out to be overconfidence, it is OK --- that means the observation in that case cannot be generalized without meeting many negative evidence, which will decrease the frequency of the conclusion. In that is, even if the confidence is high, the belief will not be selected to guide the system's actions.

Pei