Discussion on Inductive Learning about Dynamic Data Our scenario on the realm of Driving o ences considering a small portion of it in a usual tra c light. Consider four cars c1, c2, c3 and c4, and a tra c light tl1 on a street s1, as depicted in Figure 1.
The categorization process of information from pure data or learned in
unsupervised arti cial neural networks is still manual, especially in the labeling phase.
Such a process is fundamental to knowledge representation [
Connectionist approaches are capable of extracting information from
articial neural networks, but categorizing them as symbolic knowledge have been
little explored. The obstacle lies on the di culty to nd logical justi cation from
response patterns of these networks [
We shall address the discoveries of our on-going investigation on the problem
of inductively learning (IL) from dynamic data by applying a novel framework for
neural-symbolic representation and reasoning called share Neural Multi-Space
(NeMuS) used in the Amao system[
The logical entities considered are based on dynamic nature of the data[
There are four moments of interest.M1: All cars are moving; M2: c1 stopped on street; M3: tl1 signals warning, so c2 has stopped; and M4: tl1 stops blinking yellow and goes to stop sign (red), then c3 has stopped.
M1 M2 M3 M4 ~warning(tl1,w1). ~go(tl1,g1). ~move(c1,t3). ~move(c2,t3). ~move(c3,t3). move(c4,t3).. go(tl1,g0). move(c1,t0). ~move(c1,t1). ~move(c1,t2). move(c2,t0). move(c2,t1). ~move(c2,t2). move(c3,t0). move(c3,t1). move(c3,t2). move(c4,t0). move(c4,t1). move(c4,t2). during(t0,t2,g0). during(t2,t2,w0). during(t3,t3,g1). during(t3,t3,w1).
Change through time of an entity (car or tra c light) is represented by a change from positive to negative literal of move, warning and go. The goal is to identify which cars have committed a tra c light or driving o ense. Tra c regulations would point that c1 and c4 violated such laws. c1 is blocking (it stopped) tra c on s1 while tl1 indicates to go, and c4 is moving when tl1 is indicating to stop. For lack of space, we consider just the target block offence(C) with positive example block offence(c1) and negative ~block offence(c2), and the target driving offence(C) with positive example driving offence(c4) and negative ~driving offence(c3). The following (unsual long) hypothesis should be generated. block_offence(C); car(C); traffic_light(TL); is_at(C,S); is_at(TL,S); move(C,TA); go(TL,GA); ~move(C,TB); warning(TL,W1); during(TA,TB,GA); during(TX,TY,W1). driving_offence(C); car(C); traffic_light(TL); is_at(C,S); is_at(TL,S); move(C,TA); go(TL,GA); move(C,TB); ~go(TL,GB); during(TA,TX,GA); during(TY,TB,GB).
Shared NeMuS codes allow us to know that (1) the car and tra c light are on the same street, and (2) the car has the same direction of the street. Predicate code 2 can be ignored inasmuch as it is unnecessary information, because it is a rule that involves carriage movement and obedience to tra c light. Amao gets the bindings relations (occurrences) the given objects as positive and negative examples. As c1, c2, c3, and c4 are cars they belong to the same region of predicate codes. is at() relating to s1, both have is direction() with r (right), and have a single object di erent that also relates through is at () with s1, the tl1. The di erence between the positive and negative examples lies in their action predicates, in which c1 performs an action before any change occurs in t1. We, not in Amao a automatic mechanism, also noticed that the predicate is direction () and r do not relate in any way to another object or to action predicates. Thus, we can ignore this information in the construction of a hypothesis. By inverse uni cation, Amao nds a linkage pattern between is at(C,S) and is at(TL,S), and thus connecting the car and the tra c light. 3
The example explored here is small, and yet we have a long rule. An example with more information, such as velocity, position of the car and people on the street,their relations we will have many ways to nd hypotheses. We aim to overcome this challenge by using shared NeMuS weight to to group the predicates that form an intermediate concept, an abstraction, so that we can add only the predicates needed for the rules.