activation propagation

In BAsCET, the activation value is propagated from a semantic node to another.

Let's start from the example shown in the link explanation.

/----------------\                             /--------------\
|   S: birthday  |                             |    S: cake   |
+----------------+                             +--------------+
| CI:  80        |     /-----------------\     | CI: 70       |
| AV: 100 %      +-----+ T: eat | W: 95% +-----+ AV:  0%      |
| DR:   2        |     \-----------------/     | DR:  5       |
| Ag: ComputeDay |                             | Ag: CookCake |
\----------------/                             \--------------/

Propagating the activation value of birthday through the link eat to the node cake will give the following Concept Network:

/----------------\                             /--------------\
|   S: birthday  |                             |    S: cake   |
+----------------+                             +--------------+
| CI:  80        |     /-----------------\     | CI: 70       |
| AV:  98 %      +-----+ T: eat | W: 95% +-----+ AV: 86%      |
| DR:   2        |     \-----------------/     | DR:  5       |
| Ag: ComputeDay |                             | Ag: CookCake |
\----------------/                             \--------------/

The activation value AV^t+1_i of a node i at the instant t + 1, after propagation, is expressed as the sum of its old activation value AV^t_i and the other nodes' influence I_i, minus a deactivation D_i, depending on its decay rate DR_i.

AV^t+1_i = AV^t_i + I_i - D_i

The influence of other nodes could be given by this classical formula:

I_i = (Σ_j≠i A_j x W_ij) / 100

but it lets an unbalanced influence between nodes with many neighbours (influencing them) and nodes with almost none.

That's the reason why BAsCET use a little more complicated influence, with a logarithmic behaviour.

As the birthday node has no incoming link, I_birthday is null.

D_birthday = 100 x 2 / 100 = 2

So, its new activation value AV¹ = AV⁰ + I - D = 100 + 0 - 2 = 98.

As far as the cake node is concerned, it is different: its activation value is null, and so is its deactivation. However, it is influenced by birthday:

I_cake = (A⁰_birthday x W_{birthday,cake}) / ( 100 x Div_cake ) = 100 x 95 / ( 100 x Div_cake ) = 95 / Div_cake

Div_cake = ln 4 / ln 3 ~ 1.0986, so I_cake ~ 86.

At last, A¹_birthday = 0 + 86 - 0 = 86

In this example, one could add a candle node, that would be associated to the cake and birthday symbols. One could add a link from cake to candle labeled by birthday; so, when birthday and cake are both activated, this link activate candle.