Please have a look at the above video…it is necessary to do so so you understand the following text.
On that video we had three boxes. One where the premise was placed, one which was the mapping procedure for modus ponens, and one which happened to show the conclusion.
This time around the premise box will be a database. so we will feed the sequence of words in a text into the grid with different sentences having different colors and different words in each sentence having different shades of that color…note that there will not be enough colors for a typical text so we will have to find a way of representing our own version of color model that is not based on the real one. as you will see this frees us up in more ways than one.
This system has two layers of abstraction. firstly, we can talk of the lower layer where words are literally adjacent to other words. we will change which particular ones during training. And then on another level of abstraction we have sentences adjacent to other sentences. The adjacencies of words contain this information in the way that color is distributed among them in the database. so now we do not have a rule that says what color adjacent words have. We will need to have a database that contains the relative colors between cells. this is necessary. This relativity is not strictly color, if you follow me, because the color was determined while feeding in the data in the database.
The relativity represents a form of bias that will enable the following to work. Sentences that provide information such as an example of modus ponens will stand in relation to each other in a certain way. ALL sentences that lend themselves to modus ponens derived information will stand in the same relation which will be visible in the large-scale structure produced by the many colors of all the cells in the grid representing the database. And ALL statements that lend themselves to produce additional information by disjunctive syllogism (for example) will also stand in a certain relation to each other. In short, the data base will contain all the derivative knowledge possible from its contents because all possible proofs are contained in the way its color structure is set up.
That leaves us only with the need to extract it. Remember the modus ponens box. This takes on a new dimension. The modus ponens box becomes a generic question box. What we would like is for a question to be phrased, and then adjust the colors in this box, then when this box is placed over the database the relevant answer is given in the resultant box.
so we will need to train the system to both store information in such a way that the sentences stand in relationships that complete full proofs of all the information in the database and also the question grid must contain a relationship between cells that makes it possible to extract the relevant information.
the thing we are hard wiring into the system is the proof system. When performing a proof the modus ponens operation accepts certain types of statements and these statements are that type because of the words they contain
. In the video we arranged the adjacencies of the words so that they contained the disposition to “react” with the modus ponens box in order to give the correct answer. Because the modus ponens box was chosen randomly at the start of the training programme, it was unlikely that the particular adjacencies we initialized would react in this was. So training became changing the adjacencies so that this would occur. Now in the extension of this idea we have whole sentences standing in relation to each other in terms of the adjacencies between words. The individual words themselves each have a disposition to appear in the premise or conclusion of a proof or a part of a proof. Even. Eg.during training we will get the system to pick up on this disposition and hardwire it into the system. Then when sentences stand in relation to each other some of those relationships will be in terms of a stage in a proof. I. E.the statements “if I hit my head on something I will get a head ache’ and I hit my head on something”… Therfore I get a headache… These three sentences will stand in relation the same way they would have in the video example. I. E because of the way the individual words are related I. E the adjacencies, that is if they were input into the system but to get the conclusion out we need some sort of filter to identify which information we want, that filter will be the second grid we place over the first. This second grid will change according to what question is asked. During training we will input a database that we know before hand what information can be deduced from its contents, then we get the second grid and ask a question. The relationship between the cells in this second grid will be hardwired randomly but we will not change the wiring after initialisation, again the colours that those two will give, will probably not work, so we add a bias to each word in the database so the function /question box happens to perform to give the answer. We do this with many examples basically supervised training… At the end we can input a whole new database and we can get the information we want using the learnt biases,.