Current mood:

accomplished

My Non-Turing AI hypothesis, part 2 (Definitions and key concepts).
As I've laid out before, the basics of making an AI that can do all the basic functions of a true mind requires us to understand how that mind works.I laid out the basic mechanisms of sensation, perception, and conception as the three integrals of said AI. Now I need to explain the part of conception in detail.

This part has been the hardest for me to break down compared to the other two, because there are few, if any, analogs for conception in the computing world, even in the theories of hypercomputation and non-Turing computation there are no key methods to represent the process. So, I've had to puzzle over this part for better on two years by myself as I study for my degree. What I found is that certain kinds of logic seem to represent the process of conception in small, refined parts. Natural logic gives us a general form for which we make our inferences, like Modus Ponens, which is found to be the most intuitive form of logic that any person can learn to utilize. Predicate Logic, or Quantifier based logic is another example of how we group sets of logic based on whether a variable quantity can be fulfilled, even though it is simply an addition to Natural logic, it can be counter intuitive at times unless a person is taught what the symbols for the quantifiers mean and what they do to a given 'formula' in it. And there are many other kinds of logic, which I'm still studying that also seem to fill the gaps in describing conception of people [Intuitive logic is one kind that I find interesting, but I need more time to consider it.]. Ultimately, all these kinds of logic have an underlying function of conception which binds them together to allow me to assume that each kind describes a part of human conception.

I started using Natural logic as the basis for my work, but I found I needed to add my own form of quantifiers like those found in Predicate Logic, but not based entirely on them. First, lets look at a classic Natural logic form, Modus Ponens.

P -> Q
P
-
.: Q

What is going on here is that the first part is the declaration that one thing implies another. And which the primary thing (P) is confirmed then it follows that the secondary is confirmed too (Q). This form works well when just discussing this in the form of a single instance like an individual event, or a single instance correlation between two phenomena and the like. It doesn't work well when describing how it works all on its own or over all possibilities across all phenomena of all times of all spaces. Essentially, it's a reduced form for what I call, 'abstracta.' Abstracta is as the name implies, an collection of abstractions, but specifically they are 'objects' from which an individual mind can operate upon to parse any data that is found. So, if you had a random set of data that seemingly had no format, it is conceivable that with abstracta you could find correlations. Understand that I stated correlations, because abstracta do not confirm correlations as causations, that takes a series of assumptions which some abstracta can be based, but cannot validate in themselves explicitly. More so, an individual member of abstracta can be wrong if they are found to lead to contradictions in their 'positive' [verifying] forms, especially if given axioms or premises for a given member of abstracta leads to the specific state of contradiction. Abstracta in this context are a set of unparticulars, or knowledge that is not specified to any given entity or entities.

With that in mind, let me present how I would show Modus Ponens via an abstractum [singular form of abstracta].

P[i] then Q[i] only if P[xi] = Q[xi], but not excluding where P[xi] =/= Q[xi] when ~P[i].
P[xi]
-
:. Q[i]

Now, this borrows from Predicate Logic in the quantification modifiers where the brackets contain the letters i and x to represent specific quantities. 'I' represents a specific set of entities that can be applied to P and Q on the whole, and 'X' represents a given entity of that set. In this case, when I stated that P[xi] = Q[xi], I am stating that if two given functions correlate, then at least one of the given entities of the application set make both functions equal in quantity, but with a catch. The catch is that there can be a case where P[xi] does not equal Q[xi], if the function of P is found to be false or negated for all the set as this prevents the logical fallacy known as Denial of the Antecedent (If P then Q, ~P, therefore ~Q). In this 'toy version' of my system, the abstractum is stating that if any given implication correlation there must be at least one entity where it makes both functions equal, when the primary function is not denied/negated for it to be true. Essentially, this is what I believe makes Modus Ponens true, in that each implication requires both propositions to be shared between the same set of applicable entities or a particular entity. An example of this would be, "If it rains, then the street will get wet." What is shared between both the proposition of rain and the street getting wet is that water or some fluid is required for this to be true, but it does not imply that if does not rain that the streets can never get wet. Wetness can occur if someone spills their coffee on the street. Or if an ice truck wrecks and the ice is spilled all over the street. Or if someone runs their sprinkler and the water overflows onto the street. It just declares that for it to be true in the instance between rain and the street getting wet, both must be equal for both to correlate. What this proves is that particular instances of propositions can be isolated for their given applicable entities, but the whole form of the proposition cannot be isolated from all possible entities. And that is where my form of the Modus Ponens abstractum operates. It gives an unparticular account of a correlation in which can be applied to an 'instanced' form of itself to where it can validate or invalidate a given 'instanced' proposition. What this allows for in AI of any kind, Turing or Non, is the ability to operate on a very broad set of parameters that fit the form of the abstracta. And it implies that given sets of knowledge start at a state that is instanced, or particular, from which unparticular, uninstanced, sets of knowledge are found. So, a Turing based AI would have to have more essential or basic abstracta to develop abstractum like the Modus Ponens abstractum. This is where I find that Turing based AI cannot operate, in that there is no single instance where such an AI can find a state to halt, 'dump delta', and then use what was found to be true from its observations on other observations that are unlike said observation in particulars of the entities. A Non-Turing AI can due to the fact that it operates from working on particulars to find unparticulars [or abstracta] in its operation by comparison. In short, a Non-Turing AI has to be 'born smart' or 'born curious' to operate.

Ultimately, this is just a work in progress, which I'm still revising and researching to find if there are better methods to describe this action better. And like the other thread, any criticism, suggestions, hints, links, and etc are very much welcomed.