Are there *a priori* truths for a self-learning artificial intelligence system?

Question

Assume a group of scientists builds a self learning artificial intelligence (AI) system, consisting of the following components:

• Some input data channels and sensors, allowing the system to learn new information.
• Some output data channels and actors, allowing the system to perform experiments.
• A database of "unquestionable" (dogmatic) truths, which may be nonempty initially, and can be extended by the system upon learning or deducing further "unquestionable" truths.
• A database of "falsifiable" (empirical) knowledge, which may be nonempty initially, and can be modified by the system upon learning or interpreting further empirical experiences.
• A program controlling the interaction between the different components, like deducing "unquestionable" truths as needed, interpreting the input data channels, using the output data channels and extending or modifying the respective databases.

Are there any a priori truths in the sense of Kant for such a system? How about:

• The unavoidable implications of the limitations of the sensors, actors and the data channels?
• The implicit assumptions embedded into the structure of the program controlling the system?
• The initial content of the database of "unquestionable" truths?
• The initial content of the database of "falsifiable" knowledge?
• The moral law inside the system?
• Any truth that can ever end up in the database of "unquestionable" truths?

Answer 1

@stoicfury is right, you answered your own question.

The rules of deduction and the dogmatic contents have to be considered a priori truths for this kind of mind. Don't they? The form the basis for its reason, and they will have had their effect before they could possibly be modified by experience.

But let's go down your list:

• The unavoidable implications of the limitations of the sensors, actors and the data channels? are not knowledge, they are forms of intuition, the sort of thing that Kant imagines Euclidean space is for humans. What he machine comes to know about them is knowledge, just as we can learn geometry by experiencing space. But space itself is not known, except in the ways it shapes othe experience. It is not unquestionable. In fact Relativity proves that we can think our way past it. But it intervenes immediately in any incoming information, so this is very hard.
• The implicit assumptions embedded into the structure of the program controlling the system? are a priori knowledge, but not just he implicit ones, this whole control structure is a form of a priori reasoning.
• The initial content of the database of "unquestionable" truths? are a priori knowledge in the most normal sense, they are from before experience and cannot be modified.
• The initial content of the database of "falsifiable" knowledge? are not a priori knowledge, they are the contents of intuition, the basic sources of the machine's 'imagination'. Except for their internal origin, they are just ordinary knowledge.
• The moral law inside the system? Is not anything, it is either part of the program, or it is not necessarily even present. There is no reason to assume this thinking machine will have the same sense of 'duty' that adheres to minds with intention and all the other categories. If you give it no intention, it will have no need of morality. Also, if you fail to give it any of the other basic categories, it is not something Kant would consider a mind.
• Any truth that can ever end up in the database of "unquestionable" truths? is not a priori, if it is derived from processing, which is the machine's experience.

Answer 2

There is at least one a priori truth for such a system - and arguably a synthetic a priori truth at that - this AI system will be limited by the Church-Turing thesis. The AI in question won't always be able to solve Turing undecidable problems, i.e. there will be formal decision problems for which it can never guarantee that it will find a solution.