Formal Models in AGI Research
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Transcript of Formal Models in AGI Research
AGI Needs Formal Model
A complete AGI work should consist of 1) a theory of intelligence, in a natural language2) a formal model of the theory, in a symbolic
language3) a computer implementation of the model, in a
programming languageFormal models provide clarity and accuracy
Formal Model is not Everything
An AGI work whose model has desired formal or mathematical properties is not necessarily superior to other AGI works, because
The model may formalize an improper theory of intelligence
It may fail to guide a computer implementation AGI is not mathematics, but has clear empirical
content and engineering demand
Formal Model for AGI
For AGI, A model must start from some idealized and
simplified assumptions, but it does not mean all assumptions are equally valid
A model with improper fundamental assumptions is unlikely to be useful
A model's success in other domains does not guarantee its success here
Traditional Models
In the current AI/AGI research, the major traditions of formal model are:
Mathematical logic Theory of computation Probability theoryBut each of them has serious limitations when
applied to AGI. This talk will address the first two
The Logic of Mathematics
Mathematical logic was designed to formalize theorem-proving process, not thinking process in general
Theorem proving is the process of deriving new truth from given truth (axioms), while reasoning outside mathematics usually can neither depend on true premises, nor deliver true conclusions
Therefore, the logic of mathematics is not the logic of cognition, nor an idealization of the latter
Issues for Mathematical Logic
Uncertainty: randomness, fuzziness, ignorance, inconsistency, etc. must be handled
Ampliativity: induction, abduction, and analogy seems to say more in the conclusions
Openness: new evidence may challenge the previous beliefs of the system
Relevance: premises and conclusions cannot merely be related in truth-values, not in contents
Non-Classical Logics are not Enough
Each of the issues has been addressed by some non-classical logic, it is not enough:
The issues are addressed in isolation from each other
The modifications and extensions typically happen in grammar rules, inference rules, or axioms, without touching the semantical foundation of the logic
Non-Axiomatic Logic: Assumption
NAL assume the system has insufficient knowledge and resources, so
Empirical theory of truth: The truth-value of a statement indicates the extent to which the statement agrees with the system's experience.
Validity as evidence-preserving: An inference rule is valid if and only if its conclusion is supported by the evidence provided by its premises.
NAL provides a unified solution to the issues
Theory of Computation: Origin
Theory of computation (automata, algorithm, computability, computational complexity) was established to specify “computational” procedures in mathematics, which repeatably maps a problem instance to a predetermined solution.
Outside mathematics, a problem-solving process often cannot be specified as such a mapping, since it depends on the past history and current context, which are usually not described as part of the problem instance.
Time in Computation
Time is not a necessary part of a problem: a problem can appear in any moment, and usually it does not include a demand for response time
Time is not a necessary part of a solution: whether a response is a “solution” has nothing to do with when it is produced, as long as it takes finite time
In summary, “computation” is fundamentally time-independent, which is desired in mathematics, where procedures should be universally repeatable
Time in Adaptation
An adaptive system evolves over time, and may never repeats its internal state.
Time is a necessary part of a problem: the value of a solution decreases over time
Time is a necessary part of a solution: whether a response is a “solution” has a lot to do with when it is produced
In summary, “adaptation” is fundamentally time-dependent, where the problem-solving processes are usually not universally repeatable
Assumption of NARS
NARS (Non-Axiomatic Reasoning System) is designed by treating “intelligence” as adaptation with insufficient knowledge and resources, i.e., the system is finite, real-time, and open.
For each problem (instance), the system solves it using the available knowledge and resources at that moment. Since neither the internal state nor the external state repeat, the problem-solving process does repeat.
Conclusions
Though AGI needs formal models, the traditional models do not meet its requirements, since they are mainly built for mathematics
AGI needs formal models that are based on realistic assumptions.The system has to act according to available knowledge and resources
Models assuming sufficient knowledge and resources do not even provide proper idealizations or simplification for AGI