engleski

Logical induction

With the rapid development of AI, logicians are trying to develop robust techniques for reasoning when confronted with logical uncertainty. As opposed to empirical uncertainty, where we’re not quite sure about precise results of measurement, and therefore we must hedge our bets with respect to precise outcomes of random experiments (which is the domain of probability theory), here we are not quite sure of inner workings of a mathematical deduction system, or we simply don’t have time to simulate it in every detail. For instance, there is no sense in speaking about the probability of 87 358th digit of π being 4, since there is no empirical uncertainty we’re dealing with here, but still, there is a strong sense of that claim being somehow assigned a quantity (credence) of 10%. In order to get a consistent system, a lot of properties (of credence) must hold eventually, in the limit, whereas at every finite stage, we can have tem- porary inconsistencies which will get “ironed out” with time. To model the properties precisely, we have to take into account trading strategies and ratio- nal polynomial agents employing strategies in order to profit in the long run in the open market. More precisely, by the analogy with the probability being the feature of a strategy not enabling anybody to successfully bet against the agent in the long run, credence is a feature of the strategy not enabling anybody to profit from “open market exchange”. We will present some desired properties of such a system, and a “proof of concept” algorithm showing that such a notion is at least theoretically possible.

Logical induction

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