Logic, Reasoning and A Programming Language for Simulating Economic and Business Processes with Artificially Intelligent Agents

1 Introduction

Decision theorists rely on Bayesian processes in order to have a rigorous and clear basis for descriptions of learning and expectations formation and calculations of optimal decisions. However the assumptions of Bayesian theory are actually highly restrictive. It is necessary to update the probabilities of the exhaustive set of mutually exclusive assumptions. Often, this is in the form of an hypothesis being true with probability p or false with probability (1 - p). If there are more competing hypotheses, there can be no overlap among them. Secondly, the various items of evidence used must be mutually independent. The observation of evidence ei and the observation of evidence ej conditional upon hypothesis H must be the product of the conditional probabilities rather than the product of the probabilities plus the probability of both ei and ej. While it is always possible to choose a language of observations for which this is the case, when there are more than two observations of evidence and the various items are not independent of one another, then Bayes Law rapidly becomes intractable. For example, in most situations where learning is taking place, you would need to frequently update this language but many applications of Bayesian theory assume that this language is constant in order to retain such tractability.

This is simply one manifestation of a problem that runs right through conventional economic modelling. Uncertainty is represented as some kind of probability distribution -- often asserted to be subjective. These probability distributions imply that the agents act as if they believe they know everything that can occur to them conditional upon any action that they might take. If behaviour is represented as a process of constrained optimization, then, in addition agents must act as if they know every possible binding constraint and its effect (e.g. its shadow price).

These representations imply the assumption that information is limited relative to the information-processing and computational capacities of agents. Economic modellers and their ilk frequently claim that the assumptions are made for simplicity. This may have been acceptable in the days when modellers were laminated to analytically tractable equations due to lack of greater computational resources. Now with the advent of such modelling tools as those described here this is no longer the case and hence we do not understand why such simplicity is an overriding virtue. Now it is feasible, we think that modellers should make the best possible estimate of the cost of that simplicity in terms of relevance and accuracy of the inferences drawn from their models.

Both Bayesian and constrained-optimization representations of behaviour can be avoided by relying on some techniques derived from the field of artificial intelligence. The common attribute of many artificial intelligence techniques is that they entail a recognition that information-processing and computational capacities are limited so that exhaustive searches of the action or strategy space would take longer than the time available for completing an action or that the opportunity cost would be prohibitive. But, as with economic modellers, there is a widespread and deep concern for rigour amongst artificial intelligence scientists. Indeed, one reason artificial intelligence scientists develop and use formal logics is in order to have a rigorous and clear basis for descriptions of intelligent reasoning and implementations of artificially intelligent reasoning. These logical formalisms can provide a solid basis for modelling economic and business processes with intelligent agents.

Logic, Reasoning and A Programming Language for Simulating Economic and Business Processes with Artificially Intelligent Agents - 12 APR 96

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