Interval-based decisions for reasoning systems

This essay tries to expound a conception of interval measures that pennits a particular approach to partial ignorance decision problems. l'he \ irtue of this approach for artificial reasoning systems is mat me following questions become moot: 1. which secondary crircnon ro apply after maximi1.ing expected util ity. and �- how much indeterminacy to represent. The cost of the approach is the need for explicit epistemological foundations: for instance, a role ofacceptana with a parameter that allows various attitudes toward error. Note that epistemological foundations are already desirable for independent reasons. The development is as follows: L. probability intervals are useful and natural in A.l. svstems: 2. wide intervals avoid error, but are useless in some risk-sensitive decision-making; 3. yet one may obtain narrower, or otherwise decisive intervals with a more relaxed attitude toward error: 4. if bodies of knowledge can be ordered by their attitude to error, one should perfonn the decision analysis with the acceptable body of knowledge that allows the least error, of those that are useful. The resulting behavior differs from that of a Bayesian probabilist because in the proposal. 5. intervals based on.;;uccessive bodies of l<nowledge are not always nested: 6. the use of a probability for a particular decision does not require commitment to the probability for credence: and 7. there may be no accepcahte body of knowledge that is useful: hence. sometimes no decision is mandated. I. lnterval Measures. By now. the use of an interval measure is regarded highly for probability judgements in reasoning systems. Researchers selecting formalisms for quantifying belief have all recognized the vmucs ot' (partial)l indeterminacy in probability judgement ([Bar8l], [GLF8l], [Dil82}, [Low82].[WeH82]. [Qui83J. [Wes83] , [Gin84), (LuS84), [Str84). etc.l. [ntervals allow varying degrees of commitment in probability assertion. At the extreme-;, · P ( �) = [0. 1) ' is uncommitted. while · P ( A) = [.76..76) ' is consummate. Some ha•e Jrgued that indeterminacy captures "pre-systematic " notions of belief an