The necessity calculus is a familiar adjuvant to the possibility calculus and an uncertain inference tool in its own right. Necessity orderings enjoy a syntactical relationship to some probability orderings similar to that displayed by possibility. In its adjuvant role, necessity may be viewed as bringing possibility closer to achieving the quasi-additive normative desideratum advocated by de Finetti. Nevertheless, there are occasions when one might choose to use possibility without the help of necessity, e.g. when the full range of alternative hypotheses is unknown, or to exploit possibility's distinctive ability simultaneously to express preference as well as credibility ordering. Such situations arise in uncertain domains like the evaluation of scientific or mathematical hypotheses, where professions of belief may reflect aesthetic, utilitarian, and evidentiary considerations as much as the usual notions of credibility.
This paper uses decision-theoretic principles to obtain new insights into the assessment and updating of probabilities. First, a new foundation of Bayesianism is given. It does not require infinite atomless uncertainties as did Savage s classical result, AND can therefore be applied TO ANY finite Bayesian network.It neither requires linear utility AS did de Finetti s classical result, AND r ntherefore allows FOR the empirically AND normatively desirable risk r naversion.Finally, BY identifying AND fixing utility IN an elementary r nmanner, our result can readily be applied TO identify methods OF r nprobability updating.Thus, a decision - theoretic foundation IS given r nto the computationally efficient method OF inductive reasoning r ndeveloped BY Rudolf Carnap.Finally, recent empirical findings ON r nprobability assessments are discussed.It leads TO suggestions FOR r ncorrecting biases IN probability assessments, AND FOR an alternative r nto the Dempster - Shafer belief functions that avoids the reduction TO r ndegeneracy after multiple updatings.r n
Is Intelligent Belief Really Beyond Logic? Abstract "Impossibility, theorems" have recently appeared in the AI literature which have been interpreted as forbidding truth-functional uncertainty calculi. Such "logicist" calculi do in fact exist. For example, case-based reasoning principles entail a truth-functional probabilityagreeing scheme whose strengths and weaknesses are not so different from those of the usual belief representation methods. No claim is made that belief modeling should be conducted exclusively along Iogicist lines, but a nontrivial common ground of intuition does exist beneath Iogicism and its alternatives. Introduction A prominent community in the world of artificial intelligence are the Iogicists. Briefly put, Iogicists hold that intelligent cognitive states, including belief states, can be faithfully emulated by some kind of logic.
The general use of subjective probabilities to model belief has been justified using many axiomatic schemes. For example, ?consistent betting behavior' arguments are well-known. To those not already convinced of the unique fitness and generality of probability models, such justifications are often unconvincing. The present paper explores another rationale for probability models. ?Qualitative probability,' which is known to provide stringent constraints on belief representation schemes, is derived from five simple assumptions about relationships among beliefs. While counterparts of familiar rationality concepts such as transitivity, dominance, and consistency are used, the betting context is avoided. The gap between qualitative probability and probability proper can be bridged by any of several additional assumptions. The discussion here relies on results common in the recent AI literature, introducing a sixth simple assumption. The narrative emphasizes models based on unique complete orderings, but the rationale extends easily to motivate set-valued representations of partial orderings as well.
This paper relates comparative belief structures and a general view of belief management in the setting of deductively closed logical representations of accepted beliefs. We show that the range of compatibility between the classical deductive closure and uncertain reasoning covers precisely the nonmonotonic 'preferential' inference system of Kraus, Lehmann and Magidor and nothing else. In terms of uncertain reasoning any possibility or necessity measure gives birth to a structure of accepted beliefs. The classes of probability functions and of Shafer's belief functions which yield belief sets prove to be very special ones.