We propose a model

We describe a model of iterated belief revision that extends the AGM theory of revision to account for the effect of a revision on the conditional beliefs of an agent. In particular, this model ensures that an agent makes as few changes as possible to the conditional component of its belief set. Adopting the Ramsey test, minimal conditional revision provides acceptance conditions for arbitrary right-nested conditionals. We show that problem of determining acceptance of any such nested conditional can be reduced to acceptance tests for unnested conditionals. Thus, iterated revision can be accomplished in a “virtual” manner, using uniterated revision.

This paper advocates the use of non-purely probabilistic approaches to higher-order uncertainty. One of the major arguments of Bayesian probability proponents is that representing uncertainty is always decision-driven and as a consequence, uncertainty should be represented by probability. Here we argue that representing partial ignorance is not always decision-driven. Other reasoning tasks such as belief revision for instance are more naturally carried out at the purely cognitive level. Conceiving knowledge representation and decision-making as separate concerns opens the way to non-purely probabilistic representations of incomplete knowledge. It is pointed out that within a numerical framework, two numbers are needed to account for partial ignorance about events, because on top of truth and falsity, the state of total ignorance must be encoded independently of the number of underlying alternatives. The paper also points out that it is consistent to accept a Bayesian view of decision-m...

In this paper, we survey some quantitative and qualitative approaches to uncertainty management based on possibility theory and present a logical framework to integrate them. The semantics of the logic is based on the Dempster's rule of conditioning for possibility theory. It is then shown that classical modal logic, conditional logic, possibilistic logic, quantitative modal logic and qualitative possibilistic logic are all sublogics of the present logical framework. In this way, we can formalize and generalize some well-known results about possibilistic reasoning in a uniform semantics. Moreover, our uniform framework is applicable to nonmonotonic reasoning, approximate consequence relation formulation, and partial consistency handling. Key words: Non-classical logics, possibility theory, conditional possibility, modal logic, conditional logic. 1 Introduction There are essentially two kinds of logical formalisms for reasoning about possibility and necessity. On the one hand, the qua...

In this paper, we will present a framework for reasoning with vague and uncertain information by fuzzy truth-valued logics. It is shown that possibilistic logic, many-valued logic, and approximate reasoning can all be embodied in the uniform framework. Keywords--- Fuzzy-truth values, many-valued logics, possibilistic reasoning, approximate reasoning I. Introduction In the realm of artificial intelligence and knowledgebased systems, one of the central problems is the representation and reasoning of incomplete information. An intelligent agent acting without the full knowledge of the environment would most need the capability of reasoning with incomplete information. It is now commonly believed that there are more than one types of incomplete information so totally different mechanisms would be needed to treat them. An extensive literature has been generated to cope with the problem and various approaches have been proposed. To name some among others, the most notable ones are probabil...