This article reveals one general scheme for creating counter examples to Bayesian confirmation theory. The reason of the problems is that: in daily life the degree of confirmation is affected not only by probability but also by some non-probabilistic factors, e.g., structural similarity, quantity of evidence, and marginal utility, while Bayesian confirmation theory considers only probabilities to measure the degree of confirmation. This article resolves these problems after some detail analyses, and proposes a new confirmation measure based on these factors.

We introduce a new operator, called rational evaluation, in belief change. The operator evaluates new information according to the agent’s core beliefs, and then exports the plausible part of the new information. It belongs to the decision module in belief change. We characterize rational evaluation by axiomatic postulates and propose two functional constructions for it, based on the well-known constructions of kernel sets and remainder sets, respectively. The main results of the paper are two representation theorems with respect to the (...) two functional constructions. We also compare and connect the evaluation operator with some related operators in belief revision, including contraction, set contraction, and prioritized multiple revision. (shrink)

When an agent can not recognize, immediately, the implausible part of new information received, she will usually first expand her belief state by the new information, and then she may encounter some belief conflicts, and find the implausible information based on her criteria to consolidate her belief state. This process indicates a new kind of non-prioritized multiple revision, called metabolic revision. I give some axiomatic postulates for metabolic revision and propose two functional constructions for it, namely kernel metabolic revision and (...) partial meet metabolic revision, with respect to which the representation theorems are proved. I also compare metabolic revision with some related works in the literature, including semi-revision, merging with integrity constraints, evaluation, and evaluative multiple revision. (shrink)

In the literature of belief revision, it is widely accepted that: there is only one revision phase in belief revision which is well characterized by the Bayes’ Rule, Jeffrey’s Rule, etc.. However, as I argue in this article, there are at least four successive phases in belief revision, namely first/second order evaluation and first/second order revision. To characterize these phases, I propose mainly four rules of belief revision based on agent’s criteria, and make one composition rule to characterize belief revision (...) as a whole. (shrink)

According to rationalists, synthetic a priori propositions convey new knowledge, whereas analytic propositions are non-informative or vacuous conceptual truths. However, as we argue in this article, each a priori proposition is necessarily true because of its semantic constituents and the way they are combined, and hence can be transformed into its equivalent analytic form. So each synthetic a priori proposition conveys only non-informative conceptual truths like analytic propositions.