Tracking probabilistic truths: a logic for statistical learning

We propose a new model for forming and revising beliefs about unknown probabilities. To go beyond what is known with certainty and represent the agent’s beliefs about probability, we consider a plausibility map, associating to each possible distribution a plausibility ranking. Beliefs are defined as in Belief Revision Theory, in terms of truth in the most plausible worlds (or more generally, truth in all the worlds that are plausible enough). We consider two forms of conditioning or belief update, corresponding to the acquisition of two types of information: (1) learning observable evidence obtained by repeated sampling from the unknown distribution; and (2) learning higher-order information about the distribution. The first changes only the plausibility map (via a ‘plausibilistic’ version of Bayes’ Rule), but leaves the given set of possible distributions essentially unchanged; the second rules out some distributions, thus shrinking the set of possibilities, without changing their plausibility ordering.. We look at stability of beliefs under either of these types of learning, defining two related notions (safe belief and statistical knowledge), as well as a measure of the verisimilitude of a given plausibility model. We prove a number of convergence results, showing how our agent’s beliefs track the true probability after repeated sampling, and how she eventually gains in a sense (statistical) knowledge of that true probability. Finally, we sketch the contours of a dynamic doxastic logic for statistical learning.

Updating the Belief Promotion Operator

In this note, we introduce the local version of the operator for belief promotion proposed by Schwind et al. We propose a set of postulates and provide a representation theorem that characterizes the proposal. This family of operators is related to belief promotion in the same way that updating is related to revision, and we provide several results that allow us to show this relationship formally. Furthermore, we also show the relationship of the proposed operator with features of credibility-limited revision theory.

Iterated Belief Revision

A discussion of the problem of extending the basic AGM belief revision theory to iterated belief revision: the problem of formulating rules, not only for revising a basic belief state in response to potential new evidence, but also for revising one’s revision rules in response to potential new evidence. The emphasis in the chapter is on foundational questions about the nature of and motivation for various constraints, and about the methodology of the evaluation of putative counterexamples to proposed constraints. Some specific constraints that have been proposed are criticized. The chapter emphasizes the importance of meta-information—information about one’s sources of information—and argues that little of substance can be said about constraints on iterated belief revision at a level of abstraction that lacks the resources for explicit representation of meta-information.

The Effect of Attribute Framing and Justification on Capital Budgeting Decisions

This study aims to analyze the effect of the attribute framing and justification on decision making through the capital budgeting process. This study also aims to examine the effect of justification as moderation on the effect of attribute framing on capital budgeting decisions. The capital budgeting decision in this study is a decision toward the proposed capital budgeting project in the form of approving or rejecting the proposed project. This study uses a quasi-experimental research design with the data taken is primary data. The quasi-experimental research was designed 2 x 2 between subjects which was conducted to 83 financial students in the Magister of Management, Diponegoro University. Data analysis techniques used in this study were one-way ANOVA and two-way ANOVA.The results of the study shows that attribute framing and justification can influence decision making through the capital budgeting process. In particular, the information that is positively presented has an impact in the higher approval of a proposed capital budgeting project. This research also concluded that justification could not reduce the effect of the attribute framing on capital budgeting decisions. This shows that belief revision theory- foundation approach cannot explain the phenomenon of this study.

Non-Classical Circular Definitions

Circular denitions have primarily been studied in revision theory in the classical scheme. I present systems of circular denitions in the Strong Kleene and supervaluation schemes and provide complete proof systems for them. One class of denitions, the intrinsic denitions, naturally arises in both schemes. I survey some of the features of this class of denitions.

Contraction and revision

An important question for proponents of non-contractive approaches to paradox is why contraction fails. Zardini offers an answer, namely that paradoxical sentences exhibit a kind of instability. I elaborate this idea using revision theory, and I argue that while instability does motivate failures of contraction, it equally motivates failure of many principles that non-contractive theorists want to maintain.