We motivate and describe a theory of belief in this paper. This theory is developed with the following view of human belief in mind. Consider the belief that an event E will occur (or has occurred or is occurring). An agent either entertains this belief or does not entertain this belief (i.e., there is no "grade" in entertaining the belief). If the agent chooses to exercise "the will to believe...

Recently Kroupa has proposed a generalization of belief functions on MV-algebras, the latter being the chosen algebraic setting for fuzzy (or many-valued) events. However, Kroupa’s belief functions evaluate the degree of belief in the occurrence of fuzzy events by taking into account (weighted) evidence on classical subsets. In other words, the focal elements, used in determining the degree of ...

A number of authors have noted that if we have degrees of truth, then we should have corresponding degrees of belief—but that these degrees of belief do not behave like subjective probabilities. So should we countenance two different kinds of degree of belief? I argue that we cannot coherently do so, and present instead a formal framework in which there is a single notion of degree of belief, w...

Probability can be used to measure degree of belief in two ways: objectively and subjectively. The objective measure is a measure of the rational degree of belief in a proposition given a set of evidential propositions. The subjective measure is the measure of a particular subject’s dispositions to decide between options. In both measures, certainty is a degree of belief 1. I will show, however...

‘Subjective probability: the real thing’ is the last book written by the late Richard Jeffrey, a key proponent of the Bayesian interpretation of probability. Bayesians hold that probability is a mental notion: saying that the probability of rain is 0.7 is just saying that you believe it will rain to degree 0.7. Degrees of belief are themselves cashed out in terms of bets—in this case you consid...

We propose a modal logic that supports reasoning about trust-based belief change. The term trust-based belief change refers to belief change that depends on the degree of trust the receiver has in the source of information.

The meaning of probabilistic weather forecasts is discussed from the point of view of a subjectivist concept of probability. The prior degree of belief of probabilities of the weather in question, for a given forecast statement, is expressed analytically as a beta function. Bzyes’ theorem is used to modify this degree of belief in the light of experience, producing a posterior degree of belief ...

In this paper I compare two different the models of two-dimensional belief change, namely ‘revision by comparison’ (Fermé and Rott, Artificial Intelligence 157, 2004) and ‘bounded revision’ (Rott, in Hommage à Wlodek, Uppsala 2007). These revision operations are two-dimensional in the sense that they take as arguments pairs consisting of an input sentence and a reference sentence. Two-dimension...