Constructive belief and rational representation

Constructive belief and rational representation

It is commonplace in artificial intelligence to divide an agent’s explicit beliefs into two parts: the beliefs explicitly represented or manifest in memory, and the implicitly represented or constructive beliefs that are repeatedly reconstructed when needed rather than memorized. Many theories of knowledge view the relation between manifest and constructive beliefs as a logical relation, with t...

Probability, rational belief and belief change

A simple model of rational belief holds that: (i) an instantaneous snapshot of an ideally rational belief system corresponds to a probability distribution; and (ii) rational belief change occurs by Bayesian conditionalization. But a priori probability distributions of the Kolmogorov sort cannot distinguish between propositions that are simply true from propositions that are necessarily true. Fu...

Belief Revision and Rational Inference

The (extended) AGM postulates for belief revision seem to deal with the revision of a given theory K by an arbitrary formula φ, but not to constrain the revisions of two different theories by the same formula. A new postulate is proposed and compared with other similar postulates that have been proposed in the literature. The AGM revisions that satisfy this new postulate stand in one-to-one cor...

Logical Omniscience and Rational Belief

Quantifying Rational Belief

Some criticisms that have been raised against the Cox approach to probability theory are addressed. Should we use a single real number to measure a degree of rational belief? Can beliefs be compared? Are the Cox axioms obvious? Are there counterexamples to Cox? Rather than justifying Cox’s choice of axioms we follow a different path and derive the sum and product rules of probability theory as ...