Skepticism: an algebraic model for uncertainty in a Boolean belief space
Callum E Cooper · 1990
The field of artificial intelligence has renewed the desire to find computational models of human reasoning and the formation of beliefs. One inherent advantage of human reasoning, over that of a machine, is the human's ability to effectively deal with uncertainty. Previous numeric models have made progress toward that goal. Skepticism is a formalized algebra consisting of a belief space and a closed binary operator over that belief space. The term skepticism comes from the fact that beliefs this theory have a degree of explicit uncertainty. The operator is defined in such a way that the conflict, within beliefs, gives rise to skepticism. The properties of the algebra are formally established and then examined as to their empirical value. A geometric model of skepticism is defined and used to establish relations between beliefs. Subsets of the belief space are found to be from restricted forms of evidence. Horizons of skepticism are established for derivable beliefs. Although this research is limited to Boolean propositions, the combination operator used in skepticism has been extended to multivalued belief spaces.