Belief Systems and Partial Spaces

One important role of belief systems is to allow us to represent information about a certain domain of inquiry. This paper presents a formal framework to accommodate such information representation. Three cognitive models to represent information are discussed: conceptual spaces (Gärdenfors [2000]), state-spaces (van Fraassen [1991]), and the problem spaces familiar from artificial intelligence. After indicating their weakness to deal with partial information, it is argued that an alternative, formulated in terms of partial structures (da Costa and French [2003]), can be provided which not only captures the positive features of these models, but also accommodates the partiality of information ubiquitous in science and mathematics.