Expanding Belnap 2: the dual category in depth

Abstract

Bilattices, which provide an algebraic tool for simultaneously modelling knowledge and truth, were introduced by N. D. Belnap in a 1977 paper entitled How a computer should think. Prioritised default bilattices include not only Belnap’s four values, for ‘true’ (t), ‘false’(f), ‘contradiction’ (T) and ‘no information’ (⊥), but also indexed families of default values for simultaneously modelling degrees of knowledge and truth. Prioritised default bilattices have applications in a number of areas including artificial intelligence.