The value of the four values

In his well-known paper "How computer should think" Belnap (1977) argues that four-valued semantics is a very suitable setting for computerized reasoning. In this paper we vindicate this thesis by showing that the logical role that the four-valued structure has among Ginsberg's bilattices is similar to the role that the two-valued algebra has among Boolean algebras. Specifically, we provide several theorems that show that the most useful bilattice-valued logics can actually be characterized as four-valued inference relations. In addition, we compare the use of three-valued logics with the use of four-valued logics, and show that at least for the task of handling inconsistent or uncertain information, the comparison is in favor of the latter. (C) 1998 Elsevier Science B.V. All rights reserved.