Local Boolean manifolds from knowledge representation systems

Abstract

We introduce a structure to represent "observations" on entities in order to obtain "knowledge" about some of their characteristic properties or attributes. This structure is based on the Pawlak's definition of "information systems" (also "knowledge representation systems") and lead us to obtain algebraic structures of lattice depending from the choice of an observational "context". The semantical algebraic structure so obtained is of local Boolean manifold whose global structure is an orthoposet which shows a nontransitivity of the implication; this behaviour could be useful for a formal algebraic approach to "non-monotonic" features of reasoning.