Local Boolean manifolds from knowledge representation systems

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.