Boolean algebras arising from information systems

In recent years a wide variety of intensional modal-like logics with the propositional operators determined by relations play an important role in a number of application areas such as spatial reasoning, cognitive agent technologies, knowledge-based systems, etc. Many of these applications require much more involved logical systems than the ordinary modal logics can offer. In one direction, one considers operations which are intended to express properties not expressible by the possibility operator, such as the inaccessibility of Humberstone [10], or the suffiency operators of Gargov et al. [6]. Such operators lead to various classes of Boolean algebras with operators, and in earlier work we have introduced the classes of sufficiency algebras (SUA) and mixed algebras (MIA) and have started an investigation of their properties [5].