Information completeness in Nelson algebras of rough sets induced by quasiorders

In this paper, we give an algebraic completeness theorem for constructive logic with strong negation in terms of finite rough set-based Nelson algebras determined by quasiorders. We show how for a quasiorder $R$, its rough set-based Nelson algebra can be obtained by applying the well-known construction by Sendlewski. We prove that if the set of all $R$-closed elements, which may be viewed as the set of completely defined objects, is cofinal, then the rough set-based Nelson algebra determined by a quasiorder forms an effective lattice, that is, an algebraic model of the logic $E_0$, which is characterised by a modal operator grasping the notion of "to be classically valid". We present a necessary and sufficient condition under which a Nelson algebra is isomorphic to a rough set-based effective lattice determined by a quasiorder.Comment: 15 page

Knowledge Representation with Ontologies: The Present and Future

Recently, we have seen an explosion of interest in ontologies as artifacts to represent human knowledge and as critical components in knowledge management, the semantic Web, business-to-business applications, and several other application areas. Various research communities commonly assume that ontologies are the appropriate modeling structure for representing knowledge. However, little discussion has occurred regarding the actual range of knowledge an ontology can successfully represent

Perceiving and Knowing as Activities

According to the tradition of most empiricists, perception is the basis for all our knowledge (at least of the world). The tradition also assumes that perception by humans is a passive activity resulting in some static states pertaining perception and belief, which are then, in some versions, modified by the mind before being passed onto memory and knowledge. Following the work of J. J. Gibson, we argue that perceiving involves many activities and actions. This is true of both visual as well as olfactory-taste perception. The main moral of this paper is that perceiving and knowing are best thought of not as involving static states, but rather as ongoing temporal activities involving change. This presumably means giving up a frozen ontology of states and moving towards something like a dynamic ontology as a basis