Knowledge and consequence in AC semantics for general rough sets

Abstract

Antichain based semantics for general rough sets was introduced recently by the present author. In her paper two different semantics, one for general rough sets and another for general approximation spaces over quasi-equivalence relations, were developed. These semantics are improved and studied further from a lateral algebraic logic and an algebraic logic perspective in this research. The framework of granular operator spaces is also generalized. The main results concern the structure of the algebras, deductive systems and the algebraic logic approach. The epistemological aspects of the semantics is also studied in this chapter in some depth and revolve around nature of knowledge representation, Peircean triadic semiotics and temporal aspects of parthood. Examples have been constructed to illustrate various aspects of the theory and applications to human reasoning contexts that fall beyond information systems.