On the order-theoretic properties of lower concept formula systems

Domain Theory and Rough Set Theory are relatively independent but have much close relationship worthy of further investigation. In this paper, we propose the notion of (orientated) lower concept formula (for short, lcf) of relational information systems and study the order-theoretic properties of the derived lcf systems. Particularly, we show that every orientated lcf system is an algebraic lattice and conversely every algebraic lattice is order-isomorphic to the orientated lcf system of an appropriate relational information system. Moreover, we obtain the one-to-one correspondence between approximable mappings and Scott continuous functions. In addition, we investigate the connection between the orientated lcf systems on the relational information systems and the topped ⋂\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bigcap $$\end{document}-structures on the lower concept lattices. Our results demonstrate the power of Rough Set Theory in studying domain structures.