1,280 research outputs found
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 , 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 -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 ,
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
Domains via approximation operators
In this paper, we tailor-make new approximation operators inspired by rough
set theory and specially suited for domain theory. Our approximation operators
offer a fresh perspective to existing concepts and results in domain theory,
but also reveal ways to establishing novel domain-theoretic results. For
instance, (1) the well-known interpolation property of the way-below relation
on a continuous poset is equivalent to the idempotence of a certain
set-operator; (2) the continuity of a poset can be characterized by the
coincidence of the Scott closure operator and the upper approximation operator
induced by the way below relation; (3) meet-continuity can be established from
a certain property of the topological closure operator. Additionally, we show
how, to each approximating relation, an associated order-compatible topology
can be defined in such a way that for the case of a continuous poset the
topology associated to the way-below relation is exactly the Scott topology. A
preliminary investigation is carried out on this new topology.Comment: 17 pages; 1figure, Domains XII Worksho
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