29,700 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
Effective field theory analysis of 3D random field Ising model on isometric lattices
Ising model with quenched random magnetic fields is examined for single
Gaussian, bimodal and double Gaussian random field distributions by introducing
an effective field approximation that takes into account the correlations
between different spins that emerge when expanding the identities. Random field
distribution shape dependencies of the phase diagrams and magnetization curves
are investigated for simple cubic, body centered and face centered cubic
lattices. The conditions for the occurrence of reentrant behavior and
tricritical points on the system are also discussed in detail.Comment: 13 pages, 8 figure
An analysis of the equational properties of the well-founded fixed point
Well-founded fixed points have been used in several areas of knowledge
representation and reasoning and to give semantics to logic programs involving
negation. They are an important ingredient of approximation fixed point theory.
We study the logical properties of the (parametric) well-founded fixed point
operation. We show that the operation satisfies several, but not all of the
equational properties of fixed point operations described by the axioms of
iteration theories
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