Title of article :
A duality between LM-fuzzy possibility computations and their logical semantics
Author/Authors :
Han, S.E Department of Mathematics Education - Institute of Pure and Applied Mathematics - Chonbuk National University, Jeonju-City Jeonbuk, Republic of Korea , Lu, L.X Department of Mathematics - College of Natural Science - Chonbuk National University, Jeonju-City Jeonbuk, Republic of Korea , Yao, W School of Sciences - Hebei University of Science and Technology, Shijiazhuang, P.R. China
Abstract :
Let X be a dcpo and let L be a complete lattice. The family L(X) of all Scott continuous mappings from X to L is
a complete lattice under pointwise order, we call it the L-fuzzy Scott structure on X. Let E be a dcpo. A mapping
g : L(E) ! M is called an LM-fuzzy possibility valuation of E if it preserves arbitrary unions. Denote by LM(E)
the set of all LM-fuzzy possibility valuations of E. The denotational semantics assigning to an LM-fuzzy possibility
computation from a dcpo D to another one E is a Scott continuous mapping from D to LM(E), which is a model
of non-determinism computation in Domain Theory. A healthy LM-fuzzy predicate transformer from D to E is a
sup-preserving mapping from L(E) to M(D), which is always interpreted as the logical semantics from D to E. In
this paper, we establish a duality between an LM-fuzzy possibility computation and its LM-fuzzy logical semantics.
Keywords :
Logical semantics , L-fuzzy Scott structure , Denotational semantics , Healthy LM-fuzzy predicate transformer , Non-determinism computation , LM-fuzzy possibility valuation
