University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065416120190201A duality between LM-fuzzy possibility computations and their logical semantics103110448710.22111/ijfs.2019.4487ENSang-EonHanChonbuk National UniversityLing-XiaLuSchool of Mathematics and Science, Hebei GEO University, Shijiazhuang City, ChinaWeiYaoHebei University of Science and TechnologyJournal Article20170801Let X be a dcpo and let L be a complete lattice. The family σL(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 : σL(E) −> M is called an LM-fuzzy possibility valuation of E if it preserves arbitrary unions. Denote by πLM(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 πLM(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 σL(E) to σM(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. https://ijfs.usb.ac.ir/article_4487_a7d1dcd17b0eb572f71d0b01813e0eab.pdf