A duality between LM-fuzzy possibility computations and their logical semantics

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Han S.E.; LU L.X.; YAO W.

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Journal: Iranian Journal of Fuzzy Systems Year:2019 | Volume:16 | Issue:1 Page(s): 103-110

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Title

A duality between LM-fuzzy possibility computations and their logical semantics

Author(s)

Han S.E. | LU L.X. | YAO W. | Issue Writer Certificate

Keywords

L-fuzzy Scott structureQ2

LM-fuzzy possibility valuationQ2

Non-determinism computationQ2

Healthy LM-fuzzy predicate transformerQ2

Denotational semanticsQ2

Logical semanticsQ2

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.

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APA: Copy

Han, S.E., LU, L.X., & YAO, W.. (2019). A duality between LM-fuzzy possibility computations and their logical semantics. IRANIAN JOURNAL OF FUZZY SYSTEMS, 16(1 ), 103-110. SID. https://sid.ir/paper/113238/en

Vancouver: Copy

Han S.E., LU L.X., YAO W.. A duality between LM-fuzzy possibility computations and their logical semantics. IRANIAN JOURNAL OF FUZZY SYSTEMS[Internet]. 2019;16(1 ):103-110. Available from: https://sid.ir/paper/113238/en

IEEE: Copy

S.E. Han, L.X. LU, and W. YAO, “A duality between LM-fuzzy possibility computations and their logical semantics,” IRANIAN JOURNAL OF FUZZY SYSTEMS, vol. 16, no. 1 , pp. 103–110, 2019, [Online]. Available: https://sid.ir/paper/113238/en

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