A duality between LM-fuzzy possibility computations and their logical semantics
Let 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...
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Published in | Iranian journal of fuzzy systems (Online) Vol. 16; no. 1; p. 103 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Zahedan
University of Sistan and Baluchestan, Iranian Journal of Fuzzy Systems
2019
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Subjects | |
Online Access | Get full text |
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Summary: | Let 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. |
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ISSN: | 1735-0654 2676-4334 |
DOI: | 10.22111/ijfs.2019.4487 |