Lattice-valued Scott topology on dcpos

This paper studies the fuzzy Scott topology on dcpos with a ∗-continuous semigroup (L, ∗) as the truth value table. It is shown that the fuzzy Scott topological space on a continuous dcpo is an ιL-sober space. The fuzzy Scott topology is completely distributive iff L is completely distributive and the underlying dcpo is continuous. For (L, ∗) being an integral quantale, semantics of L-possibility of computations is studied by means of a duality.

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