Abstract:We introduce continuous $R$-valuations on directed-complete posets (dcpos,
for short), as a generalization of continuous valuations in domain theory, by
extending values of continuous valuations from reals to so-called Abelian
d-rags $R$.
Like the valuation monad $\mathbf{V}$ introduced by Jones and Plotkin, we
show that the construction of continuous $R$-valuations extends to a strong
monad $\mathbf{V}^R$ on the category of dcpos and Scott-continuous maps.
Additionally, and as in recent work by the two auth… Show more
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