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Best regards,
		--Michael Huth.

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\newcommand{\oc}[1]{{{\rm !}(#1)}}
\newcommand{\wn}[1]{{{\rm ?}(#1)}}

\title{Linear Types and Approximation}
\author{Michael Huth, Achim Jung, and Klaus Keimel\\
Fachbereich Mathematik \\
Schlo\ss gartenstra\ss e 7 \\
64289 Darmstadt, Germany \\
\(\{ {\rm huth}, {\rm jung},
{\rm keimel}\}\){\rm \char 64}mathematik.th-darmstadt.de}

\begin{abstract}We enrich the $*$-autonomous category of complete
lattices and maps preserving all suprema with the important concept
of {\em approximation\/} by specifying a $*$-autonomous full subcategory
LFS of {\em linear FS-lattices\/}. This is the greatest $*$-autonomous
full subcategory of linked bicontinuous lattices. The modalities \(\oc {}\)
and \(\wn {}\) mediate a duality between the (lifted) upper and lower
powerdomains. The distributive objects in LFS give rise to the
{\em compact closed\/} $*$-autonomous full subcategory of {\em completely
distributive\/} lattices. We characterize algebraic objects in LFS
by forbidden substructures `\` a la Plotkin'.

\noindent {\bf Keywords:}

\noindent $*$-autonomous category, linear logic, interaction orders,
bicontinuous lattices, completely distributive lattices, upper and
lower powerdomains.