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some sentences clarified in the introduction
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section/introduction.tex

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@@ -12,31 +12,33 @@ \section{Introduction}
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The goal of those methods is to lower server-side workloads while keeping fast query execution to the client~\cite{Azzam2021}.
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The TREE hypermedia specification is an effort in that direction~\cite{ColpaertMaterializedTREE, lancker2021LDS}, that introduces the concept of domain-oriented fragmentation of large RDF datasets.
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For example, in the case of periodic measurements of sensor data, a fragmentation can be made on the publication date of each data entity.
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A fragment can be considered an RDF document published in a server.
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TREE aims to describes dataset fragmentation in ways that enable clients to easily fetch query-relevant subsets.
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The data inside a fragment are bounded with constraints expressed using hypermedia descriptions~\cite{thomasFieldingPhdThesis}.
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More precisely, each fragment describes the constraints of the data of any reachable fragment.
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In this paper, we refer to those constraints as domain-specific logical expressions.
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They can be expressions such as $?t > \text{2022-01-09T00:00:00.000000} \implies \text{ex:afterFirstSeptember}$ given that $?t$ is the date of publication of sensor data and the implication pertains to the location of the data.
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More precisely, each fragment describes the constraints of the data of every reachable fragment.
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In this paper, we refer to those constraints as domain-specific expressions.
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They can be expressions such as $?t > \text{2022-01-09T00:00:00.000000} \implies \text{ex:afterFirstSeptember}$
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given that $?t$ is the date of publication of sensor data and the implication pertains to the location of the data respecting the constraint.
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In English, the expression means ``the data produced by the sensors after the first of September are stored at \texttt{ex:afterFirstSeptember}.''
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Because of the hyperlinked nature of the documents network, clients must traverse them to find the relevant data to answer their queries.
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We propose to use Link Traversal Query Processing (LTQP)~\cite{Hartig2016} as a query mechanism to perform those queries.
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LTQP starts by dereferencing a set of user-provided URLs~\cite{Hartig2016}.
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From these dereferenced documents, links to other documents are dereferenced recursively and inserted in an internal data store.
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LDQL~\cite{hartig2016Ldql} is a theoretical query language to define the traversal of LTQP queries.
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However, LDQL is centered around nested regular expressions, thus, is not made to express the traversal of links based on domain-specific logical expressions
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However, LDQL is centered around nested regular expressions, thus, is not made to express the traversal of links based on domain-specific expressions
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such as time relations.
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The subweb specifications language (SWSL)~\cite{bogaerts_rulemlrr_2021}, allows data providers to define traversal paths concerning the information they publish.
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Thus, given that the query engine trusts the data publisher it can adapt its traversal to follow the paths given by the specification.
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Akin to LDQL, it is difficult with the SWSL to express traversal using domain-specific logical expressions, because its syntax is centered around the matching of triple patterns and not reasoning rules or evaluation of literals.
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Furthermore, SWSL does not propose a mechanism for using the query or input from the user in the source selection process, unlike LDQL.
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Akin to LDQL, it is difficult with the SWSL to express traversal using domain-specific expressions, because its syntax is centered around the matching of triple patterns and not reasoning rules or evaluation of literals.
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Furthermore, SWSL does not propose a mechanism for using the query or input from the user to impact the source selection process, unlike LDQL.
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Given those limitations, we propose to return to the more abstract concept of reachability criteria~\cite{hartig2012},
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to define a mechanism of traversal centered around rules.
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In this paper, we propose to use a boolean solver as the main link pruning mechanism for a reachability criterion to traverse TREE documents.
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The logical operators are defined by the \href{https://treecg.github.io/specification/}{TREE specification}.~\sepfootnote{sf:treeSpec}
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As a concrete use case, we consider the publication of (historical) sensor data.
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An example query is presented in Figure~\ref{lst:system} along with the triples representing the link between two documents describing sensor data following the TREE specification .
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An example query is presented in Figure~\ref{lst:system} along with the triples representing the link between two documents expressed using the TREE specification.
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\begin{figure}[h]
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\begin{minipage}{0.50\textwidth}
@@ -48,7 +50,7 @@ \section{Introduction}
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\centering
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\lstinputlisting[language=,frame=single]{code/example_tree_relation.ttl}
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\end{minipage}
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\caption{On the left, is a SPARQL query to get sensor measurements and metadata of a fragmented dataset.
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\caption{On the left, is a SPARQL query to get sensor measurements and information about the sensor.
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On the right, is the hypermedia description of the location and constraint of the next fragment located in \texttt{ex:nextNode}.
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The constraint describes publication times ($?t$) where $?t>= \text{2022-01-03T09:47:59.000000}$.}
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\label{lst:system}

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