-\subsection {Sets of attributed values.}
+\subsection {Sets of attributed values.} \label{AVSets}
The data representation model used by {\MathQL} relies on the notion of
\emph{set of attributed values} ({\av} set for short) that is, in practice,
improvement.}
Each {\av} in an {\av} set consists of a string%
\footnote{When we say \emph{string}, we mean a finite sequence of characters.}
-(that we call the \emph{head string} or \emph{value}) and a (possibly emty)
+(that we call the \emph{head string} or \emph{value}) and a (possibly empty)
multiset of named attributes whose content is a set of strings.
Attribute names are made of a (possibly empty) list of string components, so
they can be hierarchically structured.
({\ie} subsets) to improve its structure.
In the above description a \emph{set} is an \emph{unordered} finite
-sequence \emph{without} repetitions wheras a \emph{multiset} is an
+sequence \emph{without} repetitions whereas a \emph{multiset} is an
\emph{unordered} finite sequence \emph{with} repetitions.
In the present context repetitions are defined as follows:
that were tried.}
As we said, {\MathQL}.4 uses {\av} sets to represent many kinds of
-information, namely:
+information:
\begin{enumerate}
Moreover structured attribute names can encode various components of
structured properties preserving their semantics.
-\begin{figure}[ht]
+\begin{figure}
\begin{footnotesize} \begin{verbatim}
The RDF triples:
-("http://www.w3.org/2002/01/rdf-databases/protocol", "dc:creator", "Sandro Hawke")
-("http://www.w3.org/2002/01/rdf-databases/protocol", "dc:creator", "Eric Prud'hommeaux")
-("http://www.w3.org/2002/01/rdf-databases/protocol", "dc:date", "2002-01-08")
+ ("protocol", "dc:creator", "Sandro Hawke")
+ ("protocol", "dc:creator", "Eric Prud'hommeaux")
+ ("protocol", "dc:date", "2002-01-08")
The corresponding attributed value:
-"http://www.w3.org/2002/01/rdf-databases/protocol" attr
- {"dc:creator" = {"Sandro Hawke", "Eric Prud'hommeaux"}; "dc:date" = "2002-01-08"}
+ "protocol" attr {/"dc:creator" = {"Sandro Hawke", "Eric Prud'hommeaux"};
+ /"dc:date" = "2002-01-08"}
\end{verbatim} \end{footnotesize}
-\vskip-1pc
+\vspace{-1pc}
\caption{The representation of a pool of {\RDF} triples} \label{AVOne}
\end{figure}
\figref{AVOne} shows how a set of triples can be coded in an {\av}.
-Note that the word \emph{attr} separates the head string from its attributes,
+Note that the word \TT{attr} separates the head string from its attributes,
braces enclose an attribute group in which attributes are separated by
-semicolons, and an equal sign separates an attribute name from its contents
-(see \subsecref{Textual} for the complete {\av} syntax).
+semicolons, and an equal sign separates an attribute name from its contents.
In this setting the grouping feature can be used to separate semantically
different classes of properties associated to a resource (as for instance
\item
A pool of arbitrarily chosen {\RDF} triples is encoded in an {\av} set
-placing different {\av}'s the subset of triples sharing the same subject.
+placing in each {\av} the subset of triples sharing the same head string.
Note that the use of {\av} sets to build query results allows {\MathQL} queries
to return sets of {\RDF} triples instead of mere sets of resources, in the
\figref{Table} shows an {\av} set describing the properties of two resources
``A'' and ``B'' giving its table representation, in which the columns
corresponding to attributes in the same group are clustered between
-double-line delimiters%
+double-line delimiters.%
\footnote{A table with grouped labelled columns like the one above resembles a
-set of relational database tables.}.
+set of relational database tables.}
-%Another possible use of a {\MathQL} query result is for the encoding of a
-%relational database table: in this sense the indexed column is stored in the
-%subject strings, the names of the other columns are stored in attribute names
-%and cell contents are stored in attribute values.
-
-\begin{figure}[ht]
+\begin{figure}
\begin{footnotesize} \begin{verbatim}
-"A" attr {"major" = "1"; "minor" = "2"}, {"first" = "2002-01-01"; "modified" = "2002-03-01"};
-"B" attr {"major" = "1"; "minor" = "7"}, {"first" = "2002-02-01"; "modified" = "2002-04-01"}
+"A" attr {/"major" = "1"; /"minor" = "2"},
+ {/"first" = "2002-01-01"; /"modified" = "2002-03-01"};
+"B" attr {/"major" = "1"; /"minor" = "7"},
+ {/"first" = "2002-02-01"; /"modified" = "2002-04-01"}
\end{verbatim}
\begin{center} \begin{tabular}{|c||c|c||c|c||}
-\hline & {\bf ``major''} & {\bf ``minor''} & {\bf ``first''} & {\bf ``modified''} \\
+\hline & \textbf{``major''} & \textbf{``minor''} & \textbf{``first''} & \textbf{``modified''} \\
\hline ``A'' & ``1'' & ``2'' & ``2002-01-01'' & ``2002-03-01'' \\
\hline ``B'' & ``1'' & ``7'' & ``2002-02-01'' & ``2002-04-01'' \\
\hline
the set of the head strings (dimension 1), the attributes in each group
(dimension 2), the groups in each {\av} (dimension 3) and the contents of each
attribute (dimension 4).
-
The metadata defined in the table of \figref{Table} will be used in subsequent
examples.
-For this purpose assume that \TT{first} and \TT{modified} are the components
-of a structured property \TT{date} available for the resources ``A'' and ``B''.
+For this purpose assume that ``first'' and ``modified'' are the components
+of a structured property ``date'' available for the resources ``A'' and ``B''.
\item
-The value of an {\RDF} property is encoded in a single {\av} distinguishing
-three situations:
+The value of an {\RDF} property is encoded in an {\av} distinguishing three
+cases:
\begin{itemize}
other components are stored in the {\av} attributes as in the case 1.
\item
-If the property is structured and its value does not have a main component,
-the {\av} head string is empty and the components are stored in the
-attributes.
+For the value of a structured property without a main component, the head
+string is empty and the components are stored in the attributes.
\end{itemize}
-\begin{figure}[ht]
+\begin{figure}
\begin{footnotesize} \begin{verbatim}
First example, one instance:
-"" attr {"major" = "1"; "minor" = "2"}; no main component
-"1" attr {"minor" = "2"}; main component is "major"
-"2" attr {"major" = "1"} main component is "minor"
+ "" attr {/"major" = "1"; /"minor" = "2"} no main component
+ "1" attr {/"minor" = "2"} main component is "major"
+ "2" attr {/"major" = "1"} main component is "minor"
Second example: two separate instances:
-"" attr {"major" = "1"; "minor" = "2"}, {"major" = "1"; "minor" = "7"}; no main component
-"1" attr {"minor" = "2"}, {"minor" = "7"} main component is "major"
+ "" attr {/"major" = "1"; /"minor" = "2"},
+ {/"major" = "1"; /"minor" = "7"} no main component
+ "1" attr {/"minor" = "2"}, {/"minor" = "7"} main component is "major"
Third example: two mixed instances:
-"" attr {"major" = "3", "6"; "minor" = "4", "9"} no main component
+ "" attr {/"major" = "3", "6"; /"minor" = {"4", "9"}} no main component
\end{verbatim} \end{footnotesize}
-\vskip-1pc
+\vspace{-1pc}
\caption{The representation of the structured value of a property}
\label{AVTwo}
\end{figure}
\figref{AVTwo} (first example) shows three possible ways of representing in
-{\av}'s an instance of a structured property \TT{id} whose value has two
-fields ({\ie} properties) \TT{major} and \TT{minor}.
-In this instance, \TT{major} is set to ``1'' and \TT{minor} is set to ``2''.
-The representations depend on which component of \TT{id} is chosen as the
-main component (none, \TT{major} or \TT{minor} respectively).
+{\av}'s an instance of a structured property ``id'' whose value has two
+fields ({\ie} properties) ``major'' and ``minor''.
+In this instance, ``major'' is set to ``1'' and ``minor'' is set to ``2''.
+The representations depend on which component of ``id'' is chosen as the
+main component (none, ``major'' or ``minor'' respectively).
Several structured property values sharing a common main component can be
encodes in a single {\av} exploiting the grouping facility: in this case the
attributes of every instance are enclosed in separate groups.
\figref{AVTwo} (second example) shows the representations of two instances of
-\TT{id}: the previous one and a new one for which \TT{major} is ``1'' and
-\TT{minor} is ``7''.
+``id'': the former and a new one for which ``major'' is ``1'' and ``minor'' is
+``7''.
Note that if the attributes of the two groups are encoded in a single group,
the notion of which components belong to the same property value can not be
recovered in the general case because the values of an attribute form a set
-and thus are unordered. \newline
-As an example think of two instances of \TT{id} encoded as in \figref{AVTwo}
+and thus are unordered.
+As an example think of two instances of ``id'' encoded as in \figref{AVTwo}
(third example).
\item
\item
The boolean value \emph{false} is stored as an empty {\av} set, whereas
-a non-empty {\av} set may be interpreted as the boolean value \emph{true}.
+an inhabited {\av} set may be interpreted as the boolean value \emph{true}.
The default representation of \emph{true} is a single {\av} with an empty
head string and no attributes.
\end{enumerate}
-{\MathQL} defines five binary operations on {\av} sets: two unions, two
+{\MathQL} defines five core binary operations on {\av} sets: two unions, two
intersections and a difference. The first four are defined in terms of an
operation, that we call \emph{addition}, involving two {\av}'s with the same
head string.
\begin{itemize}
\item
-With the \emph{set-theoretic} addition, the set of attribute groups in the
+with the \emph{set-theoretic} addition, the set of attribute groups in the
resulting {\av} is the set-theoretic union of the sets of attribute groups in
-the operands.
+the operands;
\item
-With the \emph{distributive} addition, the set of attribute groups in the
+with the \emph{distributive} addition, the set of attribute groups in the
resulting {\av} is the ``Cartesian product'' of the sets of attribute groups
in the two operands.
-In this context, an element of the ``Cartesian product'' is not a pair of
-groups but it is the set-theoretic union of these groups where the contents of
-homonymous attributes are clustered together using set-theoretic unions.
+Here an element of the ``Cartesian product'' is not a pair of groups but it is
+the set-theoretic union of these groups where the contents of homonymous
+attributes are clustered together using set-theoretic unions.
\end{itemize}
\figref{Addition} shows an example of the two kinds of addition.
-\begin{figure}[ht]
+\begin{figure}
\begin{footnotesize} \begin{verbatim}
Attributed values used as operands for the addition:
-"1" attr {"A" = "a"}, {"B" = "b1"}
-"1" attr {"A" = "a"}, {"B" = "b2"}
+ "1" attr {/"A" = "a"}, {/"B" = "b1"}
+ "1" attr {/"A" = "a"}, {/"B" = "b2"}
Set-theoretic addition:
-"1" attr {"A" = "a"}, {"B" = "b1"}, {"B" = "b2"}
+" 1" attr {/"A" = "a"}, {/"B" = "b1"}, {/"B" = "b2"}
Distributive addition:
-"1" attr {"A" = "a"}, {"A" = "a"; "B" = "b2"}, {"B" = "b1"; "A" = "a"}, {"B" = {"b1", "b2"}}
+ "1" attr {/"A" = "a"}, {/"A" = "a"; /"B" = "b2"},
+ {/"B" = "b1"; /"A" = "a"}, {/"B" = {"b1", "b2"}}
\end{verbatim} \end{footnotesize}
-\vskip-1pc
+\vspace{-1pc}
\caption{The addition of attributed values}
\label{Addition}
\end{figure}
-Now we can discuss the five operations between {\av} sets that we mentioned
-above:
+Now we can discuss the five operations between {\av} sets:
\begin{itemize}
\item
-The two unions ocorresponds to the set-theoretic union of their operand where
-the {\av}'s sharing the head string are are added either set-theoretically or
+The two unions corresponds to the set-theoretic union of their operand where
+the {\av}'s sharing the head string are added either set-theoretically or
distributively as explained above (thus we have a set-theoretic union and a
distributive union in the two cases). In this context the empty {\av} set
plays the role of the neutral element.
\item
The two intersections are the dual of the above unions: they contain the
-{\av}'s whose head string appears in each argument where {\av}'s sharing the
-head string are added either set-theoretically or distributively as before.
+{\av}'s whose head string appears in each argument where the {\av}'s sharing
+the head string are added either set-theoretically or distributively as before.
The distributive intersection has the double benefit of filtering the
common values of the given {\av} sets, and of merging their attribute groups
\figref{Binary} shows how the above operations work in a simple example.
-\begin{figure}[ht]
+\begin{figure}
\begin{footnotesize} \begin{verbatim}
Sets of attributed values used as operands for the operations:
-"1" attr {"A" = "a"}; "2" attr {"B" = "b1"}
-"2" attr {"B" = "b2"}
+ "1" attr {/"A" = "a"}; "2" attr {/"B" = "b1"}
+ "2" attr {/"B" = "b2"}
Set-theoretic union:
-"1" attr {"A" = "a"}; "2" attr {"B" = "b1"}, {"B" = "b2"}
+ "1" attr {/"A" = "a"}; "2" attr {/"B" = "b1"}, {/"B" = "b2"}
Distributive union:
-"1" attr {"A" = "a"}; "2" attr {"B" = {"b1", "b2"}}
+ "1" attr {/"A" = "a"}; "2" attr {/"B" = {"b1", "b2"}}
Set-theoretic intersection:
-"2" attr {"B" = "b1"}, {"B" = "b2"}
+ "2" attr {/"B" = "b1"}, {/"B" = "b2"}
Distributive intersection:
-"2" attr {"B" = {"b1", "b2"}}
+ "2" attr {/"B" = {"b1", "b2"}}
Difference:
-"1" attr {"A" = "a"}
+ "1" attr {/"A" = "a"}
\end{verbatim} \end{footnotesize}
-\vskip-1pc
+\vspace{-1pc}
\caption{The binary operations on sets of attributed values}
\label{Binary}
\end{figure}
projects / helm.git / blobdiff