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changes the presentation of the 'multiplicity' function, as discussed…
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hartig committed Oct 3, 2023
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Expand Up @@ -8965,10 +8965,10 @@ <h3>Basic Graph Patterns</h3>
<div class="defn">
<p><b>Definition: <span id="defn_Multiplicity">Multiplicity</span></b></p>
<p>Given a multiset&nbsp;<var>Ω</var> of solution mappings and a solution
mapping&nbsp;<var>μ</var>, we write <var>multiplicity<sup><var>Ω</var></sup></var>(<var>μ</var>)
mapping&nbsp;<var>μ</var>, we write <var>multiplicity</var>(<var>μ</var>&nbsp;|&nbsp;<var>Ω</var>)
to denote the number of times <var>μ</var> appears in <var>Ω</var>.</p>
<p>Similarly, given a solution sequence&nbsp;<var>Ψ</var> and a solution
mapping&nbsp;<var>μ</var>, we write <var>multiplicity<sup><var>Ψ</var></sup></var>(<var>μ</var>)
mapping&nbsp;<var>μ</var>, we write <var>multiplicity</var>(<var>μ</var>&nbsp;|&nbsp;<var>Ψ</var>)
to denote the number of times <var>μ</var> appears in <var>Ψ</var>.</p>
</div>
<section id="BGPsparql">
Expand Down Expand Up @@ -9262,8 +9262,8 @@ <h3>SPARQL Algebra</h3>
<p>Let Ω be a multiset of solution mappings and expr be an expression. We define:</p>
<p>Filter(expr, Ω) = { μ | μ in Ω and expr(μ) is an expression that has an
effective boolean value of true }</p>
<p><a href="#defn_Multiplicity">multiplicity</a><sup>Filter(expr, Ω)</sup>(μ)
= <a href="#defn_Multiplicity">multiplicity</a><sup>Ω</sup>(μ)</p>
<p><a href="#defn_Multiplicity">multiplicity</a>( μ | Filter(expr, Ω) )
= <a href="#defn_Multiplicity">multiplicity</a>( μ | Ω )</p>
<blockquote>
Note that evaluating an <code>exists(pattern)</code> expression uses the dataset and
active graph, D(G). See the <a href="#defn_evalFilter">evaluation of filter</a>.
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