introduces a function called multiplicity as a replacement for the notation 'card[Ω](μ)'; related to #108 (comment)

Author: hartig

spec/index.html

@@ -8942,15 +8942,15 @@ <h3>Basic Graph Patterns</h3>
           <a href="https://en.wikipedia.org/w/index.php?title=Multiset">multiset</a>, 
           also known as a <i>bag</i>. A multiset is an
           unordered collection of elements in which each element may appear more than once. It is
-          described by a set of elements and a cardinality function giving the number of occurrences of
-          each element from the set in the multiset.</p>
+          described by a set of elements and a function giving the multiplicity of each of these
+          elements (i.e., the number of times the element is contained in the multiset).</p>
         <p>Write μ for solution mappings.</p>
         <p>Write μ<sub>0</sub> for the mapping such that dom(μ<sub>0</sub>) is the empty set.</p>
         <p>Write Ω<sub>0</sub> for the multiset consisting of exactly the empty mapping
-          μ<sub>0,</sub> with cardinality 1. This is the join identity.</p>
+          μ<sub>0,</sub> with multiplicity 1. This is the join identity.</p>
         <p>Write μ(x) for the solution mapping variable x to RDF term t : { (x, t) }</p>
         <p>Write Ω(x) for the multiset consisting of exactly μ(?x-&gt;t), that is, { { (x, t) } }
-          with cardinality 1.</p>
+          with multiplicity 1.</p>
         <div class="defn">
           <p><b>Definition: <span id="defn_algCompatibleMapping">Compatible Mappings</span></b></p>
           <p>Two solution mappings μ<sub>1</sub> and μ<sub>2</sub> are compatible if, for every
@@ -8962,8 +8962,15 @@ <h3>Basic Graph Patterns</h3>
         <p>If μ<sub>1</sub> and μ<sub>2</sub> are compatible then μ<sub>1</sub> ∪ μ<sub>2</sub> is
           also a mapping. Write merge(μ<sub>1</sub>, μ<sub>2</sub>) for μ<sub>1</sub> ∪
           μ<sub>2</sub></p>
-        <p>Write card[Ω](μ) for the cardinality of solution mapping μ in a multiset of mappings
-          Ω.</p>
+        <div class="defn">
+          <p><b>Definition: <span id="defn_Multiplicity">Multiplicity</span></b></p>
+          <p>Given a multiset&nbsp;Ω of solution mappings and a solution
+            mapping&nbsp;μ, we write multiplicity<sup>Ω</sup>(μ) to denote
+            the number of times μ appears in Ω.</p>
+          <p>Similarly, given a solution sequence&nbsp;Ψ and a solution
+            mapping&nbsp;μ, we write multiplicity<sup>Ψ</sup>(μ) to denote
+            the number of times μ appears in Ψ.</p>
+        </div>
         <section id="BGPsparql">
           <h4>SPARQL Basic Graph Pattern Matching</h4>
           <p>A basic graph pattern is matched against the active graph for that part of the query.
@@ -8986,8 +8993,8 @@ <h4>SPARQL Basic Graph Pattern Matching</h4>
             <p>μ is a <b>solution</b> for BGP from G when there is a pattern instance mapping P such
               that P(BGP) is a subgraph of G and μ is the restriction of P to the query variables in
               BGP.</p>
-            <p>card[Ω](μ) = card[Ω](number of distinct RDF instance mappings, σ, such that P = μ(σ)
-              is a pattern instance mapping and P(BGP) is a subgraph of G).</p>
+            <p><a href="#defn_Multiplicity">multiplicity</a><sup>Ω</sup>(μ) = number of distinct RDF instance mappings, σ, such that P = μ(σ)
+              is a pattern instance mapping and P(BGP) is a subgraph of G</p>
           </div>
           <p>If a basic graph pattern is the empty set, then the solution is Ω<sub>0</sub>.</p>
         </section>
@@ -9255,7 +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>card[Filter(expr, Ω)](μ) = card[Ω](μ)</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>
           <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>.