Selection (relational algebra)

<h2 id="generalized-selection">Generalized selection</h2>
<p>A generalized selection is a <a href="/facts/Unary_operation/kb6CkgsX">unary operation</a> written as 
  
    
      
        
          σ
          
            φ
          
        
        (
        R
        )
      
    
    {\displaystyle \sigma _{\varphi }(R)}
  
 where 
  
    
      
        φ
      
    
    {\displaystyle \varphi }
  
 is a <a href="/facts/Propositional_formula/eEV8YrAI">propositional formula</a> that consists of <a href="/facts/Atomic_formula/s9WMnbqT">atoms</a> as allowed in the normal selection and, in addition, the logical operators ∧ (<a href="/facts/Logical_conjunction/62uyyn1d">and</a>), ∨ (<a href="/facts/Logical_disjunction/jbI2EGlM">or</a>) and 
  
    
      
        ¬
      
    
    {\displaystyle \lnot }
  
 (<a href="/facts/Negation/q5AQBvBj">negation</a>). This selection selects all those <a href="/facts/Tuple/BI1HIxL8">tuples</a> in R for which 
  
    
      
        φ
      
    
    {\displaystyle \varphi }
  
 holds.
</p><p>For an example, consider the following tables where the first table gives the relation Person and the second the result of 
  
    
      
        
          σ
          
            
              Age
            
            ≥
            30
             
            ∧
             
            
              Weight
            
            ≤
            60
          
        
        (
        
          Person
        
        )
      
    
    {\displaystyle \sigma _{{\text{Age}}\geq 30\ \land \ {\text{Weight}}\leq 60}({\text{Person}})}
  
.
</p>
<table><tbody><tr><th>                              Person                      {\displaystyle {\text{Person}}}  </th><th>                              σ                                    Age                        ≥            30                         ∧                                       Weight                        ≤            60                          (                  Person                )              {\displaystyle \sigma _{{\text{Age}}\geq 30\ \land \ {\text{Weight}}\leq 60}({\text{Person}})}  </th></tr><tr><td><table><tbody><tr><th>Name</th><th>Age</th><th>Weight</th></tr><tr><td>Harry</td><td>34</td><td>80</td></tr><tr><td>Sally</td><td>28</td><td>64</td></tr><tr><td>George</td><td>29</td><td>70</td></tr><tr><td>Helena</td><td>54</td><td>54</td></tr><tr><td>Peter</td><td>34</td><td>80</td></tr></tbody></table></td><td><table><tbody><tr><th>Name</th><th>Age</th><th>Weight</th></tr><tr><td>Helena</td><td>54</td><td>54</td></tr></tbody></table></td></tr></tbody></table>
<p>Formally the semantics of the generalized selection is defined as follows:
</p>

σ
          
            φ
          
        
        (
        R
        )
        =
        {
         
        t
        :
        t
        ∈
        R
        ,
         
        φ
        (
        t
        )
         
        }
      
    
    {\displaystyle \sigma _{\varphi }(R)=\{\ t:t\in R,\ \varphi (t)\ \}}

<p>The result of the selection is only defined if the <a href="/facts/Property_(philosophy)/mejP0slr">attribute</a> names that it mentions are in the header of the relation that it operates upon.
</p><p>The generalized selection is expressible with other basic algebraic operations. A simulation of generalized selection using the fundamental operators is defined by the following rules:
</p>

σ
          
            φ
            ∧
            ψ
          
        
        (
        R
        )
        =
        
          σ
          
            φ
          
        
        (
        R
        )
        ∩
        
          σ
          
            ψ
          
        
        (
        R
        )
      
    
    {\displaystyle \sigma _{\varphi \land \psi }(R)=\sigma _{\varphi }(R)\cap \sigma _{\psi }(R)}

σ
          
            φ
            ∨
            ψ
          
        
        (
        R
        )
        =
        
          σ
          
            φ
          
        
        (
        R
        )
        ∪
        
          σ
          
            ψ
          
        
        (
        R
        )
      
    
    {\displaystyle \sigma _{\varphi \lor \psi }(R)=\sigma _{\varphi }(R)\cup \sigma _{\psi }(R)}

σ
          
            ¬
            φ
          
        
        (
        R
        )
        =
        R
        −
        
          σ
          
            φ
          
        
        (
        R
        )
      
    
    {\displaystyle \sigma _{\lnot \varphi }(R)=R-\sigma _{\varphi }(R)}

<h2 id="computer-languages">Computer languages</h2>
<p>In computer languages it is expected that any <a href="/facts/Truth-value/SY4e2w8l">truth-valued</a> expression be permitted as the selection condition rather than restricting it to be a simple comparison.
</p><p>In <a href="/facts/SQL/UjQLJcYm">SQL</a>, selections are performed by using WHERE definitions in <a href="/facts/Select_(SQL)/cYnKkmFo">SELECT</a>, <a href="/facts/Update_(SQL)/IQz2IKpz">UPDATE</a>, and <a href="/facts/Delete_(SQL)/gyapLh6T">DELETE</a> statements, but note that the selection condition can result in any of three truth values (<i>true</i>, <i>false</i> and <i>unknown</i>) instead of the usual two.
</p><p>In <a href="/facts/SQL/UjQLJcYm">SQL</a>, general selections are performed by using WHERE definitions with AND, OR, or NOT operands in <a href="/facts/Select_(SQL)/cYnKkmFo">SELECT</a>, <a href="/facts/Update_(SQL)/IQz2IKpz">UPDATE</a>, and <a href="/facts/Delete_(SQL)/gyapLh6T">DELETE</a> statements.
</p>

<h2 id="external-links">External links</h2>
<ul><li><a href="http://cisnet.baruch.cuny.edu/holowczak/classes/3400/relationalalgebra/#selectionoperator">http://cisnet.baruch.cuny.edu/holowczak/classes/3400/relationalalgebra/#selectionoperator</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Codd, E.F. (June 1970). "A Relational Model of Data for Large Shared Data Banks". Communications of the ACM. 13 (6): 377–387. doi:10.1145/362384.362685. <a href="/wiki/E.F._Codd" target="_blank">/wiki/E.F._Codd</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
</ol>

Selection (relational algebra) open-in-new

Selection (relational algebra)