Changes

Line 1,661: Line 1,661:  
|}
 
|}
   −
Equivalent expressions for this concept are recorded in Definition 10.
+
Equivalent expressions for this concept are recorded in Definition 10.
    
<br>
 
<br>
Line 1,681: Line 1,681:     
D10e. {<o, s> C OxS : <o, s, i> C R for some i C I}
 
D10e. {<o, s> C OxS : <o, s, i> C R for some i C I}
 +
</pre>
   −
The dyadic relation RSO that constitutes the converse of the denotative relation ROS can be defined directly in the following fashion:
+
<br>
 +
 
 +
The dyadic relation <math>L_{SO}\!</math> that is the converse of the denotative relation <math>L_{OS}\!</math> can be defined directly in the following fashion:
   −
Den(R)= RSO  = {<s, o> C SxO : <o, s, i> C R for some i C I}.
+
{| align="center" cellpadding="8" width="90%"
 +
| <math>\overset{\smile}{\operatorname{Den}(L)} ~=~ L_{SO} ~=~ \{ (s, o) \in S \times O ~:~ (o, s, i) \in L ~\text{for some}~ i \in I \}.</math>
 +
|}
    
A few of the many different expressions for this concept are recorded in Definition 11.
 
A few of the many different expressions for this concept are recorded in Definition 11.
    +
<br>
 +
 +
<pre>
 
Definition 11
 
Definition 11
   Line 1,707: Line 1,715:     
D11g. {<s, o> C SxO : <o, s, i> C R for some i C I}
 
D11g. {<s, o> C SxO : <o, s, i> C R for some i C I}
 +
</pre>
 +
 +
<br>
    +
<pre>
 
The "denotation of x in R", written "Den(R, x)", is defined as follows:
 
The "denotation of x in R", written "Den(R, x)", is defined as follows:
 
Den(R, x)  =  {o C O : <o, x> C Den(R)}.
 
Den(R, x)  =  {o C O : <o, x> C Den(R)}.
12,080

edits