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Directory:Jon Awbrey/Papers/Cactus Language (view source)

Revision as of 21:20, 25 January 2009

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Rules like these can be chained together to establish extended rules, just so long as their antecedent conditions are compatible.  For example, Rules&nbsp;1 and 2 combine to give the equivalents that are listed in Rule&nbsp;3.  This follows from a recognition that the function <math>\upharpoonleft Q \upharpoonright ~:~ X \to \underline\mathbb{B}</math> that is introduced in Rule&nbsp;1 is an instance of the function <math>f : X \to \underline\mathbb{B}</math> that is mentioned in Rule&nbsp;2.  By the time one arrives in the "consequence box" of either Rule, then, one has in mind a comparatively fixed <math>Q \subseteq X,</math> a proposition <math>f\!</math> or <math>\upharpoonleft Q \upharpoonright</math> about things in <math>X,\!</math> and a variable argument <math>x \in X.</math>
    
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Rules like these can be chained together to establish extended rules, just so long as their antecedent conditions are compatible.  For example, Rules 1 and 2 combine to give the equivalents that are listed in Rule 3.  This follows from a recognition that the function {X} : U -> B that is introduced in Rule 1 is an instance of the function f : U -> B that is mentioned in Rule 2.  By the time one arrives in the "consequence box" of either Rule, then, one has in mind a comparatively fixed X c U, a proposition f or {X} about things in U, and a variable argument u C U.
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Rule 3
 
Rule 3
  
Jon Awbrey
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