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Directory:Jon Awbrey/Papers/Differential Logic and Dynamic Systems (view source)
Revision as of 15:30, 23 January 2008
, 15:30, 23 January 2008→Review and Transition: bind expressions with
The briefest expression for logical truth is the empty word, usually denoted by ε or λ in formal languages, where it forms the identity element for concatenation. To make it visible in this text, I denote it by the equivalent expression "(())", or, especially if operating in an algebraic context, by a simple "1". Also when working in an algebraic mode, I use the plus sign "+" for exclusive disjunction. Thus, we may express the following paraphrases of algebraic forms:
The briefest expression for logical truth is the empty word, usually denoted by ε or λ in formal languages, where it forms the identity element for concatenation. To make it visible in this text, I denote it by the equivalent expression "(())", or, especially if operating in an algebraic context, by a simple "1". Also when working in an algebraic mode, I use the plus sign "+" for exclusive disjunction. Thus, we may express the following paraphrases of algebraic forms:
:{|
:{| cellpadding="4"
| ''A'' + ''B'' || = || (''A'', ''B'')
| ''A'' + ''B''
| =
| (''A'', ''B'')
|-
|-
| ''A'' + ''B'' + ''C'' || = || ((''A'', ''B''), ''C'') || = || (''A'', (''B'', ''C''))
| ''A'' + ''B'' + ''C''
| =
| ((''A'', ''B''), ''C'')
| =
| (''A'', (''B'', ''C''))
|}
|}
One should be careful to observe that these last two expressions are not equivalent to the form (''A'', ''B'', ''C'').
One should be careful to observe that these last two expressions are not equivalent to the form (''A'', ''B'', ''C'').
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