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Directory:Jon Awbrey/Papers/Propositional Equation Reasoning Systems (view source)
Revision as of 16:54, 17 August 2009
, 16:54, 17 August 2009→Analysis of contingent propositions: convert graphic
With that preamble behind us, let us turn to consider the case of semiosis, or sign transformation process, that is generated by our first proof of the propositional equation <math>E_1.\!</math>
With that preamble behind us, let us turn to consider the case of semiosis, or sign transformation process, that is generated by our first proof of the propositional equation <math>E_1.\!</math>
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We are in the process of examining various proofs of the propositional equation <math>\texttt{(} p \texttt{(} q \texttt{))(} p \texttt{(} r \texttt{))} = \texttt{(} p \texttt{(} q r \texttt{))},</math> and viewing these proofs in the light of their character as semiotic processes, in essence, as sign-theoretic transformations.
We are in the process of examining various proofs of the propositional equation <math>\texttt{(} p \texttt{(} q \texttt{))(} p \texttt{(} r \texttt{))} = \texttt{(} p \texttt{(} q r \texttt{))},</math> and viewing these proofs in the light of their character as semiotic processes, in essence, as sign-theoretic transformations.
The second way of establishing the truth of this equation is one that I see, rather loosely, as ''model-theoretic'', for no better reason than the sense of its ending with a pattern of expression, a variant of the ''disjunctive normal form'' (DNF), that is commonly recognized to be the form that one extracts from a truth table by pulling out the rows of the table that evaluate to true and constructing the disjunctive expression that sums up the senses of the corresponding interpretations.
The second way of establishing the truth of this equation is one that I see, rather loosely, as ''model-theoretic'', for no better reason than the sense of its ending with a pattern of expression, a variant of the ''disjunctive normal form'' (DNF), that is commonly recognized to be the form that one extracts from a truth table by pulling out the rows of the table that evaluate to true and constructing the disjunctive expression that sums up the senses of the corresponding interpretations.