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Directory:Jon Awbrey/Papers/Propositional Equation Reasoning Systems (view source)
Revision as of 17:02, 11 August 2009
, 17:02, 11 August 2009→Discusssion: merge paragraphs
===Discusssion===
===Discusssion===
The task at hand is to build a bridge between model-theoretic and proof-theoretic perspectives on logical procedure, though at present we construct it at a point so close to the common source of these two streams it may not seem worth the candle at all.
The task at hand is build a bridge between model-theoretic and proof-theoretic perspectives on logical procedure, though for now we join them at a point so close to their common source that it may not seem worth the candle at all. The substance of this principle was known to Boole in the 1850's, tantamount to what we now call the ''boolean expansion'' of a propositional expression. The only novelty here resides in a certain manner of presentation, in which we will prove the basic principle from the axioms given before. One name for this rule is the ''Case Analysis-Synthesis Theorem'' (CAST).
The substance of this principle was known to Boole in the 1850's, tantamount to what we now call the ''boolean expansion'' of a propositional expression. The only novelty here resides in a certain manner of presentation, in which we will prove the basic principle from the axioms given before. One name for this rule is the ''Case Analysis-Synthesis Theorem'' (CAST).
I am going to revert to my customarily sloppy workshop manners and refer to propositions and proposition expressions on rough analogy with functions and function expressions, which implies that a proposition will be regarded as the chief formal object of discussion, enjoying many proposition expressions, formulas, or sentences that express it, but worst of all I will probably just go ahead and use any and all of these terms as loosely as I see fit, taking a bit of extra care only when I see the need.
I am going to revert to my customarily sloppy workshop manners and refer to propositions and proposition expressions on rough analogy with functions and function expressions, which implies that a proposition will be regarded as the chief formal object of discussion, enjoying many proposition expressions, formulas, or sentences that express it, but worst of all I will probably just go ahead and use any and all of these terms as loosely as I see fit, taking a bit of extra care only when I see the need.