Definition talk:Interderivable

For boolean interpretations, it would make more sense to call this "semantically equivalent", because it isn't actually proven that one thing is the same as the other. In theories where the completeness theorem does not hold, this distinction is important.

While I anticipate response is along the lines of "go ahead, make a dash for it", it's not that easy and certainly not a simple and small task to separate proof theory and model theory for PropCalc. My patience has worn out on it before - but we'll get there eventually. --Lord_Farin (talk) 15:42, 19 February 2013 (UTC)


 * Yes, again this is something I have consistently failed at ... --prime mover (talk) 18:05, 19 February 2013 (UTC)


 * More analytically, it appears there are three forces active in PropLog (and the currently quite closely tied general logic):


 * Informal justification/argumentation
 * Proof-theoretic stuff
 * Model-theoretic stuff


 * where the latter two try to capture the first in a more formal manner. The soundness and completeness theorems yield the latter two equivalent, but especially the second is a bit of work and shouldn't be glossed over.


 * I will try and come up with one or more alternative approaches that attempt to separate these branches. Hopefully this will enhance the intended modular paradigm, finally allowing us to easily incorporate new branches. You have been working very hard on this in the theorem department; let me now try and see if I can contribute something meaningful on the definitions side of things. More to follow. --Lord_Farin (talk) 18:20, 19 February 2013 (UTC)