User talk:Norm

(Non-)distinct variables
The idea at User:Norm, about specifying variables that are not distinct as opposed to ones that are, is an interesting idea, and seems like it might work if, as suggested, it applies to variables and not terms and formulas (to avoid a lot of not-distinct declarations just to cover theorems like A + B = B + A or just about any theorem not involving quantifiers). As for JHilbert work in general, the source code is on github (my fork) and contributions are certainly welcome. I've also been working on making wikiproofs into a testsuite, by letting one download wikiproofs and then run it all through the verifier, expecting everything to verify except where flagged by Template:error expected, in which case it would be expected to fail. For me, the #1 priority is Wikiproofs:JHilbert definition soundness but there are plenty of other verifier projects which could be worthwhile, and we certainly are soliciting volunteers. Kingdon 06:05, 8 March 2012 (UTC)

Standard textbook predicate logic on wikiproofs (or other metamath-style systems)
Thought I should update you on my progress since March, when we last discussed representing textbook predicate logic (or some approximation) in metamath/JHilbert. I've only made minor tweaks to First-order logic in terms of substitution built on equality, which still seems like the strongest version of a traditional textbook treatment, of the ones I've tried so far.

I then tried to formulate your problem 17 as originally stated at Interface:Axioms of first-order logic as set forth in metamath problem 17 and then start deriving predicate logic at Metamath problem 17. I had two significant problems (which could be a fundamental flaw in the setup, or lack of insight on my part). The more minor was that I just couldn't get started without something like ForAllImplication. I couldn't tell whether this was a difference between the Mendelson you cite and Margaris (in which ForAllImplication is axiom A4), and I didn't (yet at least) dig up a copy of the Mendelson, but I got around this hurdle by just adding ForAllImplication as an axiom, at least temporarily. But I still had problems, which appeared to relate to the mismatch between substitution as traditionally used in a treatment like Margaris, in which substitution is used early on for many key theorems, and, which seems to require some ability to manipulate   to do much with it. I reached the tentative conclusion that even if there is some way to patch this up, it probably isn't especially natural or pedagogically useful.

I also tried to straighten up the way wikiproofs handles terms/classes versus variables/sets. This applies to substitution and equality (which of course are closely linked in all of these interfaces/proof modules). I moved term equality from Interface:Axioms of first-order logic‎ to Interface:Axiom of quantifiability. Then I provide an analog to First-order logic in terms of substitution built on equality but which just uses set.mm-style substitution of variables, not terms. The result is at First-order logic in terms of variable substitution built on equality and provides a set.mm-like predicate logic (that is, it does not preclude set.mm-style proper classes). Only real fly in the ointment here is ax11, which I'm not really sure what to do with.

I guess at least in my mind I've reached some level of comprehensiveness with the work described above. Kingdon (talk) 10:55, 10 July 2012 (UTC)