On 18 April 2017 at 09:53, Raymond Rogers <[email protected]> wrote: > > So as of now: If in combinatorial deduction I end up descending > through formulas with conditions attached > a>b ,c>0 , d<=c > and I want them to be usable for other calculations or display; > I should do something like: make a property list, associated with > the variable, that contains the acquired conditions and refer to > that list when testing/reading _values_ .
In principle that could work but actually to me it sounds like a lot of work and is probably too low level to be a practical solution for what you are trying to do, unless of course you are prepared to do a lot of work (programming). > This is fine, in combinatorics it seems that every question has > a multi-valued answer: yes, no, maybe, perhaps, well if, .... > One of my concerns is making a deduction without knowing the > restrictions imposed by the rules used; when those rules are > invoked by other rules. Raymond Rogers meet non-Aristotelian logic ... :) These issues rather quickly get out-of-hand and hence the mixed success in the current generation of automatic theorem proving systems. > Type declarations are for operators not values. Yes, in FriCAS that is a pretty good way to think about it. > BTW: thanks for explaining it in some detail and I hope I have finally > understood a little "under the hood". > After a bit more experimentation I would not be too surprised if you decide that where you really want to be is in one of these automatic theorem proving systems. Of course that depends on exactly what your goals are and how far you want to go. On the other hand a system like Sage (or even Maple, Mathematica, or even Maxima) might get you quite far if it happens that a significant amount of work has been devoted to the relevant subjects. I mention Sage in particular because of the large amount of work on combinatorics that was done by Nicolas M. Thiéry et al. https://wiki.sagemath.org/combinat http://doc.sagemath.org/html/en/reference/combinat/index.html http://doc.sagemath.org/html/en/reference/calculus/sage/symbolic/expression.html But maybe none of that quite gets you where you want to go? In FriCAS the most natural thing is to focus on the algebraic aspects of the problem rather than the "deductive aspects". I think that how best to do that in the face of the issues you mention is still very much a research problem. As I said in my previous email it seems to me that taking an "equational logic" point of view is most appropriate where the underlying issues can be expressed algebraically. Bill Page. -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
