I wonder why you enjoy talking to yourself on a public email list? ;-)
On Mon, Jun 16, 2014 at 8:48 PM, Jim Bromer via AGI <[email protected]> wrote: > I am probably wrong. The solution to finding a solution to a logical > satisfiability problem in polynomial time is probably going to be based on > a natural solution that does an accounting of the number of solutions to > the logical problem. > > Jim Bromer > > > On Sun, Jun 15, 2014 at 9:05 AM, Jim Bromer <[email protected]> wrote: > >> Traditional logic is a compressed format. Since there are so many >> possible equivalences we know that logic is not a perfectly packed >> compression method. So there is no need for a list of alternative >> compression conversion algorithms which were in a list of possible >> algorithms that was in np. (I expressed that idea incorrectly. I should >> have talked about a list of possible algorithms which were in exp space or >> something like that. If the list of possible compression-conversion >> algorithms were in np then that implies that finding an algorithm solution >> might itself be in np.) >> >> >> >> Jim Bromer >> >> >> On Sun, Jun 15, 2014 at 8:36 AM, Jim Bromer <[email protected]> wrote: >> >>> >> Of course I have no idea if this is even possible. But my next >>> question is whether the inclusion of the compression formatting with the >>> compressed string is inherently too inefficient to be useful.. >>> >>> Presuming that different classes of logical formulas could be compressed >>> in different ways, is it possible to use a single polynomial time algorithm >>> to do this? It might be possible, for example, using a numerical method to >>> choose an algorithm based on a numbering system (where an ordering of >>> algorithms might, to continue with this conjectural example, be associated >>> with a log-based number - an n-ary number - to choose the algorithm from a >>> system of algorithms which are in their entirety in np). This is too >>> complicated for me, but if the parts of the algorithms were ordered and >>> enumerated then large numbers could be used to refer to a particular >>> ordering scheme. I am just trying to establish that there could be a way to >>> express variations in how a compression conversion method might be chosen >>> even if the entire list of algorithms were themselves in np. >>> >>> But, is a compression method which includes some way to describe or >>> refer to the particular compression scheme used in the compression going to >>> be so much less efficient than a system that leaves that kind of >>> information out to make this whole idea theoretically impossible? I think >>> that it is theoretically possible. >>> >>> >>> Jim Bromer >>> >>> >>> On Sun, Jun 15, 2014 at 8:20 AM, Jim Bromer <[email protected]> wrote: >>> >>>> >>>> >>>> Jim Bromer >>>> >>>> >>>> On Sat, Jun 14, 2014 at 9:20 PM, Jim Bromer <[email protected]> >>>> wrote: >>>> >>>>> I have spent some time looking at the problem of finding a polynomial >>>>> time solution to logical satisfiability and I have come to a few >>>>> conclusions about the problem. >>>>> >>>>> There may be a natural solution, but if there is, I certainly can't >>>>> see it. >>>>> >>>>> So if this is at all feasible, a more contrived method needs to be >>>>> concocted. I believe the solution would have to use an alternative way to >>>>> compress a logical problem so that individual solutions could be turned >>>>> out >>>>> in polynomial time. I can imagine compressing-some- logical formulas that >>>>> way but I can't think of a general method. >>>>> >>>>> But, since it looks like there is no one compression formatting that >>>>> could be used for every possible logical formula I believe that a solution >>>>> - if one is feasible - would have to use different compression encryptions >>>>> for different formulas. The formulas, encoded in one of >>>>> these yet-to-be-invented compression formats would probably need to >>>>> contain >>>>> the encoding methods used to explain how they were encoded, since >>>>> different >>>>> formulas (or different classes of formulas) would have to be compressed >>>>> differently. >>>>> >>>>> But, then since a part of logical formula that had been partially >>>>> expressed in one of these formats would, using this theoretical framework, >>>>> need to be converted into another compression format for the next part of >>>>> the formula, that suggests that the compressions would have to be >>>>> converted >>>>> into other compressions without fully decompressing them and this >>>>> compression transformation would have to take place in polynomial time. >>>>> So >>>>> one compressed format would have to be transformable into another format >>>>> as >>>>> the formula was converted in a step by step fashion. >>>>> >>>>> So in conclusion: >>>>> 1. Different classes of logical formulas would have to be converted >>>>> into different compression formats and this compression would have to be >>>>> done efficiently. >>>>> 2. The new compressed formulas would have to be efficiently readable >>>>> so, in the worse case, individual solutions could be read out efficiently. >>>>> 3. The individuated compression formats would have to >>>>> include something about the encoding used for the formatting. >>>>> 4. These formats would have to be convertible into another format >>>>> efficiently in order to process the logical formula in a stepwise fashion. >>>>> >>>>> This shows that there are at least 3 different conversion or >>>>> transformation methods necessary for the new individuated compression >>>>> methods. >>>>> >>>>> An initial analysis of the structure of a logical formula might be >>>>> used to immediately convert the formula into a different format without >>>>> going through a step by step conversion- reconversion process. But even if >>>>> that was possible we would still want to be able to treat logical formulas >>>>> in a step by step manner. >>>>> >>>>> Of course I have no idea if this is even possible. But my next >>>>> question is whether the inclusion of the compression formatting with the >>>>> compressed string is inherently too inefficient to be useful.. >>>>> >>>>> Jim Bromer >>>>> >>>> >>>> >>> >> > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/212726-deec6279> | Modify > <https://www.listbox.com/member/?&;> > Your Subscription <http://www.listbox.com> > -- Ben Goertzel, PhD http://goertzel.org "In an insane world, the sane man must appear to be insane". -- Capt. James T. 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