Shame on you Ben, again! He Creative Commons licensed his mind, that's why.
AT > On 16.06.2014, at 14:52, "Ben Goertzel via AGI" <[email protected]> wrote: > > > 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 | Modify Your Subscription > > > > -- > Ben Goertzel, PhD > http://goertzel.org > > "In an insane world, the sane man must appear to be insane". -- Capt. James > T. Kirk > > "Emancipate yourself from mental slavery / None but ourselves can free our > minds" -- Robert Nesta Marley > AGI | Archives | Modify Your Subscription ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
