Well, if you want a simple but complete operator set, you can go with -- Schonfinkel combinator plus two parentheses
or -- S and K combinator plus two parentheses and I suppose you could add -- input -- output -- forget statements to this, but I'm not sure what this gets you... Actually, adding other operators doesn't necessarily increase the search space your AI faces -- rather, it **decreases** the search space **if** you choose the right operators, that encapsulate regularities in the environment faced by the AI Exemplifying this, writing programs doing humanly simple things using S and K is a pain and involves piling a lot of S and K and parentheses on top of each other, whereas if we introduce loops and conditionals and such, these programs get shorter. Because loops and conditionals happen to match the stuff that our human-written programs need to do... A better question IMO is what set of operators and structures has the property that the compact expressions tend to be the ones that are useful for survival and problem-solving in the environments that humans and human- like AIs need to cope with... -- Ben G On Tue, Jul 13, 2010 at 1:43 AM, Michael Swan <[email protected]> wrote: > Hi, > > I'm interested in combining the simplest, "most derivable" operations > ( eg operations that cannot be defined by other operations) for creating > seed AGI's. The simplest operations combined in a multitude ways can > form extremely complex patterns, but the underlying logic may be > simple. > > I wonder if varying combinations of the smallest set of operations: > > { ">" , memory ("=" for memory assignment), "==", (a logical way to > combine them), (input, output), () "brackets" } > > can potentially learn and define everything. > > Assume all input is from numbers. > > We want the smallest set of elements, because less elements mean less > combinations which mean less chance of hitting combinatorial explosion. > > ">" helps for generalisation, reducing combinations. > > memory(=) is for hash look ups, what should one remember? What can be > discarded? > > "==" This does a comparison between 2 values x == y is 1 if x and y are > exactly the same. Returns 0 if they are not the same. > > (a logical way to combine them) Any non-narrow algorithm that reduces > the raw data into a simpler state will do. Philosophically like > Solomonoff Induction. This is the hardest part. What is the most optimal > way of combining the above set of operations? > > () brackets are used to order operations. > > > > > Conditionals (only if statements) + memory assignment are the only valid > form of logic - ie no loops. Just repeat code if you want loops. > > > If you think that the set above cannot define everything, then what is > the smallest set of operations that can potentially define everything? > > ------------------------------------------------------------------ > Some proofs / Thought experiments : > > 1) Can ">", "==", (), and memory define other logical operations like & > ("AND" gate) ? > > I propose that "x==y==1" defines "x&y" > > x&y x==y==1 > 0&0 = 0 0==0==1 = 0 > 1&0 = 0 1==0==1 = 0 > 0&1 = 0 0==1==1 = 0 > 1&1 = 1 1==1==1 = 1 > > It means "&" can be completely defined using "==" therefore "&" is not > one of the smallest possible general concepts. "&" can be potentially > "learnt" from "==". > > ----------------------------------------------------------------- > > 2) Write a algorithm that can define "1" using only >,==, (). > > Multiple answers > a) "discrete 1 could use" > x == 1 > > b) "continuous 1.0 could use this rule" > For those not familiar with C++, "!" means "not" > (x > 0.9) && !(x > 1.1) expanding gives ( getting rid of "!" and "&&") > (x > 0.9) == ((x > 1.1) == 0) == 1 note "!x" can be defined in terms > of "==" like so x == 0. > > (b) is a generalisation, and expansion of the definition of (a) and can > be scaled by changing the values "0.9" and "1.1" to fit what others > would generally define as being 1. > > > > > ------------------------------------------- > agi > Archives: https://www.listbox.com/member/archive/303/=now > RSS Feed: https://www.listbox.com/member/archive/rss/303/ > Modify Your Subscription: https://www.listbox.com/member/?&; > Powered by Listbox: http://www.listbox.com > -- Ben Goertzel, PhD CEO, Novamente LLC and Biomind LLC CTO, Genescient Corp Vice Chairman, Humanity+ Advisor, Singularity University and Singularity Institute External Research Professor, Xiamen University, China [email protected] "I admit that two times two makes four is an excellent thing, but if we are to give everything its due, two times two makes five is sometimes a very charming thing too." -- Fyodor Dostoevsky ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=8660244-6e7fb59c Powered by Listbox: http://www.listbox.com
