Artificial Life Simulations

[BYTE-Smasher]

I think one of the problems with AI is that there's true and false, but no unknown or unsure....
think about it... human logic and reasoning has every bit as much to do with what we don't know as what we do know... we rarely ever think of things as absolute truths or absolute falsities.... it's never 1 or 0 to a human... it's always in the grey area... and it's that grey area that promotes us to think.... the fact that we never really know what's abolutely tru means we're constantly shifting in one direction or the other... or minds never made up...

for a computer, this is not the case... it's all defined... this is one of the major flaws of current AI... as i said above... if a = 1 then beep.... but what if we don't know what a is? what if a was never defined  (it will be passed 0 or a value from memory.. I know... but forget about that...) what if we think it's 1, but we can't quite remember because it wasn't really that important to us... our memory was best served storing something else... these are situations a computer has never experienced... and most likely never will...

[carnes]

I think one of the problems with AI is that there's true and false, but no unknown or unsure....

Fuzzy logic addresses this very issue by fuzzifying boolean values.

but the bottom line is "if a = 1 then beep"

GAs actually do not directly use logic. A GA "breeds" a population of candidate solutions. Each candidate gets a score from a performance function which influences its chances of reproduction.

ANN's are the only method that breaks the mold as it allows the machine to make predictions to inputs that it hasn't seen before.

In AI we call this "the ability to generalize." ANNs aren't the only method of generalizing. GAs are very good at generalizing. If you check out the Schema Theorem, you will see this.

but the bottom line is "if a = 1 then beep"

Some of the comments here suggest a dissappointment with logic or rule based systems. But rule/logic based systems can be powerful and effective (see http://ai.eecs.umich.edu/people/laird/papers/human-level-quake.pdf for an excellent example). Also, they are  usually much more flexible than  hardcoded  if-then-else statements.

Edit
Actually, heres a better paper on the SOAR Quake Bot:
http://ai.eecs.umich.edu/people/laird/papers/human-level-quake.pdf

[Waterman]

It takes 80 years for the "brain" supercomputer to reach it's ultimate level of intelligence.

People here want to see a computer do similar things instantly. How much time give... maybe 1 second?

80 years = 2522880000 seconds.

The PC is ... how much more stupid? I take a random 1000000000.

So how smart will the game AI be? Easy, it's 1/2522880000000000000 of the human intelligence.

Doesn't sound too promising...

On the other hand... my kids have had several years to get intelligent, but i could easily say that a 233 MHz PII is smarter... at least it obeys. hmmmm...

Really good AI should in fact not obey automatically. With an intelligent computer, if you type A at the keyboard, it should sometimes place an X onto the screen instead... or then it shouldn't do anything at all. Or something completely different, like shutting down Windows.

And then it should forget to do a whole lot of things. And sleep, of course. If you turn it on in the middle of the night, it should be angry at you.

Oops, sorry to interrupt your discussion, please go ahead! :-)

[dolmsted]

Carnes, don't take our disappointment with conventional rule based systems personally. Advances in human knowledge come from becoming dissatisfied with what is, only then will the great vistas of other possibilities appear.

Fuzzy logic has two big problems when it comes to handling uncertainty. The first is that it does not have a complete set of connective operations, that is, it cannot completely characterize the state symmetries of a system. It has the AND (symmetry test), and the INCLUSIVE OR (symmetry irrelevant test) but no anti-symmetry test. In binary logic this is done by the CONDITIONAL operation. (its negated form is the more popular IMPLICATION operation). Fuzzy logic does not have a CONDITIONAL operation.

The second problem is that it does not address the second dimension of logical uncertainty and that is the validity of the truth value itself. A form of binary logic called modal logic defines two modes, necessity (true by definition) and possibility (true by observation). It's fairly obvious that the validity measure should be extended to being represented by a normalized analog value but how to justify it and how should it propigate through the system? Some deeper theory of information processing dealing with state changes is required  :wink: .

[carnes]

don't take our disappointment with conventional rule based systems personally

Wasn't . Just having a healthy debate.

Fuzzy logic does not have a CONDITIONAL operation.

:? Hmm. Fuzzy logic does have the implication operator. Also, fuzzy expert systems extend fuzzy logic with fuzzy inference.

Fuzzy logic has two big problems when it comes to handling uncertainty.

There are some serious problems with fuzzy logic for the math purist. For example, if X is 60% likely then NOT X is 40% likely. This means that (X AND (NOT X)) is 40% likely, which should be impossible.

dolmsted, how does your approach compare to Bayesian networks?

[dolmsted]

Fuzzy logic as originally derived from consideration of set theory by Lotfi Zadah in 1964("Fuzzy Sets", Information and Control, 1964, 8:338-353) does not mention either the CONDITIONAL or the IMPLICATION operation because the operation has no justification in terms of sets. Neither did the earlier set theory fuzzy logic derivation by R.H. Wilkinson in 1963, ("A method of generating functions of serveral variables using analog diode logic". IEEE Transactions on Electronic Computers, EC12, 112-129. Since then others have proposed IMPICATION operations without justification. They just propose some operation and then test it out for some limited domain situation and claim it is an IMPICATION operation when it is not. Unless it an operation can be derived as part of a consistent theoretical approach it will lead to inconsistent results.

With the lack of an IMPLICATION operation and your example of a lack of consistency under negation (its other major problem) it is obvious that set theory by itself is not a powerful enough to provide the theoretical underpinnings for any sort of logic. Only some sort of information processing theory dealing with state changes can do that.

So I was quite pleased when during the derivation of my theory elimination of redundancy lead to the truth value metric of True to Indeterminant instead of the fuzzy logic True to False. Because of this Causal Asynchronous Logic (and its synchronous Analog Logic special case) do not have a Negation operation and so avoids the mathematical inconsistency you mentioned. To compenate for this it does have the CONDITIONAL operation.

Of course there is an earlier and perfectly good definition for IMPICATION operation from even earlier work on multivalued logic that not many people know about. The Polish logistician Jan Lukasiewicz first published it in English in 1930 under the title "Philosophical remarks on many-valued systems of propositional logic". It was reprinted in 1967 in Sorrs McCall (ed), Polish Logic 1920 - 1930, Oxford University Press. His system even has the min (AND) and max (INCLUSIVE OR) operation of fuzzy logic although they were defined in complexly terms of the IMPLICATION operation and not stated as being a simple min and max operation. Negating the IMPICATION operation produces a bounded difference operation as the CONDITIONAL operation and that is confirmed by my theory for the synchronous special case.

So what I want to emphasize is that if-then statements are not the same as IMPLICATION operations. Even using a threshold as some fuzzy expert systems do is not an IMPICATION operation. A threshold or "winner take all" operation makes a system  decision, it does not test for state symmetries.

I would like to add that I always found Zadah's lack of a citation Wilkinsons paper as disgraceful and dishonorable. Zadah was a member of the IEEE at the time researching analog systems so he must have known of the paper. His orignal paper did contain a footnote mentioning multivalued logic but that footnote is eliminated in later reprints.

That is all for now. I will address Bayesion networks later.

[carnes]

Unlike fuzzy logic, Boolean logic is mathematically sound. I think that a good system of logic should be a superset (or extension or generalization) of Boolean logic. I don't see how your logic system can represent Boolean logic, since it cannot represent FALSE. Also how could the COMPLEMENT operator be represented, since we know that the complement of a TRUE symbol is FALSE?

[dolmsted]

Ah, but is boolean logic really mathematically sound in general? Is the absence of evidence the same as evidence for absence (falsity)? Boolean logic cannot make this distinction with it NEGATION (COMPLIMENT) operation and it lead to problems when the IMPLICATION operation is used. Because of this Boolean logic is not mathematically sound in all domains.

The IMPLICATION operation ASSUMES that a statement is true in the absence of direct contradictory evidence. In other words it has an inherent truth assumption. The statement "clouds" imply "rain is true unless directly contradicted by no rain occuring with the presence of clouds.

clouds imply rain

clouds, rain then implication true
no clouds, rain then implication assumed true as rain my be associated with other things
clouds, no rain then implication false
no clouds, no rain then implication is assumed true since it can't be tested

turn it around (rain implies clouds)

rain, clouds then implication true
no rain, clouds then implication assumed true as clouds my be associated with other thing
rain, no clouds then implication false
no rain, no clouds then implication assumed true since it can't be tested

From experience only the second implication is true.

Are their any situation where a truth assumption is bad? Replace rain with a bush and clouds with preditor. Should an animal ever assume that just because no bushes are around that preditors are not around? I don't think so. Yet Boolean logic by itelf has no mechanism to address associations that have an "I don't know" option when an association can't be tested. (one can always design a circuit to detect this condition and over ride the IMPLICATION result but that requires a hard wired exception handler for every possibility and that is not possible in an unrestricted domain).

But the real proof of Boolean logic inconsistency is in the area of mathemetical proofs (which are done with logic). Early in the 1900's Bertrand Russell tried to use Boolean logic to prove the foundations of mathementics and failed. In 1931 Kurt Godel published a theorem showing why. It stated that any formal logical theory rich enough to include all the forumulas of number theory must have some formulas be undecidable if the theory is to be consistent. That is such a theory must be deliberately incomplete and ambiguous if it is to be logically consistent. His second theory, which is a corollary of the first asserts that the consistency of such a theory is impossible to prove by methods "formilizable within the theory".

So Boolean logic with a truth value metric of true to false is inconsistent where association assumptions must be made.

[BYTE-Smasher]

clouds imply rain

clouds, rain then implication true
no clouds, rain then implication assumed true as rain my be associated with other things
clouds, no rain then implication false
no clouds, no rain then implication is assumed true since it can't be tested

turn it around (rain implies clouds)

rain, clouds then implication true
no rain, clouds then implication assumed true as clouds my be associated with other thing
rain, no clouds then implication false
no rain, no clouds then implication assumed true since it can't be tested

From experience only the second implication is true.

uhm, just because all balls are round, doesn't mean everything round is a ball.......
just because rain implies couds, doesn't mean you need rain to have clouds......

boolean logic does not claim that if one thing is true, another will always be true... it's all based on how you use it... in fact, boolean was originally used to SOLVE such problems.... it's existed for ages in philosophy circles... this was it's primary function....

the fact is,
if rain = true then clouds = true
you can not determine whether rain = true based on the fact that clouds = true....
you don't have the data you need to do so... and if you've got a program that tries to, you are defying logic.... it has nothing do do with the fact that it's boolean logic... it's a lack of data.... boolean or not, you'll run into the same problem... even with analog states, this is very difficult to do, if not impossible... what do you define as sure? what do you define as unsure? what do you define as undefined?

the fact is, boolean logic is probably the best system we have for solving such problems if used properly.... what we need to do though, is add one digit to the equasion....

we have true and false... on and off... we need a halfway state.....

what I suggest is we start using positive, negative, and 0

+1 = true         = on         =   positive
0    = unknown = halfway =  unsure
-1  =  false        = off        =   negative

this not only works well with logic, but also with computing, as there are not 2 solid states to electricity, but in fact, 3.... v+, 0, v- ...... trinary computing

[dolmsted]

The above example is based on the classic IMPLICATION operation "not a or b". It is the boolean expression used in syllogisms such as "if x then y".

You can always code in more robust rules as you suggest but those would only be good for a known and limited domain. In other words the code would be especially made for a certain environment.

Anyway the correct set of fundamental analog logic operations involving only truth values between 0 and 1 for state symmetry characterizations are the AND (passes the maximum value, like fuzzy logic), INCLUSIVE OR (passes the least value among its inputs like fuzzy logic), and the CONDITIONAL (a bounded difference operation in which the result cannot go negative unlike fuzzy logic).  As you can see the fundamental Boolean operations are a special case of these operations if only 1 and 0 are used and the truth value metric is either True of False. The IMPLICATION operation is simply a negated CONDITIONAL.

These analog logic operations are in turn a special case of the Causal Asynchronous operations.

The question as to whether to extend the logic metric to True, Indeterminant, False is simply a question of redundancy. I just think that a True and Indeterminant metric can handle all the state symmetry characterizations especially when using the subtraction in the CONDITIONAL operation (its similar to the complement or negation operation "1 - input" in Boolean logic). Actually during the derivation of the Causal Asynchronous system the metric of True, Indeterminant, False came out first. I just simplified it since it did seem redundant. Yet if the simpler metric turns out not to be sufficient then the longer metric is fully consistent with the theory. (although the brain doesn't seem to need it. You would need some sort of negative or anti-impulse. Hmm like anti-matter particles in physics?).

[carnes]

proof of Boolean logic inconsistency ...

Dolmsted, I think you mean to say that the domain of Boolean logic is limited. Of course we all know that Boolean logic is mathematically consistant.

The domain of Boolean logic does not directly includce with the following:
1) Uncertainty probability and statistics
2) Non-Boolean values like real numbers

But the real proof of Boolean logic inconsistency is in the area of mathemetical proofs (which are done with logic). Early in the 1900's Bertrand Russell tried to use Boolean logic to prove the foundations of mathementics and failed. In 1931 Kurt Godel published a theorem showing why. It stated that any formal logical theory rich enough to include all the forumulas of number theory must have some formulas be undecidable if the theory is to be consistent. That is such a theory must be deliberately incomplete and ambiguous if it is to be logically consistent. His second theory, which is a corollary of the first asserts that the consistency of such a theory is impossible to prove by methods "formilizable within the theory".

This indicates the need for algorithms (i.e. computing machines), not the failure of Boolean logic. It has been proven that every problem that is decidable by some algorithm can be decided by a Turing machine. Because Boolean logic does not express algorithms, it is insufficient to "prove the foundation of mathematics".

Hmm like anti-matter particles in physics?

:| I think a hybrid logical system comprising both a Bayesion network and a set of boolean predicates on the network could deal with both logic and uncertainty. Even better, neural nets can be created to deal with uncertainty, logic,  and arbitrary values. ANNs are perhaps the best model of low-level cognition. Because of the complexity of high-level cognition, high-level cognition is usually best modeled by other means.

[dolmsted]

Yes, the main point was to show that Boolean logic is only consistent within a rather narrow domain. As I now see it information processing has three levels of domains. The lowest is Boolean logic, the next more general is Probabilistic Multivalued Logic, and the most general of all is a Causal Asychronous System.

Bayesian networks as well as the multivalued logic system mentioned earlier are actually combined in the second level. First Bayesian networks are a unidirectional conditional probability network in which the output having the highest probability gives the answer (that is defines the state of the system). The probability values range from 1 indicating that the meaning represented by the network line absolutely exists (is true) to 0 indicating that the meaning has not evidence for its existence (is indeterminate). The probability values are combined with the summation operation (probabilistic AND operation).

By why limit yourself to only using probability operations? In a finite state machine (finite automata) the next state in the sequence of states must be selected from the most likely identification of the present state and the most preferred transition path from the present state. Since the first deals with state identification that requires using the state symmetry tests (logic operations). The second deals with state transitions and that requires the use of probabilities. So all one needs is a logic system that matches the uncertainy use in probability and which is a direct generalization of Boolean logic. That logic is multivalued logic with a true to indeterminant truth value metric.

Causal Asynchronous systems are able to handle even more uncertainty, the uncertainty that comes during the process of determining the truth and probability values in the first place and propagating those second dimensional uncertainties through the system.

So as you suggested modeling with even the second level system should be much more powerful and robust than any mixture of existing techniques. Mixures of incompatable techniques tend to be fragile, breaking down outside of very narrow operating limits.

[dolmsted]

Well, after sitting on the paper for 6 months the editor of Information and Computation decided to reject the paper because it doesn't belong in his journal but instead belongs either in a neural journal or a control systems journal. After all the paper didn't even have theorems! (neither did Claude Shannon's paper on Communication Theory. These ground breaking papers are instead full of examples and explanations)

Needless to say I am appalled at the narrow mindedness of this. The following is taken from their website describing the type of papers they are looking for:

Information and Computation welcomes original papers in all areas of theoretical Computer Science and computational applications of Information Theory. Survey articles of exceptional quality will also be considered. Particularly welcome are papers contributing new results in active theoretical areas such as

Biological computation and computational biology
Computational complexity
Computer theorem-proving
Concurrency and distributed process theory
Cryptographic theory
Data base theory
Decision problems in Logic
Design and analysis of algorithms
Discrete optimization and mathematical programming
Inductive inference and learning theory
Logic & constraint programming
Program verification & model checking
Probabilistic & Quantum computation
Semantics of programming languages
Symbolic computation, lambda calculus and rewriting systems
Types and typechecking

Anyway, more screenshots can be found at my website at http://www.neurocomputing.org. These are the last screenshots I made with BlitzBasic. All future work will be done with TV3D. I also took the liberty of improving the abstract of the paper so it will hopefully be clearer.

[GoodVillain]

OMJ! This spam bot was created before the image verification. Ban the bot and move on....