Disclaimer: I know little about AI, physics programming and fuzzy logic... I just like to make posts with interesting speculations, based on nearly unresearched ideas. So if Fuzzy Logic is a branch of logic which tries to deal with the uncertainty of things. Instead of presenting things as having a status of 1 or 0. It will present them as "nearly" X... So I wonder what kinds of applications such logic / mathematical systems could have in terms of computer games? Maybe one could use it to present degrees of uncertainty in Aiming, so instead of having a precise location that the computer knows the player to be in (which it will then fire at with some artificially induced innacuracy)... then it could instead use some kind of Fuzzy system to say that the target is in plain sight, and may be between point x and point y, it will then fire at this point which may not be 100% accurate (and may then have extra artificial innacuracy added on top of this). Or instead of KNOWING that there is an enemy here, then instead it will think that the player is in position X or on the other side of the room in position Y. Which would simulate uncertainty. So for instance, the AI could be made to act more cautious as it wouldn''t be sure HOW MANY enemies it was dealing with (are there a few Orcish Guards around the corner that it may alert). Of course such uncertainty values could be reduced by the application of any "Scouting" that the AI has done, or simple Sound based checks.. for gunfire/ heavy_breathing.

I feel a clarification is in order before this discussion goes further.

Fuzzy Logic is concerned with degrees of truth of a proposition. In Aristotlean logic, the proposition "John is tall" would have a subjective binary value depending on who was evaluating the proposition. Fuzzy Logic permits (but doesn not guarantee) an assessment of objective truth of states of the form "John is tall" or "X belongs to the set Y". Fuzzy Logic is a Truth Maintenance System and suffers from the same problems as other such systems.

Probability theory on the other hand is concerned with degrees of belief. Put another way, an assignment of a probability of p to a proposition is a measure of how confident one is that the proposition is true. To assign a probability to "John is tall" would be to estimate how likely it is that John is tall, rather than short, tiny, huge or some other size in the height scale.

Probabilistic representations of uncertainty are therefore measuring our degree of uncertainty in our knowledge of events, rather than some inherent uncertainty in the events. Of course, probabilistic systems suffer from certain pitfalls as well!

I hope this has helped with a little enlightenment.

Cheers,

Timkin

quote:Original post by Timkin
I feel a clarification is in order before this discussion goes further.

Fuzzy Logic is concerned with degrees of truth of a proposition.

Thank you Timkin. I was going to jump in here and point that out.
And your explanation was just what was needed.

Eric

Timkin wrote:
Fuzzy Logic is concerned with degrees of truth of a proposition. In Aristotlean logic, the proposition "John is tall" would have a subjective binary value depending on who was evaluating the proposition. Fuzzy Logic permits (but doesn not guarantee) an assessment of objective truth of states of the form "John is tall" or "X belongs to the set Y". Fuzzy Logic is a Truth Maintenance System and suffers from the same problems as other such systems.

While I agree with what you said, I just wanted to add something that I thought might be important. In formal logic "John is tall" is true XOR false. Not both true and false, and not some third alternative. It''s not true or false depending on who''s evaluating it, it''s true XOR false because calssical logic is based on the belief that there are facts "In the world" so to speak. So is probability theory just like you said, but not fuzzy logic which deals with degrees of truth. I don''t really think that you should treat fuzzy logic as an alternative to classic propositional or predicate logic though. That kind of logic specifically deals with statements that are true XOR false. "John is tall" isn''t a very good example, "John is 1.76 meters tall" is better. Either he is, or he isn''t. I would say fuzzy logic is a way to reason about continously varying variables, not an alternate way of doing logic. They deal with different types of statements. But hey, I''m no expert so feel free to rip my arguments to shreds

quote:Original post by Anonymous Poster

While I agree with what you said, I just wanted to add something that I thought might be important. In formal logic "John is tall" is true XOR false. Not both true and false, and not some third alternative. It''s not true or false depending on who''s evaluating it, it''s true XOR false because calssical logic is based on the belief that there are facts "In the world" so to speak.

That''s not stricltly true actually. First Order Logic can be subjective or objective. Indeed, any truth maintenance system is simply a mechanism by which to infer the truth values of inference results, given the truth values of inputs (e.g., premises in deductive logic). There is no restriction that such a system must only be applied to objective truths. There may or may not exist an objective truth relating to the statement "John is tall" but it is certainly the case that I can apply a subjective truth to the statement and perform FOL on my knowledge base to infer other results related to this predicate.

quote:Original post by Anonymous Poster
So is probability theory just like you said

Actually, I didn''t say that probability theory ''is based on the belief that there are facts "In the world"''. Indeed, probabilities may be objective or subjective.

quote:Original post by Anonymous Poster
I don''t really think that you should treat fuzzy logic as an alternative to classic propositional or predicate logic though.

I don''t believe anyone was suggesting that. Fuzzy Logic and FOL are two very different beasts. There are those that believe Fuzzy Logic is the answer to the ills of FOL, however that camp is dwindling fast.


Cheers,

Timkin

quote:That''s not stricltly true actually. First Order Logic can be subjective or objective. Indeed, any truth maintenance system is simply a mechanism by which to infer the truth values of inference results, given the truth values of inputs (e.g., premises in deductive logic). There is no restriction that such a system must only be applied to objective truths. There may or may not exist an objective truth relating to the statement "John is tall" but it is certainly the case that I can apply a subjective truth to the statement and perform FOL on my knowledge base to infer other results related to this predicate.

Yes, my point was just that if some of the basic principles of logic are true then, if you''re so inclined, you can draw certain knowledge theoretic conclusions from that. Namely, that there is such a thing as facts, propositions that are true XOR false. Of course, you can just ignore that, and just treat FOL as a useful method for gettting true deductions from a set of premises. My point was just that, for FOL to be able to deduce anything correct, there must be facts to start from. Subjective truths are fine, as long as they are facts, i.e. true XOR false. Otherwise, it doesn''t work.

quote:Actually, I didn''t say that probability theory ''is based on the belief that there are facts "In the world"''. Indeed, probabilities may be objective or subjective.

Sorry, my fault. What I meant to say was that probability theory also assumes facts, in contrast to fuzzy logic which handles degrees of truth. You said this already, but I thought the whole subjective/objective thing was a little confusing. I just wanted to emphasize that fuzzy logic is very different from FOL, since the first post by Ketchaval seemed to treat them as alternatives.

I am starting a new thread to discuss "possibility in AI", whilst removing any overt references to possibly incorrect interpretations of fuzzy logic.

A little knowledge is a dangerous thing, but can start some interesting ideas!