Null-A

[geni]

Non-Aristotelian logic

Ok this is the new buzzword I've run into from an anti science guy.

All I know is

http://en.wikipedia.org/wiki/Null-A

Can anyone traslte this into simple english and give me some idea of it's significance (and if it has any major flaws).

[crimresearch]

From an *anti*-science proponent? Or are they making some sort of tie in from Wolfram's 'New' science back to fuzzy logic, and then back to non-Aristotelian?

The Van Vogt stories were a lot of fun...IIRC one of the examples was to ask someone if that house over there was blue..an Aristotelian answer would be 'Yes', because it was observed to be no other color...a null-A answer would be 'I have no idea...the side I can see looks blue'.

(Sorry if I've botched that, I read the books in the late 50s to early 60s).

[Dr Adequate]

Sci-fi rubbish (http://vanvogt.www4.mmedia.is/worldof.htm) and also rubbish sci-fi. I bought the book, second hand. It's like an exercise in how badly you can write a science fiction novel.

Mind you, so is the Celestine Prophecy.

* starts punching inanimate objects *

[Robin]

The words scientific proof with scare quotes round them. I will certainly be wasting my valuable time on this.

[LW]

Originally posted by geni
Can anyone traslte this into simple english and give me some idea of it's significance (and if it has any major flaws).

Short answer: non-classical logics are useful when solving many practical problems. But if someone tries to argue something philosophical from them, then that someone is likely in error.

Longer answer (from perspective of a person working on computational logic):

A logic has syntax and semantics. The syntax tells what formulas belong to the language, and the semantics assigns a meaning (in the form of truth values) to the formulas. The best-known example is the classical logic with two truth values and standard definition of connectives. (Or, if you want to get really Aristotelean, you could have standard definition of syllogisms but we don't want to get in there).

Classical logic has several weaknesses when you try to use it to solve real-world problems. First, if you don't allow function symbols, you have too little expressive power. Here I use expressiviness in the same sense as a high-level programming language is more expressive than assembly: you can do everything with both but it is easier to do so with a high-level language. In logic this means that translating the problem into the language of classical logic is cumbersome: the translation will be big and even a slightest mistake renders the result completely useless.

Second, if you do allow function symbols, you have too much expressive power. Because then you have an incomplete proof system with all the quirks entailed by that. This means that you have to be even more careful in the formulation of your problem. Also, dealing with the decidable part of full predicate logic is computably more difficult than doing reasoning without function symbols.

Third, classical logic is monotonous, meaning that if some formula A is the logical consequence of the set of formulas S, then A will be logical consequence of any set of formulas that contains S. This property causes problems when you want to model something based on incomplete information. For example, you would like to express statements such as: "a healthy adult bird can usually fly", but it is very cumbersome to do so with classical logic.

Finally, if a set S is contradictionary, then everything is its consequence. This is a problem in many real-world applications where the input data may contain errors (for example, two copies of a student database may have different adresses for a student). Classical logic doesn't provide any support for isolating the contradictionary parts and doing inferences on the consistent part.

The idea of using different logics is that then you can get just the right amount of expressiviness for your problem so that it has a natural encoding with it and the semantics is not too computationally difficult to solve.

The multivalued logics are meant to address the third and fourth weaknesses. In my own personal opinion the three-valued semantics are the most useful of those. There you have the truth values: true, false, unknown. For example, with the set of sentences:

(I) A
(II) A -> B
(III) A and not C -> D
(IV) A and not D -> C

we have the three-valued model where A is true because of (I), B is true because of (I) and (II), but both C and D are unknown because they are defined with a cycle: if C is false, then D is true and if D is false, then C is true, and we have no reason (yet) to make the choice between C and D. (The three-valued semantics are often minimal model semantics meaning that we couldn't set both C and D true since then one of them would be true without having a justification for it).

Many implementations of non-classical semantics work by translating the input into classical propositional logic and then calling some standard solver for it, but it is possible to also make direct solvers for them.

[LW]

Originally posted by geni
http://en.wikipedia.org/wiki/Null-A

Forgot to add: I've read quite a lot of papers on nonclassical logics: default reasoning, stable semantics, abduction, circumscription, stationary semantics, well-founded semantics, partial model semantics, paraconsistent logics, multi-valued logics, etc, etc.

But this was the first time I've ever encountered the term 'Null-A'. No logician that I know uses it.

[crimresearch]

I don't know that it was ever intended to exist outside of some science fiction plots.

But it is fun to mention Van Vogt's name and watch the Scientologists start foaming at the mouth.

[drkitten]

Originally posted by LW

Third, classical logic is monotonous,...

I think the word you were looking for is monotonic, unless you were in my Introduction to Logic class back at Whatsamatta U. and wanted to comment on the professor's lecture style. In which case, of course, I withdraw the comment and agree with you.

Another problem I should point out with "classical logic" is that, even with all the bells, whistles, and trimmings, it's still not expressive enough for some aspects of reasoning. You already mentioned, for example, that a set of contradictory premises allows you to infer anything, whether causally connected or not. This also shows, though, that classical logic is not very good (how's that for an understatement) at counterfactual reasoning, or at drawing conclusions from "what if" statements, or at resolving paradoxes by decising which premise to reject.

Classical logic is also very bad at reasoning about probabilistic connections, or even at inferring the difference(s) between a causal link, a correlation caused by a shared (joint) cause, or a correlation caused simply by dumb luck. (How would you even express the idea of "A caused B"?)

One of the most important aspects of "traditional" non-Aristotelian logic (if you can use that phrase without wincing) is the rejection of the so-called "Law of the Excluded Middle." That is to say, it is not necessarily the case that, for any proposition A, either A is true or not A is true. Although this statement is "intuitively" obvious, there are also strong arguments against it, of which one of the strongest and easiest to understand is simple context:

For example, one of the complaints that I've seen made about Steve Nash (the most recent NBA Most Valuable Player) is that he was "too short." (Those complaints have stopped recently, for obvious reasons.) But let's look at this -- the man is six-foot-three, and would easily be the tallest man in my department if he would deign to accept that kind of a pay cut. Similarly, the new Miami Dolphin's quarterback is "too short," despite being well above average height. Obviously, the truth value of whether a person is "short" depends not only upon the statement itself, but the context in which it is made -- and so the statement P can be false in one context while not-P is also false in another context. We can't simply state that "Steve Nash is short or he isn't."

So there's a lot of interesting work available in non-classical logics. "Null-A," I agree, is a term of art that most logicians wouldn't be familiar with. But they'll all recognize phrases like "intuitionist logics" or "non-monotonic logics."

The most important question : what was the anti-science guy using this buzzword for? Because I strongly suspect that he doesn't actually know what it means, and that the logical theories he wishes to espouse don't actually support his position(s).

[Bodhi Dharma Zen]

Originally posted by LW
Forgot to add: I've read quite a lot of papers on nonclassical logics: default reasoning, stable semantics, abduction, circumscription, stationary semantics, well-founded semantics, partial model semantics, paraconsistent logics, multi-valued logics, etc, etc.

But this was the first time I've ever encountered the term 'Null-A'. No logician that I know uses it.

shhh dont show yourself on lifegazer's nor interesting ian's threads. You could provide them with the tools they need, so we all would lose the amusement that is involved in their threads, well specially those from LG, II is, at least, more of a gentleman.

[RandFan]

Originally posted by Dr Adequate
Mind you, so is the Celestine Prophecy. Awful book. And the undercurrent that it had some importance or relevance was silly and stupid. "Oh you just have to read this book" my friends told me. "Why?" I demanded after I read it.

[Eleatic Stranger]

(How would you even express the idea of "A caused B"?)

"Caused(A,B)"?

Of course, you're right that unlike English the if-then usage doesn't capture causation, but still it would be relatively easy to do something like the above. (Of course, determining the extension so as to define the predicate might be a little tricky, but when you're trying to talk about the world it's always a little hard nailing down your domain.)

[LW]

Originally posted by Eleatic Stranger
(Of course, determining the extension so as to define the predicate might be a little tricky, but when you're trying to talk about the world it's always a little hard nailing down your domain.)

And that is precisely why you often want to use some other logic than classical predicate logic: if you choose you logic well, you don't have to use as many tricks in expressing the problem domain.