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>> Generally speaking, logical modelling is too limited for good concept representations

In principle, First Order Logic and equivalent languages can represent anything that can be represented in natural language. The problem is that in practice it is very hard to transfer into a logic language all the knowledge you might need for a useful system.

In fact, this was one motivation for at least one branch of machine learning- the work from Ryszard Michalski, Claude Sammut, Ranan Banerji, Steven Vere, Brian Cohen and later rule-learners like Quinlan's decision tree learners and of course all the later work in Inductive Logic Programming by Plotkin, Shapiro, Muggleton etc. These are all rule-learning systems, that can avoid the knowledge acquisition bottleneck that probably did in for purely rule-based expert systems in the '90s (i.e. getting experts to transfer their knowledge into rules).

I rather agree that further progress in AI will require a, let's say, synchretistic approach- like I say in another comment, the obvious thing for me is to use deep learning for perception, logic for inference and probabilistic modelling to deal with the noisy world. There are some people working in that sort of direction, with different amounts of emphasis on each of the three approaches. For instance, Josh Tenenbaum at MIT, Evans and Grefenstette at DeepMind, Luc De Raedt at KU Leuven, Kristian Kersting at Dortmund, Lise Getoor also at MIT, Pedro Domingos at Washington, and many others.

Apologies for all the name-dropping without links. Let me know and I can provide them if required.

I suspect you may have a hard time representing all the implications, subtexts, and allusions in a play by Shakespeare with First Order Logic.

It seems more likely that First Order Logic can be represented by a subset of natural language.

Otherwise, I agree. I don't understand why everyone has been concentrating so hard on probabilistic ML when there are many applications where inductive inference is more efficient and powerful.

That’s not obvious. Do you have any reason for thinking so?

> In principle, First Order Logic and equivalent languages can represent anything that can be represented in natural language.

Is there any proof about an existing non-leaky abstraction between natural language and First Order Logic (or logic in general)? Afaik there is none, but I might me wrong. For example (one amongst thousands): “I don’t like you” can actually mean (and it often does) the exact opposite, and the same can be said of a simple statement like “I am ok” which also can mean the exact opposite. Natural language is a very hard problem.

Well, going by formal language theory, FOL is equivalent to a universal Turing machine, which is probably also the full expressive power of human language. Therefore, everything that can be said in human language should in principle be possible to say in FOL. I don't think this is controversial.

Notice again that I don't think this is feasible in practice. At least not with hand-crafted FOL expressions and certainly not with existing technology.

I'm not sure what "non-leaky abstraction" means. Would formal language theory fit the bill?

Yeah but humans don't have a single consistent logical model for all reasoning - i believe that all my models can be in fol, but i don't believe that they can be unified in fol

Dennett aims to solve this using heterophenemenology:

https://en.m.wikipedia.org/wiki/Heterophenomenology

In this framework, utterances can be studied without taking their truth value at face value.

Very interesting, I'll have to think a lot about that.

Oh, I'm not saying anything about how humans think, or model the world. FOL is a formal language. It can express the same things that natural language can express and you can do reasoning in it (actually- let's say "inference" because reasoning is a bit of a loaded term), but I make no claim that it's how humans really think.

I mean, I don't believe that is true any more that I believe calculus, or linear algebra are the way we think. Those are just formal systems that we can use to get various results about the world- but is that how we really think inside our heads? I kind of doubt it.

I'm just talking about the expressive power of first-order predicate calculus here, not about whether it's a good model for human intelligence.

Does it matter, though? Understanding sarcasm or other forms of language twisting seems like only important for a very advanced and specific set of applications. There's another post in the front page about the death of a gorilla that was able to do signs language. I'm sure nobody cared if he could catch jokes.

> In principle, First Order Logic and equivalent languages can represent anything that can be represented in natural language.

I doubt this is the case since natural language makes a lot of use of metaphors, and our concepts are probably mostly based on the types of bodies we have and how we interact with the world. See embodied cognition and writings of Lakoff and Mark Johnson.

In principle, but not consistently over various cases. Wikipedia shows some examples where it breaks down

Look into the field of computational semantics. There is absolutely nothing in your comment which cannot be represented in existing logics. Metaphors and such are no problem.

There is ambiguity in natural languages so the determination of underlying meaning is at best probabilistic, but we have ways of handling that too.

Lexical and computational semantics may be superior to FOL, (for machine translation, at least) but they've been around now for a very long time without showing much promise toward thawing past AI Winters. I've not heard anyone propose their adoption as the missing next step toward modeling general knowledge across all AI problem spaces.

In fact, populating a LS/CS knowledgebase with requisite facts was a game stopper when they were first invented and still pose challenges of scale that remain unsolved decades later. If it accomplished anything, Cyc proved that manual curation alone of a rich database of propositions is depressingly infeasible. So how does one automatically curate a general fact KB, no matter what semantic model the facts take? I don't think expressiveness of the propositional representation will ever decide that question.

I’m not sure what you are saying. Computational semantics parses sentences to possible interpretations in first order, or higher order logics. It is not some sort of alternative to FOL. And it is still a rapidly developing field.

I'm trying to suggest (perhaps badly) that formal models of logic modeling like LS / CS have an innate achilles heel (from what I've seen): either A) the knowledgebase is precise but tiny, and will remain so because it had to be meticulously hand crafted to comply with a formal semantic model, or B) the KB is representationally sloppy but big and scaleable, because it was populated automatically and informally (probabilistically), thereby forever limiting its amenability to precise models of reasoning. To wit, you may have your cake, but the morsel is so tiny you'll starve.

I think this tradeoff in quality vs quantity has been central to the inability of most Good Old Fashioned AI (GOFAI) formal symbolic methods to 1) scale up beyond toy academic clean-room problems (from the admittedly little I've seen of commercial LS/CS), as well as 2) support the flexibility and imprecision needed to deal with a messy ill-defined very big world with a seemingly unknowable number of unknowns.

It may be that this venerable yin v yang of knowledge modeling will forever bedevil AI. I don't have the sense that any techniques in the past 30 years have really made headway in breaking this log jam. Deep nets have just tilted the playing field in its favor, so long as we're willing to ignore fussy details like dependence, FOL, and causality.

That describes the weaknesses of existing academic attempts not the theory in any way. I could say the same things of machine learning actually.

I agree totally that a "non-pure" deep learning approach is going to be necessary in pushing the field forward. World shattering results from new deep architectures like AlexNet are becoming more and more rare and improvements are becoming incremental. Language models, for example, showed some impressive results in recent years, but we're still a long long way from generating realistic and useful text. I'm not sure if throwing more data at larger architectures will get us there. Maybe, maybe not.

The work by Tenenbaum at MIT is a particularly interesting mix of psychology, computational statistics, and neuroscience. It really challenges the commonly repeated notion that neural networks are completely unrelated to actual brains.

One problem with first order logic is that it is too powerful.

There is a direct trade-off between the expressiveness of your representation and your ability to reason about it.

I'm going to assume you mean the computational complexity of working with such an expressive representation. If so, then that is correct. historically, working such an expressive representation blows out computationally. But, we've resolved that issue with our graph engine. that is, its been shown that algorithms take time proportional to N-cubed where N is the number of graphs in the knowledge base. with our graph engine, we encode graph structures and ontology in a Cognitive Signature, and we can find closely matching signatures in log(N) time. the log-time algorithms scale to the size of the web.

>In principle, First Order Logic and equivalent languages can represent anything that can be represented in natural language

If you include a semantics for supervaluationism (Sorites paradox, Keefe on vagueness)!

Thinking of it, I'd love to train a NN against human responses to '"is this a heap, yes/no?" +/-1 grain, repeat'.

I think this is the perspective the "Society of the Mind" book by Marvin Minsky took at their time. When a software like Mathematica makes symbolic operations it is doing AI, the same for things like the Z3 solver.

Very astute. Some folks here at Kyndi used to work with Minsky. One of our favorite quotes is: "what magical trick makes us intelligence? The trick is that there is no trick. The power of intelligence stems form our vast diversity, not from any single, perfect principle." What we see now in AI/ML is not diversity, but rather attempts at the single perfect principle. We don't believe that is the path forward. Rather, you need to figure out how to tightly couple different approaches (e.g., symbolic and statistical learning approaches) to form a more powerful, flexible, and explainable model of AI.

AGI will need to be able to learn and represent any symbol system, just like we can. And it doesn't have to be that good at it(we arn't). There's millions of knowledge bases all around. You'll need something with a generative imagination. We model so much more than labels and relation ships.

Imagine a speech, by president Obama. Where you can actually hear his words. or imagine a ball dropping. We just use words to convey the basic idea. How many hairs does a bald person have?

And if we have a misunderstanding we just adjust our system. New word we use context, including social context etc.

Let me suggest something that will turn everything upside down...

How much of our “logical reasoning” about the world is just really strong correlations?

Look, AlphaGo Zero beat the best chess programs by just precomputing MCTS. What does that say about finding the optimal solution to a problem?

It seems MCTS beats even AlphaBeta search, by far.

So when you talk about applying rules, you’re using a system that tried to reduce the system to a few rules and maybe recursively use them. That may work for some things. Certainly it seems to work amazingly for physics. But that’s the unreasonable effectiveness of mathematics.

Ultimately what if I suggested that “understanding something” with huge vectors or monte carlo search is actually far deeper understanding than a few rules?

I am talking about the actual territory not the map. Yes the model is neat and tidy but the model is just simple enough so that humans can understand!

What if an AI can no more explain its solutions to a human than a human can explain human decisions to a cat?

That's like saying that causation doesn't matter; correlation will suffice. But the causal directionality of separating subject from object in a relation is essential to forming or sharing an idea usefully. In the synthetic game worlds you mention, causality is decided by play sequence. But at no point does the agent ever have to employ abstraction, or 'think about thinking', which diminishes the needed depth of thought greatly.

No, probability alone simply isn't expressive enough to support higher cognition. At best it will deliver a purely reactive agent, no more cognizant than Kahnemann's knee-jerk level of thinking.

Funny that you say that. David Hume said that you can’t meaningfully prove causation, only describe things and speak about about correlation.

Also time is a local phenemenon. You can’t simply compare A and B time if A and B are really far apart. When you get to really small scales you would be hard pressed to find which event happened before the other, so you get uncaused events like Virtual Particles in quantum mechanics.

And when you have tons of complexity then what do you mean by cause and effect instead of correlation?

https://www.quantamagazine.org/omnigenic-model-suggests-that...

I won't challenge Hume; I'm referring only to the fact that a causal relation implies necessity: B can't happen unless A acted to cause it. Probability can't provide this insight, it can only encourage or discourage it. The agent must formulate a mental model of the relation in order to hypothecate the presence of necessity / causality between a pair of events. A model that lacks that ability (e.g. probability) can lead to all sorts of nonsense in interpreting events, like proposing causality. Or at least meaning by connecting a baseball pitcher's hat color with the weather on game day.

BTW, precision isn't necessary for relative time to have great value in a huge fraction of possible world events. Obviously all you need is relative temporal sequence to disprove causality - since the batter can't hit until the pitcher throws.

In a great many event pairs, a lot of temporal precision Is unnecessary. Often it's only approximate relative time that matters, since the mental task intuits all the temporal constraints needed for understanding event coupling, like knowing the parent child relation implies the relative ages of each and much more latent info that may or not be relevant to a given interpretive task at hand.

And what I am saying is that when you say A implies B you’re making a ton of assumptions. If those assumptions are violated (eg all swans are white, all men are taller than all women) then suddenly you have caveats and hedges.

So what you actually use is not Propositional Logic / Boolean Algebra but Bayes’ Theorem. You only use rules of inference because you make assumptions.

I am saying that may work sometimes but those models are not exact.

In general, I agree that for avery complicated task that a machine intelligence performs far better than any human being, human-like reasoning might be just impossible. The logical formula might be too long to be reasonable to any human.

But from another side, current AI has a hard time to perform ordinary human reasoning at all. Those reasoning mostly contains a few logical clauses. Why?

Human like logic usually hide the common sense or context in other words. There is no absolute logic like FOL when we talk about human like logic. The traditional rule based AI system fails because of that.

On the other hand, deep learning are very strong at representing these hidden common sense and context. Look at the word2vec.

We now are at a point to combine these two approaches together not to build AlphaGo, but enable ordinary human like reasoning.

At least that is my hope.

The geometric approach is promising. I am working on a project that implements it. It is still a work in progress but things are moving along quite nicely. You can read more about IEML at https://pierrelevyblog.com/my-research-in-a-nutshell/the-bas...

The researcher, Prof. Levy, is French :)

> Maybe good AI requires a combination of symbolic approaches for the knowledge representation, deep parsing for NLP and semantics/discourse models, and machine learning for pattern recognition tasks of any kind.

I totally agree.

that's what we (Kyndi) think. Good AI requires ML, NLP, and KRR. ML to acquire the knowledge on which to reason, KRR to represent and reason, and NLP as the glue that holds everything together.