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.
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.
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.
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?
https://en.m.wikipedia.org/wiki/Heterophenomenology
In this framework, utterances can be studied without taking their truth value at face value.
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.
There is a direct trade-off between the expressiveness of your representation and your ability to reason about it.
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.
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.
There is ambiguity in natural languages so the determination of underlying meaning is at best probabilistic, but we have ways of handling that too.
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 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.
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'.
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.
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?
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.
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.
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...
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.
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.
The researcher, Prof. Levy, is French :)
I totally agree.
The currently trendy "AI" looks more like massive data mining with powerful ML to me, that's very good for certain tasks but brings us nowhere near real AI. The knowledge representation problem has not yet been solved. In order to get even just a convincing simulation of AI, let alone real AI, we need a large common sense knowledge base / computational ontology.
One perhaps promising approach are geometric meaning theories/concept representations that allow for logical combinations. For example, Diederik Aerts works in this area. However, to be honest, I don't have the math skills to evaluate his approach. Generally speaking, logical modelling is too limited for good concept representations - especially classical 90s AI like in default reasoning and other nonmonotonic logics -, whereas traditionally geometric representations suffer from problems with representing logical inference and quantification. IMHO, that's a problem worth looking at. (Admittedly, I'm a bit biased towards symbolic AI like the people in this article.)