I'm pretty sure that the semantics of natural language are a lot more complex than can be accounted for by these seemingly very ad-hoc translations into comparatively straightforward FOL formulas, as are given in this paper. A common approach for the understanding of NL semantics from a strictly formal POV is Montague semantics https://en.wikipedia.org/wiki/Montague_grammarhttps://plato.stanford.edu/entries/montague-semantics/ - even a cursory look at these references is enough to clarify the level of complexity that's involved. Very loosely speaking one generally has to work with multiple "modalities" at the same time each of which, when understood from the POV of ordinary FOL, introduces its own separate notion of abstract "possible worlds" (representing, e.g. an agent's set of beliefs) and ways in which these "worlds" can relate to one another. More complex cases will usually degenerate in some sort of very generic "game semantics" https://en.wikipedia.org/wiki/Game_semanticshttps://plato.stanford.edu/entries/logic-games/ where any given use of natural language is merely seen as a "game" (in the abstract strategic, game-theoretical sense) with its own set of possibly very ad-hoc 'rules'. The philosopher Ludwig Wittgenstein https://en.wikipedia.org/wiki/Ludwig_Wittgensteinhttps://plato.stanford.edu/entries/wittgenstein/ gave quite a good description of both of these approaches (from a very naïve approach based on a supposedly straightforward translation to some kind of abstract logic, to a far richer one based on notions of strategies and games) to a "formal" understanding of natural language, throughout his extensive philosophical inquiry.
Which is to say, I'm not sure how this paper's results are generally expected to be all that useful in practice.
Your argumets and links are interesting, I hope to study these materials some day.
But.
To be useful in practice the approach does not need to work in all cases of natural language usage. Even if works in some limited cases there may be useful applications.
The authors evaluate their approach on two datasets. One is LOGIC consisting of learning examples of logical fallacies. The other is LOGICCLIMATE, consisting of logical fallacies collected from real world news articles about climate change.
So a possible practicle utility for the approach - spot individual wrong sentences in a long article and highlight them.
Another real world example. I propose a solution at work, based on some statistics. And a colleague dismisses it by saying that there is a book "6 Ways to Lie with Statistics". If there was a smart assistant in the room who gently explained his logical fallacy to the colleague, it would save a lot of efforts for me and made the discusdion more productive. I doubt the difficulties you mention apply to this simple case.
"And a colleague dismisses it by saying that there is a book "6 Ways to Lie with Statistics"."
Except, that's going in the right direction towards a better argument: empiricism requires your statistics to be peer reviewed for errors or deception before being believed. That takes a skilled individual.
So, you either think they're very good at statistics or you want them to put faith in your work. Otherwise, they need a smart assistant they trust to review the statistics. Then, they have increased confidence in your solution but it still might be wrong.
Maybe I’m missing something, but how is calling out every time a news article cites a government agency as an appeal to authority a list of logical fallacies?
I've worked on classical NLP models for quite some time, and this indeed looks way too simple to be of any practical use. If you mention Montague, I'm going to refer you to "Pedro owns a donkey," the poster kid sentence for Discourse Representation Theory. That's 1980s work, and for simple sentences it's already complicated beyond what the OP article suggests, and fails on anything remotely complex. I think it goes 2nd order the moment a complement is introduced (I think that ...).
And even if you can translate a sentence into a predicate, you haven't begun understanding what lies behind all those predicates. E.g., "Zelensky is ready to work under Trump's 'strong leadership' after 'regrettable' showdown." What good does it do to have that in FOP?
It looks like classic models of NLP semantics mostly punt on the "logical" point of view precisely due to these difficulties, and focus mostly on the more surface level problem of describing how each word of the source text correlates with a deeper description of the "meaning" of the text as a whole. So it is simply assumed that the meaning of the text as a whole must be derived compositionally from the meaning of each part (usually described by a somewhat ad-hoc "frame" structure), but exactly what that entails in a "logical" sense is left unspecified. UMR (Universal Meaning Representations) seems to be a typical example of such a system https://github.com/umr4nlp/umr-guidelines/blob/master/guidel... The expected use case seems to be something like building a common intermediate language for an automated translation system; individual meaning elements can then be "mapped" in a useful way, even across different languages, but there's not much interest apparently in "inferring" further knowledge from what one already has, or even on verifying that any given inference is valid (as proposed by OP).
Even beyond that you have a ton of pragmatics post-grice to deal with. Computing implicatures is complex and requires a lot of knowledge about context etc. The truth value of a statement and the 'truth value' of a speech act are pretty different things - not sure it's really feasible to convert between them.
Text that is written in Natural Language is open to interpretation. There are many formal statements that can be said to interpret a given Natural Language text. Can we determine which formal representation is correct? What about most useful?
The obvious answer to these questions is, "no". There is no such thing as a conclusive interpretation. If there was, then Natural Language wouldn't be ambiguous in the first place!
So we're all doomed to constantly misinterpret each other forever, right? No? We humans use Natural Language all the time, and usually figure out what the other person actually means!? How do we do it? Are we all just really good at guessing?
No, we have something better: context.
Context exists both in and around Natural Language text. Context determines which formal meaning is used to interpret the text. If we don't know which context is appropriate, there may be clues in the text itself that help us construct one that is useful or correct.
---
I've been trying to work out an approach to language processing that interprets text into logical formalisms (arbitrary meaning). I call them "Stories". A Story is an arbitrary interpretation of text. A Story is never conclusive: instead it is used as arbitrary context to interpret the next text. I call this process "Backstory".
We could even do the process backwards, and "write" an arbitrary formalism (meaning) in the same language/style/voice as a previously interpreted Story.
Given enough example instances of Story, we should be able to read and write to each other through explicitly shared context. I call this process "Empathizing". I call my idea the Story Empathizer.
I'm definitely out of my depth when it comes to the details, though...
I find humans have variation in ability for this as well though. Like some people need waaay more context, and need everything spelled out in granular detail to understand a topic, vs others who can more easily adapt, pick up clues and other relevant context information.
I don't think that's the reason it won't be very useful. I think there are two reasons it won't be very useful:
1. Most natural language arguments are not sound because the argument is not deductive logic. Most natural language arguments are persuasive, not formal reasoning.
2. Formal logic is method of preserving truth. It doesn't really create truth. That makes it a lot less useful. Critically, while a deductively valid argument has a true conclusion if all the premises are true, an invalid argument can still have a true conclusion. Formal logic, then, is very narrow.
This is why finding a logical fallacy in an argument is often not convincing by itself. It doesn't say "your logic is flawed therefore I am right". It says "your logic is flawed and therefore should be revised and improved."
> Most natural language arguments are not sound because the argument is not deductive logic. Most natural language arguments are persuasive, not formal reasoning
related notes that there is some evidence that
"Language is primarily a tool for communication rather than thought" [1]. ie, that language is neither necessary nor sufficient for the so-called psychic thinking process. It serves as a communication mechanism. Meanwhile, there is a hypothesis that the psychic thinking process lies beyond computation as we know it [2] in the form of turing machines etc.
One way to slightly mitigate the difficulties of nuance in language when translating to formal arguments is to attwmpt to always steelman the argument. Afford it all the guarded language and nuance you can, and then formalize in premises and conclusion.
This would also make interaction much more civil as well, given so much proclivity to do the opposite (straw man).
It's not a perfect approach, but it helps. LLMs are quite decent at steelmanning as well, because they can easiky pivot language to caveat and decorate with nuamce.
It could be useful for domains in which all or at least many problems are solvable (i.e., they can be stated and satisfied) with first-order logic.
It could also be useful as a lower-level component of general-purpose systems that internally rely on chains of thought computed by sub-component LLMs.
would be interesting if they had adversarial/null llms attempting the noisy nlp reductions as well. then one could make arguments about the sturdiness of the noisy bit.
It was Gottfried Leibniz who envisaged the end of philosophic disputes, replacing argument with calculation.
"if controversies were to arise, there would be no more need of disputation between two philosophers than between two calculators. For it would suffice for them to take their pencils in their hands and to sit down at the abacus, and say to each other (and if they so wish also to a friend called to help): Let us calculate."
I wonder if anyone else thought that that's how most of the world worked when they were a kid. I thought that most people would reason through everything, and if they couldn't, they would take it home as sort of homework and finish it there.
I wonder if Gödel’s incompleteness can somehow map to the map vs. territory distinction.
The impossibility to exhaustively and precisely put humanity in words, like the impossibility to have provably correct and complete model of reality, is like the impossibility to have a fully precise map.
The biggest danger is elevating the newly created map to the position of your new, much more simplistic, territory that supersedes the original one, with all of its quirks and fidelity.
I have a pet theory that most inefficiency is about self-consistency (or lack thereof), whether that's in human-human or human-machine communications (e.g. program code).
If only. Ethics are reached via consensus. Two calculators can indeed produce different results if the axioms supporting them differ.
And good luck calculating some of these axioms, such as "Why is it my duty not to kill someone?" You could argue, "Well in the end, a society enabling such behavior at scale would be no society at all," to which one might reply, "I have no interest in letting others do as I do.", and you can't calculate away violent sociopaths. The rest of us derive our principles from functioning mammalian emotional circuits, but at some level we rest our case on subjective axioms.
This is probably too big a topic for a whole side-branch on this, but modern meta-ethics teaches a range of possible approaches. Some notions of ethics are relativist, and are about the fact that moral norms are produced by some given society. But under some constructions that's just a procedural truism rather than a position on the content or the nature of morality itself.
Then you have moral realism, a perfectly respected position, which can encompass things like utilitariansim and other ism's. And this might seem silly derail, and I'm trying not to, but this is important at the end of the day, because "ethics is reached via consensus" can mean a lot of things that cash out with completely different practical implications. It's the difference between, for instance, deciding we need to be consensus oriented and vote, or be research oriented and concerned with deepening our scientific understanding of things like insect consciousness and whether the physical effects of sleep deprivation fall under the traditional definition of torture.
>And good luck calculating some of these axioms
Not wrong, they can easily get computationally intractable. So I think one has to account to some degree for uncertainty. Here again, I worry that the intended upshot is supposed to be that we simply give up or treat the project of moral understanding like a cosmically impossible non-starter. I like to think there's a middle ground between where we presently stand and the hypothetical future where we've got perfect knowledge.
Absolutely not! This is cultural relativism, and frankly, it would be circular: how exactly are we converging on a consensus if not from some preexisting sense of the good?
The only defensible objective basis for the good is the nature of a thing and what actualizes the potentials determined by that nature, thus actualizing the thing as the kind of thing it is. Morality, only possible for things that have the capacity to comprehend their options for action (intellect) and choose freely among them (will) on the basis of that understanding, therefore concerns the question of whether an act performed by a thing furthers or frustrates the actualization of that thing.
By cutting off my arm for no proportionate reason, I do an immoral thing, because it is my nature to have that arm, but if I have gangrene in that arm that threatens my life, then removing the gangrene with the undesirable side effect of losing an arm is morally justifiable, even if the loss of the arm is not good per se.
Murdering a human being is gravely immoral, because it directly contradicts my nature as a social human being in a very profound and profoundly self-destructive way. However, killing a would-be murderer in defense of my life or that of another is a morally very good deed; it is in accord with my social nature, and indeed can be said to actualize it more fully in some respect.
> The rest of us derive our principles from functioning mammalian emotional circuits
Please refrain from making such silly pseudoscientific and pseudophilosophical statements.
That being said, calculation is insufficient, because such calculation is formal: it explicitly excludes the conceptual content of propositions. But concepts are the material "carriers" of comprehension of what things are. We can also analyze concepts. Now, we can say that we can calculate a formal deduction according to formal rules, but we cannot calculate a concept or its analytical products. This is the produce of abstraction from concreta. Formal systems abstract from these. They are blind to conceptual content, on purpose. And having used a formalism to derive a conclusion, we must interpret the result, that is, we must reassign concepts to symbols that stand in for them. So formal systems are useful tools, but they are tools.
Well, we can have AI do what we do but it will never be tied to an emotion. You can feel a lot just adding 2+2 (maybe someone held a gun to your head once). What does philosophy say about philosophy without emotion? What use is it to us without our human context? The philosophy of a tiger is not relevant to me mostly because I don't feel most of the things a tiger feels.
Prolog has always had DCGs (Definite Clause Grammars) that allow you to write rules that resemble natural language grammar structures to parse and generate English sentences:
First order logic can only detect formal logic fallacies. Informal logic fallacies like ad hominem, strawman, red herring, etc. are cast in language. They can't me defined and resolved mathematically. The model should be fine tuned with examples of these informal fallacies and counter-arguments to them. Even so it won't be able to detect them in all cases, but it will at least have some knowledge about them and how to reply to them. This knowledge could be further be refined with in context learning and other prompt engineering strategies.
I would expect a true logical fallacy detector to take any natural text and spit out "unsupported assumption, unsupported assumption" over and over and over.
It sounds like the data set they use is designed to teach what logical fallacies are, which makes sense that it would do fine with it. I doubt this would do well against real-world language with things like structural ambiguity, anaphoric resolution, and dubious intent.
This is very cool and definitely a step in the right direction, however, the question remains where exactly this formalizing module should be placed in the stack. As an external api, it's clear that the model is not "thinking" in these logical terms, it just provides a translation step. I'd argue it would be better placed during inference test-time compute (as seen in these so-called reasoning models). Better yet, this formalizing step would happen at a lower level entirely, internal to the model, but that would probably require totally new architectures.
Turning English into logic basically requires understanding the language and context.
I’d you are told “we will go to the zoo or swimming pool tomorrow, if it is windy or rainy”, most readers would know the first or is exclusive (we aren’t going to both), while the second is inclusive (we will go if it is windy, rainy, or both).
This is annoying when teaching logic, from experience.
The most probable logical interpretation of a phrase, not looking at context, might not be correct.
Even something as simple as sarcasm breaks this idea, and you can have full books of metaphor that only make sense if you understand the cultural context in which they were written.
Readit News
Which is to say, I'm not sure how this paper's results are generally expected to be all that useful in practice.
But.
To be useful in practice the approach does not need to work in all cases of natural language usage. Even if works in some limited cases there may be useful applications.
The authors evaluate their approach on two datasets. One is LOGIC consisting of learning examples of logical fallacies. The other is LOGICCLIMATE, consisting of logical fallacies collected from real world news articles about climate change.
The datasets are here, if anyone is interested to see the type of natural language they try to adress currently: https://github.com/causalNLP/logical-fallacy
I guess this csv contains the LOGICCLIMATE: https://github.com/causalNLP/logical-fallacy/blob/main/data/...
So a possible practicle utility for the approach - spot individual wrong sentences in a long article and highlight them.
Another real world example. I propose a solution at work, based on some statistics. And a colleague dismisses it by saying that there is a book "6 Ways to Lie with Statistics". If there was a smart assistant in the room who gently explained his logical fallacy to the colleague, it would save a lot of efforts for me and made the discusdion more productive. I doubt the difficulties you mention apply to this simple case.
Except, that's going in the right direction towards a better argument: empiricism requires your statistics to be peer reviewed for errors or deception before being believed. That takes a skilled individual.
So, you either think they're very good at statistics or you want them to put faith in your work. Otherwise, they need a smart assistant they trust to review the statistics. Then, they have increased confidence in your solution but it still might be wrong.
Did a worse one get picked?
Did you already have a solution in place, and you were actually suggesting a change?
And even if you can translate a sentence into a predicate, you haven't begun understanding what lies behind all those predicates. E.g., "Zelensky is ready to work under Trump's 'strong leadership' after 'regrettable' showdown." What good does it do to have that in FOP?
[1] https://plato.stanford.edu/archIves/sum2011/entries/discours...
The obvious answer to these questions is, "no". There is no such thing as a conclusive interpretation. If there was, then Natural Language wouldn't be ambiguous in the first place!
So we're all doomed to constantly misinterpret each other forever, right? No? We humans use Natural Language all the time, and usually figure out what the other person actually means!? How do we do it? Are we all just really good at guessing?
No, we have something better: context.
Context exists both in and around Natural Language text. Context determines which formal meaning is used to interpret the text. If we don't know which context is appropriate, there may be clues in the text itself that help us construct one that is useful or correct.
---
I've been trying to work out an approach to language processing that interprets text into logical formalisms (arbitrary meaning). I call them "Stories". A Story is an arbitrary interpretation of text. A Story is never conclusive: instead it is used as arbitrary context to interpret the next text. I call this process "Backstory".
We could even do the process backwards, and "write" an arbitrary formalism (meaning) in the same language/style/voice as a previously interpreted Story.
Given enough example instances of Story, we should be able to read and write to each other through explicitly shared context. I call this process "Empathizing". I call my idea the Story Empathizer.
I'm definitely out of my depth when it comes to the details, though...
1. Most natural language arguments are not sound because the argument is not deductive logic. Most natural language arguments are persuasive, not formal reasoning.
2. Formal logic is method of preserving truth. It doesn't really create truth. That makes it a lot less useful. Critically, while a deductively valid argument has a true conclusion if all the premises are true, an invalid argument can still have a true conclusion. Formal logic, then, is very narrow.
This is why finding a logical fallacy in an argument is often not convincing by itself. It doesn't say "your logic is flawed therefore I am right". It says "your logic is flawed and therefore should be revised and improved."
related notes that there is some evidence that "Language is primarily a tool for communication rather than thought" [1]. ie, that language is neither necessary nor sufficient for the so-called psychic thinking process. It serves as a communication mechanism. Meanwhile, there is a hypothesis that the psychic thinking process lies beyond computation as we know it [2] in the form of turing machines etc.
[1] https://www.nature.com/articles/s41586-024-07522-w [2] https://www.amazon.com/Emperors-New-Mind-Concerning-Computer...
This would also make interaction much more civil as well, given so much proclivity to do the opposite (straw man).
It's not a perfect approach, but it helps. LLMs are quite decent at steelmanning as well, because they can easiky pivot language to caveat and decorate with nuamce.
It could also be useful as a lower-level component of general-purpose systems that internally rely on chains of thought computed by sub-component LLMs.
"if controversies were to arise, there would be no more need of disputation between two philosophers than between two calculators. For it would suffice for them to take their pencils in their hands and to sit down at the abacus, and say to each other (and if they so wish also to a friend called to help): Let us calculate."
Deleted Comment
- Kurt Gödel
The impossibility to exhaustively and precisely put humanity in words, like the impossibility to have provably correct and complete model of reality, is like the impossibility to have a fully precise map.
The biggest danger is elevating the newly created map to the position of your new, much more simplistic, territory that supersedes the original one, with all of its quirks and fidelity.
And good luck calculating some of these axioms, such as "Why is it my duty not to kill someone?" You could argue, "Well in the end, a society enabling such behavior at scale would be no society at all," to which one might reply, "I have no interest in letting others do as I do.", and you can't calculate away violent sociopaths. The rest of us derive our principles from functioning mammalian emotional circuits, but at some level we rest our case on subjective axioms.
This is probably too big a topic for a whole side-branch on this, but modern meta-ethics teaches a range of possible approaches. Some notions of ethics are relativist, and are about the fact that moral norms are produced by some given society. But under some constructions that's just a procedural truism rather than a position on the content or the nature of morality itself.
Then you have moral realism, a perfectly respected position, which can encompass things like utilitariansim and other ism's. And this might seem silly derail, and I'm trying not to, but this is important at the end of the day, because "ethics is reached via consensus" can mean a lot of things that cash out with completely different practical implications. It's the difference between, for instance, deciding we need to be consensus oriented and vote, or be research oriented and concerned with deepening our scientific understanding of things like insect consciousness and whether the physical effects of sleep deprivation fall under the traditional definition of torture.
>And good luck calculating some of these axioms
Not wrong, they can easily get computationally intractable. So I think one has to account to some degree for uncertainty. Here again, I worry that the intended upshot is supposed to be that we simply give up or treat the project of moral understanding like a cosmically impossible non-starter. I like to think there's a middle ground between where we presently stand and the hypothetical future where we've got perfect knowledge.
Absolutely not! This is cultural relativism, and frankly, it would be circular: how exactly are we converging on a consensus if not from some preexisting sense of the good?
The only defensible objective basis for the good is the nature of a thing and what actualizes the potentials determined by that nature, thus actualizing the thing as the kind of thing it is. Morality, only possible for things that have the capacity to comprehend their options for action (intellect) and choose freely among them (will) on the basis of that understanding, therefore concerns the question of whether an act performed by a thing furthers or frustrates the actualization of that thing.
By cutting off my arm for no proportionate reason, I do an immoral thing, because it is my nature to have that arm, but if I have gangrene in that arm that threatens my life, then removing the gangrene with the undesirable side effect of losing an arm is morally justifiable, even if the loss of the arm is not good per se.
Murdering a human being is gravely immoral, because it directly contradicts my nature as a social human being in a very profound and profoundly self-destructive way. However, killing a would-be murderer in defense of my life or that of another is a morally very good deed; it is in accord with my social nature, and indeed can be said to actualize it more fully in some respect.
> The rest of us derive our principles from functioning mammalian emotional circuits
Please refrain from making such silly pseudoscientific and pseudophilosophical statements.
That being said, calculation is insufficient, because such calculation is formal: it explicitly excludes the conceptual content of propositions. But concepts are the material "carriers" of comprehension of what things are. We can also analyze concepts. Now, we can say that we can calculate a formal deduction according to formal rules, but we cannot calculate a concept or its analytical products. This is the produce of abstraction from concreta. Formal systems abstract from these. They are blind to conceptual content, on purpose. And having used a formalism to derive a conclusion, we must interpret the result, that is, we must reassign concepts to symbols that stand in for them. So formal systems are useful tools, but they are tools.
https://www.metalevel.at/prolog/dcg
These aren’t logically incorrect, people who study rhetoric have just identified these as common patterns of poor persuasion.
But I don't see a pretrained model in there, so I'm not sure what to pass as `your_nli_model_name`:
It would have been a lot cooler if this was set up as a pretrained model using RL to translate.
https://github.com/lovishchopra/NL2FOL/blob/4635a81f216da2ad...
I’d you are told “we will go to the zoo or swimming pool tomorrow, if it is windy or rainy”, most readers would know the first or is exclusive (we aren’t going to both), while the second is inclusive (we will go if it is windy, rainy, or both).
This is annoying when teaching logic, from experience.
Even something as simple as sarcasm breaks this idea, and you can have full books of metaphor that only make sense if you understand the cultural context in which they were written.