Position: Reasoning is a Learnable Rule-Based Process

Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: Next we'll be talking about the paper "Position: Reasoning is a Learnable Rule-Based Process".

Jane: The paper was written by Rachel Lawrence and Jacqueline Maasch from Microsoft Research and Cornell Tech.

Tom: Stay tuned as we take you through the paper and discuss its implications.

Jane: We also have Lu with us today — senior AI researcher at Tsinghua.

Tom: We also have Meng with us today — lead engineer at a mysterious AI startup.

Jane: We also have Lalam with us today — the in-house Large Language Model.

Tom: Alright, let's get started.

Title: Tom: Welcome back to the show, everyone. Today we're digging into a paper that's got a title that just grabs you: "Position: Reasoning is a Learnable Rule-Based Process." Jane, I have to say, just reading that title got me thinking—are we about to see a big fight between the old-school symbolic folks and the modern deep learning crowd?

Jane: Oh, absolutely, Tom. And that's exactly why I love this one. The paper is basically saying, "Hey, we've been arguing about what reasoning even *is* for years, and that's a problem." They're not trying to pick a side in the symbolic-versus-neural war. Instead, they're saying we need a clear, operational definition so we can actually measure progress. It's a position paper, so it's less about new experiments and more about setting the rules of the game.

Tom: Right, and they lay out three core theses right up front. The first one is basically "define, then measure." You can't just say a model is good at reasoning if you haven't told me what you mean by reasoning. It sounds obvious, but in practice, a lot of papers just throw the word around.

Jane: Exactly. And their second thesis is the big one: reasoning is a learnable rule-based process. So they're saying it's not just an output, like a correct answer on a test. It's the *process* of selecting and applying rules to your beliefs and evidence. And crucially, they say those rules can be learned, not just hard-coded by a human.

Tom: That's the bridge, isn't it? It makes the definition friendly to modern machine learning, not just to old-school logic programming. And then the third thesis is about validity—that a reasoning process is valid if it follows the rules exactly, regardless of whether the rules themselves are "good" or lead to a true answer.

Jane: Which is a really important distinction. You can have a perfectly valid reasoning process that starts from false premises and ends up with a false conclusion. That's not sound reasoning, but it's still valid in the formal sense. The paper spends a lot of time on that difference, and I think it's crucial for how we evaluate these big language models.

Tom: And that's where they introduce this fun concept of the "reasoning zombie"—a system that talks like it's reasoning but doesn't actually have the internal mechanism to back it up. It's a nod to the philosophical zombie idea, but for reasoning instead of consciousness.

Jane: I love that. It's a really concrete way to think about the problem. We can't just look at a model's output and assume it reasoned to get there. It might have memorized the answer, or guessed, or found a statistical shortcut. The paper is pushing us to look under the hood.

Tom: So, Lu, you've been quiet. What's your gut reaction to this framing? Is this the kind of definition that could actually stick?

Lu: I think it's a very brave attempt, Tom. The authors are trying to unify a lot of history—from Aristotle's syllogisms to modern Bayesian inference—under one umbrella. The fact that they can map things like reinforcement learning and even simple n-gram models into their framework is a testament to its flexibility. But that flexibility is also its biggest challenge. If everything is reasoning, does the word lose its meaning?

Tom: That's a great point to hold onto. Let's keep that in mind as we dig into the actual definition they propose.

Summary: Jane: So, we've set the stage with the title and the big theses. Now let's get into the meat of the paper, which is their formal definition. Tom, you want to take a crack at explaining it in plain English?

Tom: I'll try. They define a "state" as a snapshot of everything the reasoner knows at any given moment. That includes its current beliefs, all the evidence it has gathered, and the set of rules it has available. Reasoning, then, is the process of applying those rules to the beliefs and evidence to create a new state. And you do that over and over again until you hit a stopping rule, which is usually your goal.

Jane: And the key part is that they split the rules into two types. There are "local rules" that update your beliefs, and "meta rules" that update your other rules. So the system can literally learn new rules on the fly. That's the "learnable" part of the title. It's not a static system; it can revise its own playbook.

Lu: And that's a really elegant way to capture how modern AI works. You can think of the local rules as the model's forward pass, and the meta rules as the training algorithm that updates the weights. The paper is essentially providing a mathematical language that can describe both a simple calculator and a massive neural network.

Meng: But here's where I start to get a little skeptical. They talk a lot about "exact rule application." In a symbolic system, that's easy to verify. You run the code, you see the steps. But in a neural network, how do you even know what the "rules" are? They're buried in millions of parameters. The paper acknowledges this, but it feels like a huge gap between the theory and the practice.

Jane: That's a fair pushback, Meng. And the paper doesn't really solve that problem. But what it does do is give us a target. It says, "If you want to claim your model is reasoning, you need to be able to point to the rules and show they're being applied exactly." For a neural network, that's a really high bar, and maybe that's the point.

Tom: They even give a concrete example with a trivial Python implementation to show how the definition works in practice. It's a simple logical reasoning task, but it demonstrates how you can audit the process and check for validity. It's a proof of concept that the definition isn't just philosophical hand-waving.

Lu: And that's what I find most valuable. The paper is essentially a call to action for the community to stop treating reasoning as an undefined buzzword. They're saying, "Here's a framework. Let's argue about it, refine it, and use it to build better evaluation benchmarks." The construct validity problem is real—if we don't know what we're measuring, our benchmarks are meaningless.

Meng: So, practically speaking, this would mean that a benchmark like "GSM8K" or "ARC" would need to be redesigned to not just check the final answer, but to verify the *process* used to get there. That's a massive undertaking.

Jane: Exactly. And it connects back to their point about chain-of-thought. They argue that CoT traces are not trustworthy explanations because they might not reflect the actual internal process. A model could generate a convincing-looking reasoning trace without actually following those steps internally. So, we need better tools to look inside the black box.

Tom: And that brings us to their concept of the "reasoning zombie" again. It's not just a thought experiment. They argue that imperfect versions of these zombies already exist in the wild. Models that get the right answer on benchmarks but are actually just doing sophisticated pattern matching.

Lu: The paper suggests that we need to be very careful about when we actually *need* a true reasoner, and when a "zombie" is good enough. For a chatbot recommending a recipe, a zombie is fine. For a system making medical decisions, you absolutely need validity guarantees.

Meng: So, the next question is, what are they actually proposing we do about it? They have a checklist, right?

Improvements: Jane: Right, Meng. The paper doesn't just stop at the definition. It includes a whole checklist for best practices in AI reasoning research. It's like a code of conduct for anyone who wants to publish a paper claiming their model can reason.

Tom: And it's pretty thorough. The first section is all about defining your terms. You have to explicitly state what the rules, beliefs, and evidence are in your specific system. You can't just say "we used a transformer." You have to say, "In this setting, the rules are the learned weights, the beliefs are the hidden states, and the evidence is the input tokens."

Meng: That's a high bar, but it's the right one. It forces researchers to be honest about what their model is actually doing. The second section is about validity. You have to prove that your transitions from one state to the next are the result of exact rule application. That's where the rubber meets the road for neural networks.

Lu: And the checklist also addresses the evaluation itself. It says you need to justify the construct validity of your benchmark. You can't just say "this dataset tests reasoning." You have to explain *why* it tests reasoning according to your operational definition. This is a direct challenge to the current culture of just throwing a new dataset out there and calling it a reasoning benchmark.

Tom: There's also a big emphasis on not conflating the process with the product. Getting the right answer on a math problem is not the same as reasoning. The checklist forces you to separate those two things and evaluate them independently.

Jane: And it goes further, into the realm of communication. It says researchers should be clear about the limitations of their systems and avoid overhyping their results. That's a direct jab at the trend of press releases saying "AI achieves human-level reasoning" when the model just did well on a specific test.

Meng: So, this isn't just a theoretical exercise. This is a practical tool. If journals and conferences adopted this checklist as a requirement, it would fundamentally change how research is done. It would slow things down, but it would make the results much more trustworthy.

Lu: And that's the core of their argument. They're not saying "don't build big models." They're saying "if you're going to claim your big model reasons, you need to be able to show your work." It's about moving from a culture of "show me the accuracy" to "show me the mechanism."

Tom: They even bring up the example of Lean, the formal theorem prover. It provides a gold standard for what valid reasoning looks like because every step is formally verified. The paper isn't saying every AI system needs to be like Lean, but it's saying that if you're in a domain where correctness is critical, you should be aiming for that level of rigor.

Jane: And that's where the "learnable" part becomes so powerful. You don't have to hand-code all those rules like they did in the old expert systems. You can learn them from data, but then you need to verify that they're being applied correctly. The paper is essentially proposing a hybrid approach where you get the flexibility of deep learning and the verifiability of symbolic systems.

Meng: So, the checklist is a roadmap for building what they call "validity by design." Instead of trying to retroactively explain a black box, you build the system so that its reasoning steps are auditable from the start.

Tom: And that's a really compelling vision. It's not about going back to the 1980s. It's about taking the best of both worlds and creating a new standard for what it means to be a trustworthy AI system.

Conclusion: Jane: Well, we've had a fantastic discussion today about "Position: Reasoning is a Learnable Rule-Based Process." We started with the problem of definitional ambiguity, and we're ending with a concrete proposal for how to fix it.

Tom: That's right. The paper gives us three core ideas to take home. First, we need to define reasoning before we can measure it. Second, we should think of reasoning as a process of applying learnable rules, not just as an output. And third, validity comes from following those rules exactly, even if the rules themselves are flawed.

Lu: And the most impactful part for me is the checklist. It's a practical tool that could really change the field. It forces researchers to be explicit about their assumptions and to justify their evaluation methods. It's a push for more rigorous, more trustworthy science.

Meng: I agree. It's a high bar, but it's a necessary one. If we're going to deploy these systems in critical domains like healthcare or law, we need to know that they're not just clever parrots. We need to know they're actually following rules.

Jane: And that brings us back to the "reasoning zombie" concept. The paper warns us that we might already have these zombies among us, and we need to be able to tell them apart from true reasoners. That's not just an academic exercise; it's a matter of public safety and trust.

Tom: So, as we say goodbye to this paper, I think the biggest takeaway is a call to action. The authors are urging the community to engage with their definitions, to argue with them, to refine them. They don't claim to have the final answer, but they're providing a starting point for a much-needed conversation.

Jane: And that's what makes this paper so exciting. It's not the end of the story; it's the beginning of a new chapter. It's a challenge to all of us to be more rigorous in how we talk about and build AI reasoning.

Tom: Well said, Jane. That's all the time we have for this one. Thanks to Lu and Meng for joining us, and to all our listeners out there. We'll be back soon with another paper, but for now, this is Tom and Jane signing off.