Laboric uncertainty is neither aleatoric nor epistemic

By Richard D. Lange ca. May 2026

A common refrain in both AI and theoretical neuroscience is that agents must deal with uncertainty. AI is interested in engineering effective agents and neuroscientists are interested in reverse-engineering the incredibly capable agent that is the human brain, so both disciplines engage with the idea of an "optimal" or "ideal" agent. As the usual story goes, a hypothetical optimal agent ought to use (or behave as if they are using) probability theory to make sense of the world and to make decisions. Put differently, "ideal" agents are supposed to follow the prescriptive rules set forth by Bayesian Decision Theory (BDT). Knowing about BDT is not essential to understanding anything else in this post. I mention it only because I want to convey the scope of the claims made by proponents of BDT and probability theory (of which I am sometimes one). Probability and BDT purport to characterize the optimal solution to all of sensing, decision-making, control, and learning. This is a big and broad-reaching framework! Further, the fact that this framework cuts across AI and neuroscience makes it quite appealing to those of us in the "NeuroAI" space seeking a common theoretical understanding of both bots and brains.

A taxonomy of different types of uncertainty

Say you agree with the premise that an "ideal" agent is uncertain about some things and their degree of uncertainty can/should influence their behavior. Two questions you might have are: what is the agent uncertain about, and why are they uncertain about it?

Let's survey a few visible sources and see what we find in the literature. A 2017 paper by Alex Kendall and Yarin Gal asks in its title, “What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?”. Their answer is aleatoric uncertainty and epistemic uncertainty. Kevin Murphy's popular 2012 textbook "Machine Learning: A Probabilistic Perspective" (and its 2022 updates) likewise categorizes uncertainty into aleatoric and epistemic types. The wikipedia article on uncertainty quantification lists a variety of sources of uncertainty, but ultimately falls back on these same two categories: aleatoric and epistemic. We could keep going and we would keep finding, with essentially no exceptions, that different authors all seem to agree on the why question: uncertainty arises due to alea and episteme. My main argument is that this list is incomplete and we ought to have terminology for a third kind of uncertainty.

Not all of these authors are talking about exactly the same thing. Differences between these authors' views is primarily a difference in the what question. If you are someone focused primarily on perception or inference problems, you will tend to think about the uncertainty an ideal agent has about the present state of the world given current sensory inputs. If you are instead someone focused primarily on learning problems, you will tend to think about uncertainty an ideal agent has about the parameters of their own internal model(s).

The what and why questions are distinct. You can have both aleatoric and epistemic kinds of uncertainty about either states or parameters. This is summarized in the following 2x2 table where what terms are along the rows and why terms are along the columns.

A brief introduction to aleatoric and epistemic flavors of uncertainty

The term aleatoric comes from the Latin word alea meaning dice or gambling. Some helpful word-associations are that we talk about aleatoric uncertainty when we talk about "randomness", "chance", "noise", etc. Aleatoric uncertainty is at play when we say

“I’m uncertain about XYZ because the process that generates it is inherently random.”

A direct translation of aleatoric uncertainty into the world of decision-making agents would be any situation where an agent is literally betting on the outcome of a random event like gambling on the roll of a die. It's perhaps unsurprising that such an agent ought to know something about probability to make good decisions. But aleatoric uncertainty is more general than literal random-prediction problems; it also matters for inference. A classic example in computer (and biological) vision is that, in low light, individual pixel values fluctuate due to thermal noise in the sensor and due to random timing of photons arriving at the sensor. This makes low-light images look "grainy": there is "noise" in the measurement itself. If the $\text{world}\to \text{image}$ process is itself inherently noisy, then an agent tasked with inferring $\mathrm{p}(\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{l}\mathrm{d}|\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{g}\mathrm{e})$ may be uncertain about the precise state of the world due to aleatoric reasons. This kind of uncertainty is sometimes called "objective" because random processes happen out there in the world, measurably, externally from the agent, and verifiable by a third party.

The term epistemic comes from the Greek word episteme meaning knowledge. Some word-associations for epistemic uncertainty include "ambiguity", "missing data", "occlusion", etc. Epistemic uncertainty is at play when we say

“I’m uncertain about XYZ because I’m lacking some disambiguating information”

A classic example from vision is occlusion. When one object blocks the view of another, we are uncertain about the details of the farther object. The tricky thing about epistemic uncertainty is that it often is resolved with a single correct answer. There is a particular occluded object with a particular identity and particular characteristics. We do not sense those properties but infer them. Someone looking at the same scene from a different perspective may possess that key "disambiguating information," so different agents will have different epistemic uncertainties simply in virtue of having different perspectives on the same scene. In this sense, and in contrast to aleatoric uncertainty being "objective," epistemic uncertainty is sometimes associated with the idea of "subjective probability." If you find it strange or counterintuitive to apply the language of probability to describe events that have a single well-defined correct answer, then suffice it to say that you are in good historical company. But thanks to the works of 20th century figures like de Finetti, Cox, and Jaynes (and probably many others I haven't read), we have a nice coherent mathematical theory establishing that any logical agent uses probability to calculate their subjective degree of belief about any ambiguous but non-random event. For a good introduction to this I highly recommend reading the first few chapters of Jaynes' book "Probability Theory: the Logic of Science."

Taking stock of the story so far, we have two types / two flavors / two answers to the "why" question of uncertainty:

1. Why #1: aleatoric uncertainty. Sometimes the world is "inherently random." Agents are then uncertain of things for aleatoric reasons. Probability is the language used to describe randomness, so ideal agents use probabilistic calculations to deal with aleatoric uncertainty.
2. Why #2: epistemic uncertainty. Sometimes the world is "ambiguous" from an agent's perspective but has a single well-defined state (or parameter value). For less obvious reasons, probability theory is again the tool of choice for ideal agents to reason about such situations.

Introducing "laboric" uncertainty

I argue that the above picture is incomplete and that there is a third kind of uncertainty besides aleatoric and epistemic. I'll call it "laboric" for now and attempt to defend this coinage, but I'll also sketch some other potential names below.

The earliest example I can find articulating that there is something missing in the classic story of probability theory is a 1967 paper by Ian Hacking title "Slightly More Realistic Personal Probability". ("Personal" and "Subjective" probability can be taken as synonymous here). The following examples illustrate the idea:

1. How certain are you that 1010101 is a prime number?
2. What about 1010105?

I don't know about you, but I would say that I am uncertain about whether 1010101 is a prime number upon first encountering this question. And this uncertainty is neither aleatoric nor epistemic! Nothing about this question involves randomness nor ambiguity. You know (I assume) what a prime number is. And you know what the number "1010101" is. Or perhaps you need me to clarify that this is in fact a base-10 number system (epistemic uncertainty about which number system we're using), but once that is resolved you still don't immediately know whether or not 1010101 is prime. With all noise and ambiguity removed, all that's left is the task of working out whether or not 1010101 is in fact prime. I, for one, cannot do that quickly in my head (perhaps without some tricks). But perhaps I know that most numbers are not prime, so after a moment's reflection I would say that I would be "willing to bet" that 1010101 is not prime, but I would not bet a ton of money on it. Compare this to the 1010105 example. One might quickly recognize that any number ending in '...5' must be divisible by 5 number and know for certain that it is not prime. After just a moment's consideration, I would be willing to bet quite a lot that 1010105 is not prime. I'm able to do this because I have a mental trick or shortcut that makes the calculation easy for the second case, but I can't apply that shortcut in the first case.

More generally, Laboric uncertainty is at play when we say

“I’m uncertain about XYZ because I haven’t the time/energy/resources to work it out.”

A moment's reflection should reveal that this kind of uncertainty is pervasive in all aspects of our lives. The prime number example illustrates that the act of doing some internal mental calculation can move something from ambiguity to certainty, and that even precise mathematical statements might be deemed "uncertain" by an agent who does not see the value in investing their precious resources (time, energy, etc) in working it out. Thus, not all logically-true statements are assigned probability 1 by an agent who is judiciously allocating their compute resources. So far this is only a very minor elaboration on the point made by Hacking back in 1967.

Importantly, this is not a restatement of Gödel's incompleteness theorem. The incompleteness theorem shows that there are true statements which are undecidable given arbitrarily large resources. An agent on a budget of "feasible" computation will be uncertain about even more things. For further ideas along these lines, I recommend reading Scott Aaronson's essay "Why philosophers should care about computational complexity." His essay makes the point that the distinction between feasible/infeasible computation can be as philosophically rich as the computable/incomputable distinction, and while philosophers have embraced the latter there is relatively little work engaging with the former.

Certainly not everything an agent does is a mathematical or logical test like finding the prime factors of integers. In fact I will concede that a negligible amount of what the human brain does is directly analogous to prime factorization. Let us pivot and consider the case for laboric uncertainty in visual perception. Try these two examples, and try to answer each in less than 1/4 of a second (start the timer when you first look at the image):

3. In the left image below, is the star on the interior or exterior of the closed curve?
4. What about the right image?

This is a classic test of visual reasoning. And if you are like most humans, you will find that the answer to the left image and right image are both clear (left: star is outside, right: star is inside), but that the left example requires a greater amount of 'mental effort.' The implication is that, just like the primality of 1010101 and 1010105, we are initially uncertain until we apply some effort. Further, there are 'hard' examples requiring processing (left squiggle, primality of 1010101) and there are 'easy' examples for which we can apply some shortcut to arrive at certainty quickly (right squiggle, primality of 1010105).

The other feature revealed by this example is that resource constraints are not just a matter of laziness. There may be externally-imposed time limits. Consider a self-driving car processing images from its many cameras and needing to decide within milliseconds if what it sees is a safety concern. We could just as easily talk about a human driver in a similar situation; in both cases there is a vehicle controlled by an 'agent', and that agent is under some serious time pressure to make sense of what they are sensing and make decisions. This time pressure means that they may be uncertain about things even if some slow-motion replay of the scene would make all relevant information clear and certain. Again, this uncertainty is not a matter of randomness nor of missing information: a car-driving agent may simply need time to process what they are seeing.

We can motivate the real-world impacts of laboric uncertainty outside of perceptual problems but staying in the realm of driving. I argue that I would be a better and safer driver if I had the ability to instantly plan and reroute. Planning a novel route through a familiar area involves some mental simulation and ruling out alternatives. It has happened to me before that I pull out of my neighborhood going one way only to realize I should have gone the other way. I might then take a longer route, make a u-turn, or otherwise make some maneuver to correct my mistake. Thankfully this has never caused any explicit harm, but applying this example at scale, I would feel safer in a world where all drivers have a clear and correct plan in mind before they get going than a world where u-turns and other course-corrections are commonplace. If only my mental planning had been instantaneous!

Imagine you are tasked with assessing the impact of uncertainty on human or AI car-driving safety. Applying the textbook definitions of uncertainty, you consider the impact of aleatoric factors (camera noise, weather conditions like rain, etc.) and epistemic factors (occlusion, novel objects, etc.), I'd argue that you would have formed an incomplete picture. Laboric uncertainty is a third kind of uncertainty that has practical impacts on the design and assessment of decision-making agents. But the field does not have a term for "uncertainty due to limited resources" or "uncertainty due to time pressure" or the like. There is value just in naming this third kind of uncertainty to make it part of the conversation. My pitch is "laboric"; some alternatives are mentioned below.

A note on probability and laboric uncertainty

Many students are taught that probability is the mathematical formalization for expressing and working with uncertainty. This is correct for aleatoric and epistemic uncertainty, but laboric uncertainty may be a different beast. An important point hiding in this framing is that uncertainty is fundamental, while probability is the tool we use to address it. Here's my best attempt at explaining the history and open problems here as I see them:

• The way an ideal agent handles aleatoric uncertainty is essentially by enumerating or counting possibilities. As mentioned above, when things are truly random, it is pretty unobjectionable to use probability theory to describe and weight possible states and possible outcomes. Kolmogorov formalized the axioms of probability from set theory and this kind of "enumerate/measure/count" perspective. In terms of using probability as an expression of uncertainty, this is the least objectionable of the three.
• The way an ideal agent handles epistemic uncertainty is trickier. What is the probability that there is another car approaching the intersection, hidden behind a truck? There either is or isn't, and it is at best awkward to think about "randomizing" infinitely many situations just like this one. This is the tension between "objective/subjective" probability or the tension between "frequentist/Bayesian" approaches to statistics. A celebrated set of results by Cox (which I learned about by reading Jaynes) and by Savage all point to a really interesting idea: you can arrive at a system that is equivalent to Kolmogorov's (i.e. probability theory), where the laws of probability are not axiomatic but are themselves derived from some other desiderata. Cox showed that an equivalent-to-probability system falls out of extending Aristotelian logic from mere "True/False" values to "plausible" values. Meanwhile, Savage (and de Finetti) showed that a "rational" agent whose behavior meets certain axiomatic conditions must behave as if reasoning with probability internally.

So, an agent can be uncertain for aleatoric reasons or for epistemic reasons, but in either case the rational/logical/ideal thing to do is to use the mathematical system of probability to express that uncertainty. This is an awfully convenient coincidence. It means we only need one mathematical system to express and reason about aleatoric and epistemic problems.

What about laboric uncertainty? The short answer is that this is an open problem (as far as my reading of the literature goes). We simply don't know if the "ideal" or "rational" way to handle laboric uncertainty is to enumerate weighted sets of outcomes. The trouble is that probability theory itself tacitly assumes that $p(x)$ , the "weight" assigned to some event $x$, is itself accessible to the agent. This is the problem pointed out by Hacking in 1967. A computationally bounded agent might only be able to compute some approximate weights $\tilde{p}(x)$ and who's to say that those approximate weights obey Kolmogorov's axioms? The answer seems to depend a lot on what $x$ is an what capabilities the agent has. It's a tricky problem.

Here's a concrete example, returning the the "planning" problem. It's well known that any game of perfect information (tic tac toe, chess, Go, othello, etc.) always has a "best" move from any board position. Not hard to find it for tic tac toe, but for more complex games like chess and go, what do our best game-playing bots do? They have a policy function which takes in the current game state and produces a probability distribution over actions. Planning algorithms like MCTS then invest computation to iteratively refine that probability distribution. Using our new terminology, MCTS is a computational process which reduces the agent's laboric uncertainty about what the best move is. So this is a system with entirely laboric uncertainty (the game state is provided unambiguously, the rules of the game are known perfectly) where state of the art methods express that uncertainty with a probability distribution in the form of a policy function. And yet, it is an open problem to prove that an ideal agent uses probability to solve problems such as this in the first place.

A nod to related ideas

A literature search for "bounded rationality" or "bounded optimality" or "satisficing" will turn up a trove of work from the 80s and 90s — roughly one to two major AI hype cycles ago — in which researchers grappled deeply with the problem of designing AI systems that get as close as possible to the BDT ideal on a limited computation budget. That perspective fell out of favor as neural networks took over and compute became cheap, but "metareasoning" is making a comeback now that compute is once again a limiting factor. There is a close connection between laboric uncertainty and metacognitive AI, which is a (re)emerging field.

By far the most relevant related work comes from a literature I didn't know existed until a reader pointed it out after this post first went up: "logical uncertainty." The mathematical roots go back to Gaifman's 1964 work on assigning probabilities to sentences of formal logic, and to Hacking's paper that I referenced above. The "logical uncertainty" label came out of the AI-alignment world in the 2010s — Demski's "Logical Prior Probability," and especially MIRI's Questions of Reasoning Under Logical Uncertainty and Logical Induction. Their motivating example echoes my prime-number exercise: you know a program, you don't know its output, and no amount of randomness is involved, only a lack of completed computation. This is fundamentally the same phenomenon: uncertainty due to not-yet-running-a-computation is a kind of laboric uncertainty, and it comes with sixty years of technical machinery (which I now get to read up on myself). What "logical uncertainty" it doesn't obviously do is generalize past the symbolic case, i.e. nobody has tried to make "is the star inside the curve" a question you answer with a logical inductor, and I don't think you'd want to. Concepts like time and resource constraints apply generally to all sorts of non-turing-machine entities like squishy biological neural circuits. So I'll say it this way: logical uncertainty is the deductive/symbolic special case of laboric uncertainty, worked out in far more formal detail than anything in this post, and laboric is my attempt at naming the bigger genus it belongs to — one that also covers perception and real-time control and more "biological" resource constraints.

Rate Distortion Theory gets at some of the underlying ideas of inference or decision-making on a resource budget, but the budget isn't always "resources" and the "distortion" isn't always framed as uncertainty. RDT is very useful for thinking about bounded optimality but isn't as general as I would like, and it's not part of the typical uncertainty-quantification story. Maybe an RDT expert can correct me here.

For steps toward formalizing laboric uncertainty itself, V-entropy and V-information from Xu et al.'s "A Theory of Usable Information Under Computational Constraints" is a good start. The very recent "epiplexity" paper also looks like it's reaching for something similar, though I confess I haven't had a chance to read it closely yet. I take further indirect inspiration from "Outcome Indistinguishability" (Dwork et al.), which frames randomness and probability as properties events have only relative to a particular, limited predictor — which is, when you say it out loud, a very laboric-sounding idea.

Alternative names

"Alea" comes from Latin and "Episteme" comes from Greek. So there is perhaps a Western classics tradition at play here and we should seek a Latin or Greek root for our new uncertainty-due-to-resource-limits. Good news! "Labor" is both Latin and English and can elicit ideas of "work" or "resources." There is also an argument to be made that English has replaced Latin and Greek as the global lingua franca, so a term coined in 2026 would be better coined in English than in the less-widely-known Latin and Greek. Fun fact: the tradition in biology of naming species in Latin seems esoteric to modern ears but began at a time when Latin was one of the most widely-understood languages in the world. So this is what I like about "laboric": it communicates the key idea in English, which is the default for science communication these days, but it also has a nod to the classical roots of alea and episteme.

Still, it's fun to think about some other classically-motivated terms. But I speak neither Latin nor Greek, so I cannot confidently stand behind these translations. Please get in touch if you have a correction (or a suggested term!)

• Mesonic uncertainty: from the Greek "mesos" meaning resource or the means to an end. I like the "means" connotation.
• Aergic uncertainty: Aergia is a character from mythology, the Greek personification of laziness. Also nice that "Aerg" sounds like "urge" or "erg" and therefore accidentally conveys some idea of effortfulness. But the trouble with 'laziness' is that it suggests a deliberate lack of work rather than a resource constraint.
• Socordic uncertainty: Socordia is to Latin what Aergia is to Greek.
• Kopocic uncertainty: Kopos is Greek for "work"
• Ignavic uncertainty: Ignavia is Latin for "sloth"
• Aporik uncertainty: from Greek aporia (being at a loss, blocked from the path forward), which has a nice philosophical pedigree and captures the sense of “I know the answer is out there, I just can’t reach it yet” (thanks to Ralf Haefner for this suggestion)