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Task Teory

What it is	A systematic framework for describing, comparing, and analyzing tasks, independent of any specific agent. Provides the foundations for evaluating intelligent systems empirically (measurable outcomes, repeatable experiments, controlled variables).
Purpose	In AI today, evaluation is benchmark-driven (ImageNet, Atari, Go) but lacks a unifying science. Task theory proposes such a foundation: comparable to physics for engineering. It lets us treat tasks as objects of study, enabling systematic experimentation in Empirical Reasoning Systems (ERS).
Task vs. Environment	A Task is a desired transformation of the world (e.g., get ball into goal). The Environment is the context where variables evolve. Together: ⟨Task, Environment⟩. In ERS, this separation allows us to ask: what is the structure of the problem? before asking how the agent solves it.
Agent Separation	Describing tasks independently of the agent prevents conflating “what is to be achieved” with “who/what achieves it.” This is central for ERS: it allows us to evaluate reasoning systems across different domains and agents.
Why Important	Enables: (1) Comparison of tasks across domains; (2) Abstraction into task classes; (3) Estimation of resource needs (time, energy, precision); (4) General evaluation of reasoning systems, beyond one-off benchmarks.
Example Analogy	In physics, wind tunnels test many airplane designs under the same controlled conditions. In ERS, task theory plays a similar role: controlling task variables so that reasoning systems can be compared fairly.

Task: How it Hangs Together

T: A Task	T = { G, V, F, C }
G: Goal	Set of desired states or outcomes. Goals define what counts as “success” from the observer’s perspective. Example: robot reaches waypoint within 1m tolerance.
V: Variables	V = { v₁, v₂, … }. Measurable and manipulatable aspects of the environment relevant to the task. Observer defines these formally (e.g., position, temperature); agent may only have partial/noisy access.
F: Transformation Rules	Describe how variables evolve (physics, rules of a game, causal dynamics). These are objective world relations, available in principle to the observer. Agents must infer or approximate them.
C: Constraints	Boundaries of what is possible (time, energy, error bounds, resource limits). Again, observer’s perspective = formal definition; agent’s perspective = experienced as difficulty or failure when limits are exceeded.
Simple Task	Few variables, deterministic (press a button).
Complex Task	Many variables, uncertainty, multi-step (cooking, multi-agent negotiation).

Intricacy & Difficulty

Intricacy (Observer)	Structural complexity of a task, derived from number of variables, their couplings, and constraints in {V, F, C}. Defined independently of the agent (Eberding 2021).
Effective Intricacy (Agent)	How complicated the task appears to an agent, given its sensors, prior knowledge, reasoning, and precision. For a perfect agent, effective intricacy → 0.
Difficulty	A relation: Difficulty(T, Agent) = f(Intricacy(T), Agent Capacities). Same task can be easy for one agent, impossible for another.
Example	Catching a ball: Observer sees physical intricacy (variables: position, velocity, gravity, timing). Agent: a human child has low effective intricacy after learning; a simple robot has very high effective intricacy.
Connection to ERS	Difficulty is the bridge between objective task description (for observers) and empirical performance measures (for agents). ERS requires both views: tasks must be defined in the world (observer) but evaluated through agent behavior.

Dimensions of Task Environments (Thórisson et al., 2015)

Determinism	Whether the same action in the same state always leads to the same result (deterministic) or whether outcomes vary (stochastic).
Ergodicity	The degree to which all relevant states can in principle be reached, and how evenly/consistently they can be sampled through interaction.
Controllable Continuity	Whether small changes in agent output produce small, continuous changes in the environment (high continuity) or abrupt/discontinuous ones (low continuity).
Asynchronicity	Whether the environment changes only in response to the agent (synchronous) or independently of it, on its own time (asynchronous).
Dynamism	Extent to which the environment changes over time without agent input; static vs. dynamic worlds.
Observability	How much of the environment state is accessible to the agent (full, partial, noisy).
Controllability	The extent to which the agent can influence the environment state; fully controllable vs. only partially or weakly controllable.
Multiple Parallel Causal Chains	Whether multiple independent processes can run in parallel, influencing outcomes simultaneously.
Number of Agents	Whether there is only a single agent or multiple agents (cooperative, competitive, or mixed).
Periodicity	Whether the environment exhibits cycles or repeating structures that can be exploited for prediction.
Repeatability	Whether experiments in the environment can be repeated under the same conditions, producing comparable results.

Why Task Theory Matters for Empirical Reasoning

For Science (Observer)	Provides systematic, measurable, repeatable description of tasks — necessary for empirical study of reasoning systems. Comparable to controlled experiments in physics or biology.
For Engineering (Agent & System Design)	Allows construction of benchmarks that measure generality (performance across task classes), not just single skills. Supports systematic curricula for training agents.
For Empirical Evaluation (ERS Core)	Clarifies whether failure is due to the task (high intricacy, under-specified goals) or the agent (limited sensors, reasoning). Enables falsifiable claims about system capability.
Reflection	In ERS, intelligence boils down to: Given a formally defined task, how well does an agent reason about it empirically, under uncertainty and constraints? Task theory provides the shared language to answer this.

Discussion Prompts

Question	Observer Angle	Agent Angle
————	—————–	————–
How is a “task” different from a “problem” in classical AI?	Problem = symbolic puzzle; Task = measurable transformation in a world	Must act in the world to achieve it
Why must tasks be agent-independent?	To compare systems systematically	Otherwise evaluation collapses into “how this agent did”
Can you think of a task with low intricacy but high difficulty for humans?	Observer: low variable count	Agent: limited memory/attention makes it hard (e.g., memorizing 200 digits)
What role does causality play in defining tasks?	Observer: rules F define dynamics	Agent: must infer/approximate causal relations from data
How does a variable-task simulator (like SAGE) help ERS?	Observer: controls task parameters systematically	Agent: experiences wide range of tasks, supports empirical generality tests

Center for Analysis and Design of Intelligent Agents

Table of Contents

Task Teory

Task: How it Hangs Together

Intricacy & Difficulty

Dimensions of Task Environments (Thórisson et al., 2015)

Why Task Theory Matters for Empirical Reasoning

Discussion Prompts