The Syntax and Semantics of Goals: A New Perspective on Goal Representation in Cognitive Science

Cognitive science and computer science have long treated "goals" as central cognitive states that organize and guide purposeful behavior. A new paper on arXiv, The Syntax and Semantics of Goals, proposes an illuminating analytical framework: rather than treating goals merely as constraints on behavior, we should understand them as representations with syntactic and semantic structure. This perspective connects goal research to classical problems in linguistics and logic, and opens up new avenues for discussing goal design in intelligent systems.

Why Goals Are a Form of "Representation"

In traditional understanding, a goal is a cognitive state that combines flexibly with world knowledge to generate purposeful behavior. The paper emphasizes that goals are fundamentally compositional representations — their content is directly relevant to rational behavior. In other words, goals are not isolated signals; like sentences in a language, they are built from more basic components according to certain rules.

This framing matters. When we treat goals as representations, we must ask: what is their "content," how is it encoded, and what are the differences between different encodings? This closely parallels the linguistic distinction between "syntax" (how form is organized) and "semantics" (what meaning that form points to). The authors draw on precisely this pair of concepts to analyze the form and meaning of goals.

The Syntax-Semantics Interface Analogy

The most insightful contribution of the paper is mapping goal research onto the syntax-semantics interface from linguistics and logic. In linguistics, the same meaning can be expressed by different syntactic structures, and syntactic structures have expressive limits. Goals are no different.

The Question of Expressiveness

The authors point out a question worth asking: is a given "goal language" expressive enough to characterize the behaviors we care about? If a goal representation cannot describe a certain type of behavior, then no matter how intelligent the agent, it cannot set that behavior as a goal. This is directly relevant to the choice of goal specification language in intelligent systems design.

The Question of Equivalence

Another question is whether different goal representations might characterize the same behavior. This is analogous to different logical formulas being semantically equivalent. If two formally distinct goals lead to identical rational behavior, they are equivalent at the semantic level. Distinguishing form from meaning helps us identify which differences are substantive and which are merely notational redundancy.

The syntax-semantics interface is a central topic in formal linguistics and logic, concerned with how formal structures map to meaning. The syntactic level focuses on rules for arranging symbols and structural relationships (e.g., parse trees, derivation rules), while the semantic level concerns how these structures are interpreted in models or in the world (e.g., truth conditions, referents). Two syntactically distinct expressions may share the same semantics (e.g., active and passive sentences), while a single syntactic structure may admit multiple semantic readings (ambiguity). Applying this interface to goal research means we must examine both how a goal is "written" (in what language or logical formula) and what it "means" (what actual behavioral constraints that representation imposes) — rather than conflating the two. This is the theoretical prerequisite for avoiding distortions in goal specification.

From Constraints to a Design Space

Goals have traditionally been viewed as fixed entities that impose constraints on desirable behavior. The paper proposes an inversion: we can also study constraints on goal representations themselves.

This means goals are no longer an isolated given, but are situated within a larger design space. Different goal representations involve trade-offs among expressiveness, designability, and computational efficiency: some representations are concise but limited in expressiveness, while others are highly expressive but computationally expensive. The authors synthesize several bodies of work characterizing different properties of goal representations, treating them as distinct coordinates within this design space.

For AI systems, this framework has practical implications. Whether it's reward functions in reinforcement learning, goal conditions in planning systems, or instruction-following in large language models, all of these fundamentally involve choosing a goal representation. Understanding the formal and semantic properties of these representations helps avoid the pitfall of "seemingly specifying a goal while failing to capture the true intent."

In AI, concrete forms of goal representation span multiple technical paradigms: reinforcement learning uses scalar reward functions or reward shaping; classical planning uses first-order logic languages like PDDL to describe goal states; inverse reinforcement learning (IRL) attempts to infer goals from behavior; and the era of large language models has introduced natural language instructions as a new form of goal. Each form has its expressive limits — for example, linear reward functions cannot capture certain non-Markovian goals, while natural language goals are flexible but difficult to formally verify. The "design space" framework proposed in the paper aims to provide a unified basis for comparing these heterogeneous goal representations, enabling researchers to make principled trade-offs among expressiveness, computability, and interpretability.

The Value of Separating Form from Meaning

The paper concludes by discussing three reasons why distinguishing a goal's "form" from its "meaning" is valuable.

First, it reveals hidden assumptions we make about goals. When form and meaning are conflated, many design assumptions go unnoticed; making the distinction explicit brings these assumptions to the surface.

Second, it helps us study the interaction between higher-level cognition and motivation. Goals sit at the intersection of cognition and motivation, and analyzing them as representations allows us to more clearly characterize how they are invoked by higher-level reasoning and how they drive behavior.

Third, it isolates the dimensions along which different conceptions of goals vary. Different disciplines and systems understand "goals" differently, and the syntax-semantics framework provides a unified coordinate system that allows these differences to be compared systematically.

Summary

This paper offers no specific algorithm or model — instead, it provides a conceptual analytical lens: studying goals as representations with syntactic and semantic structure. It connects goal research across cognitive science, linguistics, logic, and AI, emphasizing foundational questions of expressiveness, equivalence, and design efficiency. For researchers concerned with agent goal-setting, reward specification, and intent alignment, this framework offers a more structured way of thinking — asking first "what form does the goal take, and what meaning does it point to" before discussing how to achieve it.

Background

Compositionality is a core principle in linguistics and cognitive science, systematically articulated by Gottlob Frege: the meaning of a complex expression is determined by the meanings of its constituent parts and the way they are combined. This principle explains why a finite vocabulary and set of grammatical rules can produce an unbounded number of understandable sentences. Treating goals as compositional representations means that complex goals can be built from simpler sub-goals according to structural rules, and the semantics of the whole can be systematically derived from the semantics of the parts. This contrasts with the traditional reinforcement learning approach of treating reward functions as scalar signals — the latter tends to be difficult to decompose and interpret, while the former naturally supports hierarchical analysis and transfer of goals.