The syntax and semantics of goals
cs.AI
Quick verdict
A position paper mapping RL goal formalisms onto the linguistic syntax-semantics split; conceptually clarifying but adds no new theorems or evidence.
Summary
Abel and Ho propose that the study of goals should borrow the syntax-semantics distinction from linguistics and logic. Goals, they argue, are compositional control states that direct rational behavior — and, as a rat-and-cheese example (Fig. 1) shows, directly composing the optimal behaviors for two goals does not yield the optimal behavior for the composed goal. Applied to reinforcement learning, reward functions act as syntactic atoms, values as their composition, and preferences over policies as the semantic content. The paper synthesizes recent results: Abel et al. (2021) prove that some Sets Of Acceptable Policies cannot be expressed by any Markov reward function, and Bowling et al. (2023) characterize when Markov rewards represent policy preferences (the four von Neumann–Morgenstern axioms plus Temporal γ-indifference). Table 1 catalogues eleven goal languages — Markov, average, risk-sensitive, distributional, constrained, lexicographic, satisficing, Blackwell-optimal, first-order logic, temporal logic, and reward programs — by dynamic-programming support and semantic expressivity. Reward shaping and value-equivalent world models are reframed as semantics-preserving syntactic operations. The main limitation: it is a purely conceptual synthesis contributing no new theorems, experiments, or formal definitions, and its analogy is argued informally.
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Assessment at a glance
3
risk flags identified
● high 0
● medium 1
● low 2
4 strengths · 4 weaknesses · 5 author questions
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Key claims under review
- Goals should be analyzed through a syntax-semantics distinction: reward functions as syntactic atoms, values as compositions of atoms, and preferences over policies as the semantic content both refer to.
- Direct composition of rational behaviors (e.g., averaging) does not preserve rationality; rational behavior must be re-derived from the composed goal (Fig. 1).
- Some Sets Of Acceptable Policies cannot be expressed by any Markov reward function (Abel et al. 2021), and a Markov reward represents a policy preference only if that preference satisfies the four vNM axioms plus Temporal γ-indifference (Bowling et al. 2023).
- Potential-based reward shaping and value-equivalent world models are semantics-preserving syntactic operations on goal and task representations.
- Goal languages form a design space whose syntactic affordances (dynamic programming, generalization) and semantic expressivity (Markov, Markov+, temporal, regex) trade off, per Table 1.
Strengths
Unifying analytical lens with a compact comparative map
Table 1 grades eleven goal languages (Markov reward through reward programs) on dynamic-programming support and semantic expressivity, giving the field its first single-view taxonomy; the framing cleanly separates questions like expressivity vs. computational affordance (Davidson & Gureckis 2024) that are usually conflated.
Faithful, accessible synthesis of two important technical results
§'The Expressivity of Goals in RL' and §'Settling the Reward Hypothesis' restate Abel et al. (2021, Thm. 4.1) and Bowling et al. (2023, Thm. 4.1: four vNM axioms + Temporal γ-indifference) at a level cognitive scientists can follow, with the reward-as-communication interpretation made explicit.
Well-chosen illustrative examples
Genuinely open research agenda
Weaknesses
No new formal or empirical contribution
The analogy is asserted more than formalized
Table 1 cells are under-justified
Cognitive-science payoff remains programmatic
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Scope & Claims
This is a conceptual position paper commissioned for a special issue of *Topics in Cognitive Science* on goal-centric perspectives, by David Abel (Edinburgh) and Mark Ho (NYU). The thesis: the study of goals should borrow the syntax-semantics interface from linguistics and logic (Montague 1970; Jacobson 2014), treating a goal's representational form as syntax and the behavior it stands for as semantics. The Introduction motivates this with two properties — goals control rational behavior, and goals are compositional — and Figure 1 stages the central tension: a rat must reach a large cheese while collecting small ones, and directly composing the optimal behaviors of two goals (π*A ⊕ π*B, e.g., by averaging) is not the optimal behavior for the composed goal (π*A⊕B), so "direct composition of rational behavior does not preserve rationality." The paper's claims: (1) in reinforcement learning (RL), reward functions are syntactic goal atoms; (2) values are compositions of atoms; (3) preferences over policies are the semantic content both refer to; (4) bridging these layers requires explicit "axioms for goals." Three open questions follow: alternative axiom sets, syntax-first vs. semantics-first starting points, and how syntactic vs. semantic constraints bind cognition.
The remaining sections cover Methodology Assessment, Statistical Evidence, Results & Reproducibility, Limitations & Risks, and Verdict & Recommendations.
- All 4 strengths & 4 weaknesses, analyzed in detail
- 3 risk flags with severity, section & reviewer questions
- Methods & statistical evidence assessment
- 5 questions a peer reviewer would ask
- Full six-dimension evaluation report & recommendations
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Frequently asked questions
What is the main idea of 'The syntax and semantics of goals'?
The paper proposes treating goals like linguistic expressions: a goal's representational form (e.g., a reward function) is its 'syntax,' while what it stands for (preferences over behaviors or policies) is its 'semantics.' This borrowed distinction from linguistics and logic clarifies how goals compose, how expressive different goal formats are, and when two goal representations mean the same thing.
What are the key technical results discussed in the paper?
The paper restates two results from earlier work. First, Abel et al. (2021): for any finite Markov decision process, there exists a partition of policies into good and bad (a 'Set Of Acceptable Policies') that no Markov reward function can express. Second, Bowling et al. (2023): a Markov reward can represent a preference over policies only if that preference satisfies the four von Neumann–Morgenstern axioms plus a fifth condition called Temporal γ-indifference.
Is this an empirical paper with experiments?
No. It is a conceptual position/review paper written for a special issue of Topics in Cognitive Science on goal-centric perspectives. It contains no experiments, datasets, code, or new proofs — only informal restatements of published theorems, worked examples (a rat reaching cheeses, marathon training), and a comparative table of eleven goal formalisms.
Why doesn't combining optimal behaviors give the optimal behavior for a combined goal?
Because the optimal behavior for a compound goal is generally not any direct combination (such as an average) of the optimal behaviors for the parts. The paper illustrates this with a rat that must reach a large cheese while collecting two small ones: composing the two rats' optimal paths can walk straight into a wall, whereas acting rationally with respect to the composed goal finds a genuinely new path. Rationality must be recovered at the level of the goal, not the behavior.
About this review
This is an AI-generated preliminary review by Evolve.Pub, produced from the openly available text of the paper. It is not peer review and does not represent the authors' views. The canonical record of the paper is at the publisher link above.
- Figure 1 was assessed from its caption and surrounding text only; the visual layout itself was not analyzable from the extracted text.
- Table 1 was extracted as text and cell assignments were read as printed, but complex formatting could introduce transcription artifacts.
- Both theorems are explicitly informal restatements; verification of Abel et al. (2021) and Bowling et al. (2023) details is outside this paper's text.
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