Axioms connecting goal syntax and semantics

Determine what semantic implications, if any, a particular compositional account of goals must have, and characterize the relationship between the syntactic and semantic properties of a goal language.

Background

The paper frames goal representations through an analogy with the syntax-semantics interface in linguistics and logic. In this framework, rewards or other representational forms provide the syntax of goals, while preferences over policies or behaviors provide their semantic content. Connecting these levels requires compositional and semantic axioms, such as assumptions governing how reward composes into value and how value determines preference.

The authors note that existing research has explored only a limited set of relations between goal syntax and semantics. The unresolved problem is to identify alternative compositional and semantic accounts and determine whether adopting a particular compositional structure constrains the semantic interpretation of goals. The problem also includes characterizing trade-offs between syntactic affordances, such as compositionality, and semantic properties, such as expressivity.

References

Open Question: Axioms for Goals? However, these are just the choices of relations between goal syntax and semantics the community has explored so far. We suggest that this framing highlights a significant conceptual opportunity to explore alternative compositional and semantic accounts of goals. Moreover, it positions us to scrutinize the needed relationship—if any—across the syntactic and semantic properties of a goal language. If we embrace a particular kind of compositional account of goal, what must this imply, if anything, about our semantic view of goals?

— The syntax and semantics of goals  (2609.19448 - Abel et al., 16 Sep 2026) in Discussion, subsection 'Open Question: Axioms for Goals?' (p. 11)

Open Question: Syntactic affordances and semantic expressivity as constraints on cognition? Lastly, a syntax-semantics distinction for goals can provide a useful analytical frame for investigating goal representations in human and animal cognition. In our view, this is not unlike studying the same cognitive process from, say, the computational versus algorithmic levels of analysis [Marr, 1982, Anderson, 1990]. Specifically, certain properties of goals may be better understood in terms of their syntactic constraints (e.g., how well they afford efficient computation) while others in terms of their semantic constraints (e.g., how well they express rational behaviors in a certain environment). Characterizing how these distinct kinds of constraints interact with one another may also shed light on rational accounts of human cognition [Griffiths et al., 2024] and their computational plausibility [Rich et al., 2020].

— The syntax and semantics of goals  (2609.19448 - Abel et al., 16 Sep 2026) in Discussion, subsection 'Open Question: Syntactic affordances and semantic expressivity as constraints on cognition?' (p. 12)