In earlier work, we introduced the framework of language-based decisions, the core idea of which was to modify Savage's classical decision-theoretic framework by taking actions to be descriptions in some language, rather than functions from states to outcomes, as they are defined classically. Actions had the form "if psi then do(phi)", where psi and phi were formulas in some underlying language, specifying what effects would be brought about under what circumstances. The earlier work allowed only one-step actions. But, in practice, plans are typically composed of a sequence of steps. Here, we extend the earlier framework to sequential actions, making it much more broadly applicable. Our technical contribution is a representation theorem in the classical spirit: agents whose preferences over actions satisfy certain constraints can be modeled as if they are expected utility maximizers. As in the earlier work, due to the language-based specification of the actions, the representation theorem requires a construction not only of the probability and utility functions representing the agent's beliefs and preferences, but also the state and outcomes spaces over which these are defined, as well as a "selection function" which intuitively captures how agents disambiguate coarse descriptions. The (unbounded) depth of action sequencing adds substantial interest (and complexity!) to the proof.

翻译：在前期工作中，我们提出了语言决策框架，其核心思想是将Savage经典决策理论框架中的行为从传统上定义为状态到结果的函数，修改为某种语言中的描述。行为具有“若psi则执行(phi)”的形式，其中psi和phi是某种底层语言中的公式，用于指定在何种情境下会产生何种效果。前期工作仅允许单步行为。然而在实践中，计划通常由一系列步骤组成。本文我们将前期框架扩展至序贯行为，使其具有更广泛的适用性。我们的技术贡献在于提出一个经典风格的表示定理：满足特定行为约束的决策者可以被建模为期望效用最大化者。与前期工作类似，由于行为基于语言描述，表示定理不仅需要构建表征决策者信念与偏好的概率函数和效用函数，还需构建定义这些函数的可能世界状态空间与结果空间，以及一个直观上反映决策者如何消解粗粒度描述的“选择函数”。行为序贯的（无界）深度为证明过程增添了显著的趣味性（和复杂性！）。