# Abstracting Situation Calculus Action Theories

arXiv: https://arxiv.org/abs/2410.14712 · HTML: https://mlsanity.com/paper/2410.14712/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 80 references that are in the map.
- First posted on arXiv 9 Oct 2024.

## Builds on (most cited first, 9 of 9)

- [Leveraging Pre-trained Large Language Models to Construct and Utilize World Models for Model-based Task Planning](https://mlsanity.com/paper/2305.14909/) (2023)
- [Features, Projections, and Representation Change for Generalized Planning](https://mlsanity.com/paper/1801.10055/) (2018)
- [Generating consistent PDDL domains with Large Language Models](https://mlsanity.com/paper/2404.07751/) (2024)
- [Bounded Situation Calculus Action Theories](https://mlsanity.com/paper/1509.02012/) (2015)
- [First-Order Logic with Counting: At Least, Weak Hanf Normal Forms Always Exist and Can Be Computed!](https://mlsanity.com/paper/1703.01122/) (2017)
- [Hierarchical Finite State Controllers for Generalized Planning](https://mlsanity.com/paper/1911.02887/) (2019)
- [Abstracting Noisy Robot Programs](https://mlsanity.com/paper/2204.03536/) (2022)
- [Abstraction of Nondeterministic Situation Calculus Action Theories -- Extended Version](https://mlsanity.com/paper/2305.14222/) (2023)
- [Automatic Verification of Sound Abstractions for Generalized Planning](https://mlsanity.com/paper/2205.11898/) (2022)

## Built on by (most cited first, 1 of 1)

- [Using Large Language Models for Abstraction of Planning Domains - Extended Version](https://mlsanity.com/paper/2510.20258/) (2025)

## Abstract (arXiv)

We develop a general framework for agent abstraction based on the situation calculus and the ConGolog agent programming language. We assume that we have a high-level specification and a low-level specification of the agent, both represented as basic action theories. A refinement mapping specifies how each high-level action is implemented by a low-level ConGolog program and how each high-level fluent can be translated into a low-level formula. We define a notion of sound abstraction between such action theories in terms of the existence of a suitable bisimulation between their respective models. Sound abstractions have many useful properties that ensure that we can reason about the agent's actions (e.g., executability, projection, and planning) at the abstract level, and refine and concretely execute them at the low level. We also characterize the notion of complete abstraction where all actions (including exogenous ones) that the high level thinks can happen can in fact occur at the low level. To facilitate verifying that one has a sound/complete abstraction relative to a mapping, we provide a set of necessary and sufficient conditions. Finally, we identify a set of basic action theory constraints that ensure that for any low-level action sequence, there is a unique high-level action sequence that it refines. This allows us to track/monitor what the low-level agent is doing and describe it in abstract terms (i.e., provide high-level explanations, for instance, to a client or manager).