# Physical problem solving: Joint planning with symbolic, geometric, and dynamic constraints

arXiv: https://arxiv.org/abs/1707.08212 · HTML: https://mlsanity.com/paper/1707.08212/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jul 2017.

## Built on by (most cited first, 4 of 4)

- [Neuro-Symbolic Artificial Intelligence: Current Trends](https://mlsanity.com/paper/2105.05330/) (2021)
- [From task structures to world models: What do LLMs know?](https://mlsanity.com/paper/2310.04276/) (2023)
- [Inferring the Future by Imagining the Past](https://mlsanity.com/paper/2305.17195/) (2023)
- [A simulation-heuristics dual-process model for intuitive physics](https://mlsanity.com/paper/2504.09546/) (2025)

## Abstract (arXiv)

In this paper, we present a new task that investigates how people interact with and make judgments about towers of blocks. In Experiment~1, participants in the lab solved a series of problems in which they had to re-configure three blocks from an initial to a final configuration. We recorded whether they used one hand or two hands to do so. In Experiment~2, we asked participants online to judge whether they think the person in the lab used one or two hands. The results revealed a close correspondence between participants' actions in the lab, and the mental simulations of participants online. To explain participants' actions and mental simulations, we develop a model that plans over a symbolic representation of the situation, executes the plan using a geometric solver, and checks the plan's feasibility by taking into account the physical constraints of the scene. Our model explains participants' actions and judgments to a high degree of quantitative accuracy.