# Learning to Ground Existentially Quantified Goals

arXiv: https://arxiv.org/abs/2409.20259 · HTML: https://mlsanity.com/paper/2409.20259/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 36 references that are in the map.
- First posted on arXiv 30 Sep 2024.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [BabyAI: A Platform to Study the Sample Efficiency of Grounded Language Learning](https://mlsanity.com/paper/1810.08272/) (2018)
- [A Benchmark for Systematic Generalization in Grounded Language Understanding](https://mlsanity.com/paper/2003.05161/) (2020)
- [The LAMA Planner: Guiding Cost-Based Anytime Planning with Landmarks](https://mlsanity.com/paper/1401.3839/) (2014)
- [The Logic of Graph Neural Networks](https://mlsanity.com/paper/2104.14624/) (2021)
- [Graph Neural Networks for Maximum Constraint Satisfaction](https://mlsanity.com/paper/1909.08387/) (2019)
- [ASNets: Deep Learning for Generalised Planning](https://mlsanity.com/paper/1908.01362/) (2019)
- [Learning General Optimal Policies with Graph Neural Networks: Expressive Power, Transparency, and Limits](https://mlsanity.com/paper/2109.10129/) (2021)
- [Generalized Planning With Deep Reinforcement Learning](https://mlsanity.com/paper/2005.02305/) (2020)
- [Learning Generalized Policies Without Supervision Using GNNs](https://mlsanity.com/paper/2205.06002/) (2022)

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

- [Planning with Dynamically Changing Domains](https://mlsanity.com/paper/2508.02697/) (2025)

## Abstract (arXiv)

Goal instructions for autonomous AI agents cannot assume that objects have unique names. Instead, objects in goals must be referred to by providing suitable descriptions. However, this raises problems in both classical planning and generalized planning. The standard approach to handling existentially quantified goals in classical planning involves compiling them into a DNF formula that encodes all possible variable bindings and adding dummy actions to map each DNF term into the new, dummy goal. This preprocessing is exponential in the number of variables. In generalized planning, the problem is different: even if general policies can deal with any initial situation and goal, executing a general policy requires the goal to be grounded to define a value for the policy features. The problem of grounding goals, namely finding the objects to bind the goal variables, is subtle: it is a generalization of classical planning, which is a special case when there are no goal variables to bind, and constraint reasoning, which is a special case when there are no actions. In this work, we address the goal grounding problem with a novel supervised learning approach. A GNN architecture, trained to predict the cost of partially quantified goals over small domain instances is tested on larger instances involving more objects and different quantified goals. The proposed architecture is evaluated experimentally over several planning domains where generalization is tested along several dimensions including the number of goal variables and objects that can bind such variables. The scope of the approach is also discussed in light of the known relationship between GNNs and C2 logics.