# An Action Language for Multi-Agent Domains: Foundations

arXiv: https://arxiv.org/abs/1511.01960 · HTML: https://mlsanity.com/paper/1511.01960/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2015.

## Built on by (most cited first, 6 of 6)

- [E-PDDL: A Standardized Way of Defining Epistemic Planning Problems](https://mlsanity.com/paper/2107.08739/) (2021)
- [A Semantic Approach to Decidability in Epistemic Planning (Extended Version)](https://mlsanity.com/paper/2307.15485/) (2023)
- [Comprehensive Multi-Agent Epistemic Planning](https://mlsanity.com/paper/2109.08301/) (2021)
- [DELPHIC: Practical DEL Planning via Possibilities (Extended Version)](https://mlsanity.com/paper/2307.15451/) (2023)
- [Depth-Bounded Epistemic Planning](https://mlsanity.com/paper/2406.01139/) (2024)
- [A Study of Belief Revision Postulates in Multi-Agent Systems (Extended Version)](https://mlsanity.com/paper/2605.02249/) (2026)

## Abstract (arXiv)

In multi-agent domains (MADs), an agent's action may not just change the world and the agent's knowledge and beliefs about the world, but also may change other agents' knowledge and beliefs about the world and their knowledge and beliefs about other agents' knowledge and beliefs about the world. The goals of an agent in a multi-agent world may involve manipulating the knowledge and beliefs of other agents' and again, not just their knowledge/belief about the world, but also their knowledge about other agents' knowledge about the world. Our goal is to present an action language (mA+) that has the necessary features to address the above aspects in representing and RAC in MADs. mA+ allows the representation of and reasoning about different types of actions that an agent can perform in a domain where many other agents might be present -- such as world-altering actions, sensing actions, and announcement/communication actions. It also allows the specification of agents' dynamic awareness of action occurrences which has future implications on what agents' know about the world and other agents' knowledge about the world. mA+ considers three different types of awareness: full-, partial- awareness, and complete oblivion of an action occurrence and its effects. This keeps the language simple, yet powerful enough to address a large variety of knowledge manipulation scenarios in MADs. The semantics of mA+ relies on the notion of state, which is described by a pointed Kripke model and is used to encode the agent's knowledge and the real state of the world. It is defined by a transition function that maps pairs of actions and states into sets of states. We illustrate properties of the action theories, including properties that guarantee finiteness of the set of initial states and their practical implementability. Finally, we relate mA+ to other related formalisms that contribute to RAC in MADs.