An Action Language for Multi-Agent Domains: Foundations
  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.
