Probabilistic Multi-agent Only-Believing.

Levesque introduced the notion of only-knowing to precisely capture the beliefs of a knowledge base. While numerous studies of only-knowing have emerged, such as the representation of probabilistic beliefs or reasoning about beliefs in an uncertain dynamical system, most remain confined to single-agent contexts. This limitation predominantly stems from an absence of a logical framework, which faithfully extends Levesque's intuition of only-knowing to multi-agent, probabilistic scenarios. In this paper, we introduce a first-order logical account with probabilistic beliefs and only-believing of many agents. We demonstrate that the categorical fragment of our account forms a KD45n modal system, and the notion of belief has behavior following the laws of probability. We also show how an agent's beliefs and non-beliefs about the environment or other agents' beliefs are precisely captured through the modalities of only-believing, which paves the way to generalize tools for interfacing with symbolic, probabilistic knowledge bases. By way of example, we demonstrate how non-monotonic conclusions including default reasoning can be handled by our account.