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 𝐾𝐷45 𝑛 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 nonmonotonic conclusions including default reasoning can be handled by our account.