Graded Distributed Belief
This work addresses formal reasoning about group beliefs in AI and logic, but it is incremental as it builds on existing belief base semantics.
The paper tackles the problem of expressing graded distributed belief in multi-agent systems by introducing a new logic that quantifies belief strength within a group, and provides a sound and complete axiomatization with PSPACE-completeness results.
We introduce a new logic of graded distributed belief that allows us to express the fact that a group of agents distributively believe that a certain fact holds with at least strength k. We interpret our logic by means of computationally grounded semantics relying on the concept of belief base. The strength of the group's distributed belief is directly computed from the group's belief base after having merged its members' individual belief bases. We illustrate our logic with an intuitive example, formalizing the notion of epistemic disagreement. We also provide a sound and complete Hilbert-style axiomatization, decidability result obtained via filtration, and a tableaux-based decision procedure that allows us to state PSPACE-completeness for our logic.