Toward multiple-agent extensions of possibilistic logic

Overview & Synopsis

Possibilistic logic is essentially a formalism for handling qualitative uncertainty with an inference machinery that remains close to the one of classical logic. It is capable of handling graded modal information under the form of certainty levels attached to classical logic formulas. Such lower bounds of necessity measures are associated to the corresponding pieces of belief. This paper proposes extensions of the possibilistic logic calculus where such weighted formulas can be attached to a set of agents or which can be embedded inside another weighted formula, for the expression of mutual beliefs. It is possible to express that all the agents in a subset have some beliefs, or that there is at least one agent in a subset that has a particular belief. The case of all-or-nothing beliefs is first dealt with before presenting the inference rules for handling graded beliefs held by multiple agents. Illustrative examples are provided. The proposed framework offers a reasonable compromise between expressive power and a computational cost close to the one of classical logic.