In the proposed Grid service discovery framework based on multiagent, agents are classified into three types: service-agent, request-agent and medium-agent. Two key issues in the framework are discussed: service description language and service matchmaking mechanism. A Fuzzy Petri nets-based service description language is proposed as a specification to publish or request for a service, Possibilistic transition is used to represent a service or request. Meanwhile, through ontology's class hierarchy, we give a semantic-based service matchmaking that can find an appropriate service for a request. Possibility and necessity measures are used to quantify the confidence levels that the service can satisfy a request, that is, support partial matching.