Motivation

The main concern of this paper is to introduce a many-valued logical calculus based on rule specialisation to model a type of cooperative communication between autonomous agents in the presence of imperfect or imprecise knowledge. Other important communicational issues such as protocols or agent communication languages are not dealt within this paper. Rather, we focus on the informational content of the communication between agents.

For the sake of simplicity and readability, we restrict ourselves to architectures of multi-agent systems composed of a set of autonomous rule-based agents communicating each other by means of message passing. Moreover, we only consider two types of asynchronous communication actions: queries and answers. Finally, external users of the multi-agent system are supposed to interact with the autonomous agents through an interface that allows them to pose queries and give answers.

In a very simplified way, the standard behaviour of traditional knowledge-based agents when communicating could be described as follows: when an agent is inquired whether a given proposition holds, the agent starts its deductive machinery in order to find out a proof for that proposition. If it succeeds, it gives back either the truth value true in the case of classical reasoning or a partial degree of truth or certainty in the case of approximate or uncertainty reasoning. If it fails, under the open world assumption, the answer is unknown.

In the case of rule-based agents, we propose to improve this simple communication process by using in a more effective way the information stored in the rule base of an agent. For instance:

1. When the user of an agent makes a query, he might be interested in knowing not only about the query itself but also about other related facts that can be useful for the problem being solved. It can be also the case that the user might be interested in knowing which conclusions can be drawn from the proposition being queried.
2. When an agent is not able to answer a query because it has not been provided with enough information, he will probably answer with the value unknown, as already commented. However, even in this case, the answer may be much more informative if the agent let the user or another agent know which is the lacking information causing the failure of the answer.

All this `hidden' information is somehow actually used by humans when cooperating in solving problems. Indeed, looking carefully at, for instance, how physicians cooperate and communicate in a diagnosis problem, it can be noticed that they may:

• condition their decisions. Suppose it is not known whether a patient is allergic to penicillin. Then a physician asked for the possibility of giving penicillin as treatment would answer: `Penicillin is a good treatment from a clinical point of view provided that the patient has no allergy to penicillin'.
• provide suggestions to be considered together with the answer of a query. Instead of strictly answering whether there is an infection or not, a physician may answer: `Pneumococcus has been isolated in the culture of sputum. In this case it is strongly suggested to make an antibiogram to the patient'.
• provide conditioned suggestions to be considered together with decisions. This would correspond to a combination of the above two communication patterns. For instance, `Ciprofloxacine is a good treatment, but if the patient is a woman breast-feeding she must stop breast-feeding'.

To model such communication patterns, we need to extend the agent answering procedure, by allowing it to answer queries with sets of formulas (rules and propositions). We propose to do it by means of a calculus based on rule specialisation. Specialisation as understood in this paper is related to the notion of partial evaluation expressed in the well known Kleene's Theorem [10]. Specialisation Calculus is based on logic, then we use the term partial deduction instead of partial evaluation [12]. Partial deduction algorithms have been used intensively in logic programming [5, 11, 13, 18, 20], mainly for efficiency purposes.