- Published 1998 in SOEN

Autonomy of an agent results in concurrence of Multiagent system t1'21, which makes it more complex to analyze the behaviors of the whole system. Since the world state may have been changed by some other concurrent actions committed by the other agents, an agent must be able to reason about changes in the world due to the occurrence of exogenous events, as well as its own actions. In our view, an agent is defined as a 7-tuple: < ,,£, B, q, E, 7, S, P>, where ,.4 is the agent's private attributes, B and q are belief set and intention set, which stand for the knowledge and desire, of an agent respectively. E, -¢ and P stand for the inner inference engine, speech act protocol and environment perceiver of an agent, which are relevant to specific implements. '7 is the set of action types. The description of an action type includes a precondition set, postcondition set, invariant condition set (must be hold before and after its execution) and consequence set, which are sets composed of first order formulae. We define AM.AS , a Multi-agent system, as a 5-tuple: <{agenh ..... agentn}, C, Y., BBC, Cse t >, where {agenh ..... agentn} denotes a set of agents, C is a global clock, E stands for a set of domain constraint rules (i.e., global invariant formulae), BBC denotes a communication area and C_set is the capability set of AMAS. Concurrent actions are the action instances whose execution duration overlap each other. According to the executive effects, concurrent actions can be classified as irrelevant concurrence, cumulative concurrence, canceling concurrence and causal concurrence. For different types of concurrence, the result situations are well defined. According to the descripton of each action type and their dependencies, we can determine the possible forms of concurrence between different action types, and generate a concurrent relation table, which is used to construct the domain constraint rules set E and new additional facts set R for concurrent actions. Given a set S of logical formulae. In order to generate the resulting situations, first we should find out all the possible worlds when set R is added in S. Our main idea is to remove some facts from S enough to ensure that for VreR (R is one or the union consequence sets of some concurrent actions), it is just impossible to prove ~ r from S, even though it could have from the original situation S. Let S ~ be the set obtained by removing some facts from S, then the resulting situation of some actions will be S ~ w R. Definition 1 Given sentence sets R and S, V is a negative proof set for R in S, if 3 r e R such that V is a negative proof set for r in S. Let FI to denote all the negative proof sets for R in S, we have: H = {T 3reR, T is a negative proof set for r in S }. Definition 2 Let H be a collection of sets Ti ( i = 1,2 ..... n). A general relevant set for H is any set H such that Hr~Ti ;e Q for every i. If for each i, there is one and only one element of Ti in H, then H is a minimal general relevant set for rI. An algorithm is provided to get the general relevant sets and minimal general relevant sets for rI. Theorem 3 Given sentences sets R and S, let H={Ti} be the set of all negative proof sets for R in S. Then the possible worlds for R in S are precisely those sets of the form SuR-I-I, where H is some minimal general relevant set of rI. After an agent has committed an action instance, the resulting situation should be unique and deterministic. However, there may be more than one possible world computed by the above algorithm, so we should ascribe a deterministic semantics for the resulting situation. We write W(R,S) to denote the set of all the possible worlds obtained by adding R into S. If W(R,S) is null (which means that either the action was canceled in the procedure of its execution, or its counterpart of an canceling concurrent actions has been executed), we define the consequence situation is the same as S. If W(R,S) is not null, we define a partial relation -~ on the set W(R,S) as: if S~ $1 c S~ $2 c Sa S, then S2 -< S1. Let Wv(R,S) be the set of all the maximal elements of W(R,S). The elements of Wv (R, S) are the nearest possible worlds to the goal situation SA. Thus, given the descriptions of each action type in C_set and the initial situation So, goal situation S~, we can obtain all the possible worlds after an action instance or concurrent actions have been executed. Then, through comparing the differences between each possible world and the goal situation S~, we can get the set Wv(R,S) , which consists of all the preferred maximal possible worlds. Next, we can select the intersection set of all the elements of Wv (R, S) as the semantics of the resulting situation.

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@inproceedings{Xiaocong1998ResearchOC,
title={Research on concurrent actions in multi-agent systems},
author={Fan Xiaocong and Chen Guanling and Zheng Guoliang},
booktitle={SOEN},
year={1998}
}