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An Agent Formal Model for Autonomous Decision-making

Linjin Wu, Dongying Wu, Jiayong Chen,Wenxiong Li

Zhengzhou Institute of Information Science and TechnologyZhengzhou, China

e-mail: [email protected]

AbstractWith the development of artificial intelligence, agent

is widely applied to the intelligent system. As the intelligent

decision at a higher sense, autonomous decision-making

directly affects the intelligent level of intelligent system. In

order to improve autonomous decision-making ability of

intelligent system, the paper aims to use formal method to

research on the process of autonomous decision-making.

Combining the feature of autonomous decision-making and

agent formal method, the paper puts forward an agent model

for autonomous decision-making, namelyADAM(Autonomous Decision-making Agent Model). The

model mainly includes five parts: data pretreatment, decision-

making response, decision-making execution, decision-making

evaluation and learning feedback. Then the paper gives the

formal description of ADAM, which realizes formal analysis

for the process of autonomous decision-making. Finally, the

paper points out the realized critical point of the model andpreliminary demonstrates validity of the model.

Keywords-agents; autonomous decision-making; intelligent

systems; formal methods

I. INTRODUCTION

Agent, appearing in the 1970s, develops with the

development of artificial intelligence. At present, agent hasbecome one of the most active research content in the fieldof the computer and artificial intelligence. The main researchcontent of agent is Agent Formal Theory, Agent Structureand Multi-Agent System [1]. Agent has been widely used inintelligent systems, such as: UAV intelligent control system,complex industrial process control, air traffic control,intelligent transportation systems and robots, etc.

Autonomous decision-making can have intelligentdecision-making autonomously according to the currentenvironmental information [2]. The characteristics ofautonomous decision-making have:

a) Intelligence: it can simulate human thinking whenfaced with different environment, making decision

intelligently.b) Autonomy: it can independently make decision, which

is not rely on the man-machine interface to interact.c) Flexibility: in face of complex and ever-changing

external environment, autonomous decision-making needshave higher flexibility so that have stronger adaptability.

d) Reliability: It can ensure the reliability andeffectiveness of autonomous decision-making.

f) Scalability: the scalability of autonomous decision-making makes the autonomous decision-making deal withthe changes in complex environment in real-time.

Therefore, Autonomous decision-making, as theintelligent decision-making at a higher sense, directlyaffects the intelligent level of intelligent system.

At present, the design and development of intelligentsystems generally use formal methods and informal methods[3]. The informal method is simple and intuitive, whichimage is rather good, but lacking in precise semantics andhaving ambiguity. The understanding for the informalmethod depends on the knowledge and experience of

developer. While formal method, on the basis ofmathematical theory, can describe the system accurately andunambiguously, meanwhile providing the tools forsystematic model simulation and validation [4].

Currently, the design and development of autonomousdecision-making system mainly use informal methods.According to the specific applied background, the informalmethod can design correspondent model. While owing to belack of precise semantics and hard to understand the fact thatthe model is depended on the knowledge and experience ofdeveloper, the formal method is little adopted.

Therefore, to improve autonomous decision-makingability of intelligent system is regarded as background, thispaper aims to use formal method to study the process of

autonomous decision-making and puts forward an agentmodel for autonomous decision-making, ADAM. Withreference to the formal method of Agent [5, 6, 7], this paperhas a formal description for ADAM model. Finally, theADAM model realized formal description for the process ofautonomous decision-making. Moreover, this paper pointsout the realized critical point of the model and preliminarydemonstrates validity of the model.

II. ADAM FORMAL MODEL

A. The Establishment of ADAM Model

According to the features of autonomous decision-making, combing with Agent theory, this paper comes upwith agent model for autonomous decision-making. Theframework of the model is given below.

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Decision-making

Control Module

Micro-Intelligent

Decision Module

Decision-makingEvaluation

D

ecision-making

Learning

Feedback

Data Pretreatment

Date

Evaluation

Perception EvaluationLearning Feedback

Application of Decision

Decision-making Response

Decision-making Execution

Decision-making

Coordination Module

Learning Feedback

Figure1. ADAM Model

As is shown in the figure, the ADAM consists of fiveparts: data pretreatment, autonomous decision-makingresponse, decision-making execution, autonomous decision-making evaluation and learning feedback.

1) Data PretreatmentThe data pretreatment is responsible for the information

integration of the collected data, and fully perceives thetrend of the current environment, providing a decision-making basis for autonomous decision-making response.The structure of data pretreatment model is given below.

Date Level

Feature Level

Decision Level

Evaluation

Learning

Feedback

Figure2. The Structure of Data Pretreatment

As shown, the process of data pretreatment conductsinformation integration on three levels: the data level,feature level and decision level [8]. Making the datacontinues to abstract levels of depth, and thus as a basis forautonomous decision-making response. Decision-makingevaluation and learning feedback constantly proceed toassess and learn feedback for data pretreatment, so that thedata pretreatment can efficiently perceive the trend ofenvironment.

2) Decision-Making ResponseAutonomous decision-making response is responsible

for responding to the decision-making data that has been

dealt with, which is the core of whole autonomous decision-making model. It includes three parts: the decision-makingcontrol module, the decision-making coordination moduleand micro-intelligent decision module. Among the threeparts, decision-making control and coordination module isresponsible for the operation, regulation and management ofthe autonomous decision-making; while micro-intelligent

decision module is the core of decision-making response,responsible for conducting autonomous decision-makingefficiently and intelligently. Decision-making evaluationand learning feedback constantly have efficiency assessmentand learning feedback for autonomous decision-making inreal-time, thus maximizing the efficiency of autonomousdecision-making.

3) Decision-making ExecutionDecision-making execution is to effectively implement

the decision-making produced by the autonomous decision-making response, therefore conducting the decision-makingapplication according to the correspondent decision-makingobjects. Decision-making evaluation and learning feedbackconduct the decision-making effect assessment and learning

feedback in real-time for decision-making execution, thusgiving full play to the efficiency of decision-makingexecution.

4) Decision-making EvaluationAssessment of autonomous decision-making is the real-

time assessment and feedback on the autonomous decision-making, including the assessment on the ability ofperceiving the trend in the data pretreatment; the assessmenton the efficiency of micro-intelligent decision module inautonomous decision-making response; the assessment ondecision-making execution. By assessing, optimize theperformance of the autonomous decision-making, andmaximize decision-making as much as possible.

5) Decision-making Learning FeedbackAutonomous decision-making learning feedback is to

have the real-time learning and feedback for autonomousdecision-making, including learning feedback on theperception of the trend in the data pretreatment; learningfeedback on the micro-intelligent decision module inautonomous decision-making response; learning feedback onthe operational decision-making execution. Through learningfeedback, constantly improve and optimize the efficiency ofautonomous decision-making system, and continuouslypromote the ability of autonomous decision-making.

B. The Formalization of ADAM Model

1) Definition1: ADAM.

= { , , , , , }.Among them, PA represents data pretreatment; RA

represents autonomous decision-making response; EXArepresents decision-making execution; EVA representsautonomous decision-making evaluation; LFA representsautonomous decision-making learning feedback; Relationrepresents the interface between them.

2) Definition2: Relation.

Let = { , , , , };= , , , 0 < , ( );

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= 1 means ai connects with aj, = 0 means notconnect, then

= =

0 1 0 1 10 0 1 1 10 1 0 1 11 1 1 0 01 1 1 0 0

.

3) Definition3: PA.= , , , , , , , , , , , : ( );

: ( ) ( );: ( ) ( );: ( ) ;

: ( ) ( ) ;: ( ) ( ) .

Among them, PIn is the set of input data state; POutisthe set of output data state; Rio is the set of possible data

pretreatment program, DL is the collection of data state indata level; CL is the collection of data state in feature level;DeL is the collection of data state in decision level; See

shows the process of perception of Agent in initial state; Fclshows the collection of program transforming from thecollection ofDL to the collection of CL; Fdel shows thecollection of program transforming from the collection ofCL to the collection ofDeL; Fdo shows the collection of

program transforming from the collection ofDeL to thecollection ofPOut; Est shows the process of determiningthe output data results, through evaluation and learningfeedback for the program of data pretreatment; Actmeansthe process of focusing on selecting a specific output datafrom specificPOut, according to the corresponding set of aprogram set; ( ) shows the power set of DL, and theother is also similar.

4) Definition4: RA.

= , , , , , , , , , = {( , )| , ( )};= {( , )| ( ), ( )};

: ( ) ;: ( ) ( ) ;

: ( ) ( ) ;: ( ) ( ) .

Among them, PRn is the input decision-making data ;RIn is the set consisting of all possible action program ofAgent; ROutis the set of all possible corresponding resultsstate to the all possible action program; Spn shows thecorrespondence between sets of decision-making data andaction program; Sio shows the correspondence between set

of program and set of result state; AIRule expresses theintelligent selection strategy of micro-intelligent decisionmodule; See shows the process of determining the currentprogram set of the corresponding pair, according to theinput decision-making data and AIRule; Est shows theprocess of determining possible result state, after ensuringthe corresponding program set through evaluation andlearning feedback; Adjustshows the process of determiningfinal result state, after ensuring the corresponding program

set through control and coordination according to AIRule;Act shows the process of focusing on selecting a specificprogram from selected programs, according to AIRule andthe corresponding result state set of a program set.

5) Definition5: EXA.

= { , , , , , , , }= {( , )| , ( )};

= {( , )| ( ), ( )};: ( ) ;

: ( ) ( ) ;: ( ) ( ) .

Among them, ERIn is the input set of decision-makingprogram;ExIn is the set of all possible control command ofAgent; Exoutis the set of all possible corresponding resultsstate to the all possible control command; Sre shows thecorrespondence between sets of decision-making programand control command; Seo shows the correspondencebetween set of control command and set of result state; Seeshows the process of determining the current controlcommand set of the corresponding pair, according to the

input decision-making program; Est shows the process ofdetermining possible result state, after ensuring thecorresponding control command set through evaluation andlearning feedback; Act shows the process of focusing onselecting a specific control command from selected controlcommands, according to the corresponding result state set ofa control command set.

6) Definition6: EVA.

= { , , , , , , , }= {( , )| , ( )};

= {( , )| ( ), ( )};: ( ) ;

: ( ) ( ) ;

: ( ) ( ) .Among them,In is the input set of evaluation data; EvInis the set of all evaluation program of Agent; EvOutis theset of all possible corresponding results state to the allevaluation program; Sie shows the correspondence betweensets of evaluation input and possible evaluation program; Sevshows the correspondence between set of evaluationprogram and set of evaluation result state; See shows theprocess of determining the current corresponding set ofevaluation program, according to the input set of evaluationdata; Est shows the process of determining possible resultstate, after ensuring the corresponding set of evaluationprogram through repeated evaluation and adjustment; Actshows the process of focusing on selecting a evaluation

program from specific evaluation programs, according tothe corresponding result state set of a evaluation program.

7) Definition7: LFA.

= , , , , , , , = {( , )| , ( )};

= {( , )| ( ), ( )};: ( ) ;

: ( ) ( ) ;

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: ( ) ( ) .Among them,In is the input set of learning feedback data;

LFIn is the set of all learning feedback of Agent; LFOut isthe set of all possible corresponding results state to the alllearning feedback program; Sil shows the correspondencebetween sets of learning feedback input and possible learningfeedback program; Slf shows the correspondence between set

of learning feedback program and set of result state; Seeshows the process of determining the current correspondingset of learning feedback program, according to the input setof learning feedback data; Est shows the process ofdetermining possible result state, after ensuring thecorresponding set of learning feedback program throughrepeated adjustment and optimization;Actshows the processof focusing on selecting a learning feedback program fromspecific learning feedback programs, according to thecorresponding result state set of a learning feedback program.

III. THE APPLICATION OF FORMAL MODEL

According to the above proposed model, ADAMconducts the formal analysis for the process of an

autonomous decision-making. Assuming the process of thesimplification of general autonomous decision-making is asshown below.

6HQVRU16HQVRU 6HQVRU

Decision Decision2 DecisionN

$XWRQRPRXV

'HFLVLRQPDNLQJ

Figure3. Simplified Process of Autonomous Decision-making

Supposing Pi are the obtained datas from Sensor1,Sensor2...SensorN, Ci are the received control commandsfrom Decision1, Decision2...DecisionN. So the process ofautonomous decision-making can be formalized as:

= { 0, 1 1 };: ( );

: ( ) ( );: ( ) ( );: ( ) ;

: ( ) ( ) ;= { | , }, ;

: ( ) ;: ( ) ( ) ;

: ( ) ( ) ;= { | , }, ;

: ( ) ;: ( ) ( ) ;

= { 0, 1 1 } , .As is shown above, the data gets the final set of control

command of autonomous decision-making, that is Con, after

through the data pretreatment of PA, the autonomousdecision-making response ofRA and the decision-makingexecution ofEXA. The process of autonomous decision-making also gets the constant learning feedback andevaluation and adjustment fromEVA andLFA. Among them,the key ofPA lies in determining appropriate program setRio, optimizing the result setPOut; the key ofRA lies in

determining proper decision-making program

RIn,optimizing the set of decision-making resultROutthroughcontrol and coordination. While the key of EXA lies indetermining appropriate set of control commandExIn,optimizing the result set of execution ExOut.

IV. CONCLUSION AND FUTURE WORK

Autonomous decision-making, as the intelligentdecision-making at a higher sense, directly affects theintelligent level of intelligent system. This paper proposesan agent formal model for autonomous decision-making,aiming at the autonomous decision-making process of thecurrent design and development of autonomous decision-making system, analyzing the feature of autonomous

decision-making and combining the formal method of Agent.The ADAM model includes five parts: data pretreatment,decision-making response, decision-making execution,decision-making evaluation and learning feedback, thispaper gives their own formal expression, aiming at thefeatures of each part. Finally, this paper uses ADAM modelto conduct formal analysis for the process of an autonomousdecision-making, and points out the realized critical point ofthe model and preliminary demonstrates validity of themodel, providing certain theoretical basis for the design anddevelopment of the system of autonomous decision-making.The future work includes: further perfect the ADAM model;theoretically demonstrate the consistency and completenessof the model; study Multi-Agent model for autonomousdecision-making under the distributed situation.

REFERENCES

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[2] A.Kakas and P.Moraitis, Argumentation based decision making forautonomous agents, Proceedings of the second international jointconference on Autonomous agents and multiagent systems, (AAMAS'03), ACM Press, 2003, 883-890.

[3] Cai Yuanli, Yu Zhenhua and Zhang Xinman. Formal modelingmethodology for Multi-Agent systems[J]. Journal of SystemSimulation, 2007, 19(4): 3151-3157.

[4] Clarke E M, Wing J M. Formal methods: state of the art and futuredirections[J]. ACM Computing Surveys(S03360-0300), 1996, 28(4):626-643.

[5] Rao A S, Georgeff M P. BDI Agents: From theory to practice.

In:Proc. of the 1st Int'1 Conf. on Multi-Agent Systems(ICMSA-95).San Francisco, 1995, 312-319.

[6] Yu Jiangtao. Rearch and application of Multi-agent models, learningand collaborative[D]. University of ZheJiang, 2003,17-23.

[7] Hu Xiaojian, Yang Shanglin and Luo He. A formalized model onAgent with probability and Utility operator[J]. Journal of ComputerRearch and Development, 2006, 43(zl): 56-59.

[8] David Lee Hall. Mathematical Techniques in Multisensor DataFusion[M]. Artech House, Norwood, 1992.

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