Model Expert System MES

M:lDEL EXPERT SYSTEM MES

Guan Jiwen , Xu Ying Department of Computer Science Jilin University Changchun, P.R.C.

ABSTRACT

The comprehensive oil log interpretation is a procedure of numerical calculation and logical (or plausible) inference . In other words, the results of preliminary inference will provide a basis for the choice of parameters of calculation formula, and then the results of numerical cal­ culation will be used as evidences for further inference, and so on and so forth. In view of this situation, we have designed a rrodel expert system (tool system) MES and established a com­ prehensive oil log interpretation expert system WELlES based on the system MES.

In MES, we introduced the concept of "TASK" to make numerical calculation intergrated with logical(or plausible) inference during the task solution. The execution of MES is a procedure of task solution. Ways of solving a task are de­ fined by Task Transformation Rules.

The Knowledge Representation is divided into two parts: 1) Task Transformation Rules, inclu­ ding Task Decomposition Rules and Task Derivation Rules; 2) Inference Rules, including Production

Rules and Procedure Rules.

We adopt Dempster/Shafer 's Evidence Theory [6] to express uncertainty.

INTRODUCTION

Rule-based expert system has come into wide application since the 70's [ 3] . Developments of MYC IN [ 1] , PROSPECTOR [ 2] , DIPMETER ADVISOR [ 4] [ 5] and other well-known expert systems have beco­ me the foundation for the development of pragma­ tic expert systems. These systems, whether colle­ ting data· fran users in the interactive way or from some on-line instruments, emphasize only logical(or plausible) inference. However, in many applied fields, for instance in the field of oil log interpretation, the procedure that experts use to solve problems is as follows: analyzing various preliminary information(qualitative inter­ pretation) and then determining the parameter values needed by further quantative interpretation and then calculating using theoretical or empiri­ cal formula and then analyzing qualitatively fur­ ther the results of calculations and so on and so forth. We hope to establish a uniform frame­ work to deal with numerical calculation and logi- Chang Minche , Zhao Jizhi Well Logging Campany Daqing Petroleum Administrative Bureau Daqing, P.R.C.

cal (or plausible) inference without irrpairing the advantages of the Rule-based system.

We began to develop a comprehensive oil log interpretation expert system in the March 1984. We have designed a rrodel expert system( or tool system) MES and a comprehensive oil log interpre­ tation expert system WELlES based on MES.

This paper will not attempt to explain the comprehensive oil log interpretation expert system WELlES in detail, but we will use it as an example to explain the system MES.

One version of MES and the system WELlES are implemented on PERKIN-ELMER 3220 in FORTRAN 7.

I ~ED�E REPRESENTATION

(?X,OBJECT,VALUE,SUPPORT,PLAUSI-

Definition : BILITY) is called an ASSERTION.

Where, in WELlES, ?X is the name of some phy­ sical information or conclusion; VALUE is the value of the OBJECT; SUPPORT is a measurement of how evidences support the VALUE of the OBJECT; PLAUSI­ BILITY is a measurement of how evidences do not oppose the VALUE of the OBJECT. We will explain these two concepts later.

Definition: T=(TN, ?TV) is called a TASK, where TN is the name of a TASK, ?TV is the value of a TASK. ?TV gets value fran {'TRUE','FALSE'}.

In MES, there is a task name for every OBJECT, respectively.

A TASK is set whenever a task name is provided to the TASK Solution Program. In the following, a task solution of our definition means a procedure to evaluate a TASK. A task solution is finished when the TASK has a value.

For every TASK T=(TN, ?TV), ?TV='TRUE' means that the solution for the TASK succeeds, and ?TV= 'FALSE' means that the solution for the TASK fails. We will explain these in detail in the Sec.IV.

Ways to solve a TASK are defined by Task Tran­ sformation Rules.

• (I) Task Transformation Rules

Task Transformation Rules include Task Decom­ sition Rules and Task Derivation Rules.

Definition: Let T=(TN,?TV) a TASK, we call

a Task Decarposition Rule, where Ti=(TiN, ?TiV),

T-P Tl" T2A · · · "Th 1 '"i 'h.

The function of Task Deccxrposition Rules is to transfonn a TASK into some subTASKs and define the way to evaluate the TASK.

Definition: Let T=(TN, ?TV) a Tasl<; ,We call T-Tl, T2, · · · , Th a Task Derivation Rule, where Ti=(TiN, ?TiV), Hi, h.

The function of Task Derivation Rules is to arrange the order of solutions for TASKs.

Left-handed parts and right-handed parts of the Decarposition Rules have some logical relations , but left-handed parts and right-handed parts of Derivation Rules do not necessarily have logical relations, but contain sequence relation.

At this point, we only give the syntax of the Task Transformation Rules. Meanings of them will be given in the Sec. IV.

(II) Inference Rules

There are two kinds of Inference Rules in the MES: 1) Production Rules, 2) Procedure Rules.

Definition: Syntax of a Production Rule is: ( ?X, OBJECT, PREDICATE, VALUE))( ·· · · · · ",.( ?X, OBJECT, PREDI­ CATE,VALUE) ~ (?X,OBJECT,VALUE,CERTAINTY)/\ ·· · " ( ?X,OBJECT, VALUE,CERTAINTY).

Definition: Syntax of a Procedure Rule in MES is:

( ?X,OBJECT, ?VALUE),······ , ( ?X,OBJECT, ?VALUE)- (?X, OBJECT,SUBROUTINE NAME,?CERTAINTY).

We will give the definition of CERTAINTY in the Sec. II.

In our opm1.on, the function of Production Rules is to bind values to some OBJECTs . In this view, we have developed the concept of RULE to include Procedure as a kind of RULE. In the above definition of a Procedure Rule, OBJECT, in every item of the condition part, is a name of a parame­ ter needed by the SUBROUTINE whose name is given in the action part. OBJECT in the action part is the name that the SUBROUTINE will bind value to. Procedure Rule can be used only backward. ?VALUE in the condition part is empty. It will be bound a value only when needed.

II REPRESENTATION OF UOCERTAINTY

Let S={sl,s2;· · ,sn).

SDefinition: m is a primary support function on 2 , if

(1) O~m(A)~l, for ACS,

(2) m(f>)=O,

(3)~ m(A)=l.

In WELlES, we especially have m(A)=O, for A~S"A,.{si}. 1 ~ i~ n.

For simplicity, we denote m( si) for m( { sj) ") . So, in WELlES, we change the fonn of the defi­ nition into:

* Definition : m is a primary support function on S, if

( 2l 2::::: m( si) ~ 1. lf1.4n

( 1) ~ m( si) , for 1 * i ~ n,

And we define m(S)=l- 1 E:m(si). We will consider fl.f n only m(si) in the following.

Let ml and m2 functions meeting the definition of primary support function, and ml(si)=ai, for 1 ~H n, m2(si)=bi, 1 ~ i 6n, ml(S)=9/, m2(S)=OJ.

We define operator QP:

Definition: We define m=mlQP m2, and l et m(si) =ci and ci=di/p, where di=ai *bi +ai *92+ 91. *bi, and p=81*92tEdi. *l.'n

Obviously, m meets the definition of primary support function and ® is both associative and carrnutative.

In fact, the above function is a simplified fonn of the Combination of Evidence formula of Derrpster /Shafer's Evidence Theory [ 6] under the condition of m(A)=O, for A~SAA%{si}, l~i~n.

Definition: We define SUPPORT function as Bl(A)-cttm(a) and PLAUSIBILITY function as Pl(A)= 1-~(a)+~m(b), Ac.s.

Obviously, Pl(A) ~ Bl(A), ACS.

In MES, uncertainty with conclusion is r epre­ sented with (Bl,Pl).

We now come to the definition of the .CERTAINTY of the condition part of an Inference Rule:

Definition: CERTAINTY of an item in the condi­ tion part of a Production Rule is defined as:

match degree*f(SUPPORT of corresponding ASSER­ TION in the Database, PLAUSIBILITY of corresponding ASSERTION in Database) , where match degree is defi­ ned as follows: ( 1) if the value of the OBJECT in the item is a symbol, match degree=( 1, match 0, otherwise

( 2) if the value of the OBJECT in the item is a number, the system WELlES has defined Match func­ tion for every predicate (e.g. GE,IN,and so on) .

Definition: CERTAINTY of the condition part of a Production Rule is defined as the value obtai­ ned by using the following rules repeatedly:

(1) if there is only one item inthe condition part of the Rule, CERTAINTY of the item is the result needed;

( 2) use a new item to replace the items connected with 1\ ,and CERTAINTY of the new item is the mini­ mum of all CERTAINTYs of the items connected withA; ( 3) use a new item to replace the items connected with v ,and CERTAINTY of the new item is the maxi­ mum of all CERTAINTYs of the items connected with v.

Definition: CERTAINTY of the condition part of a Procedure Rule is defined as the minimum of all SUPPORT values of the ASSERTIONs corresponding to the items in the condition part.

A Rule will not be invocated if its CERI'AINTY of the condition part is less than a fixed thresh­

hold.

CERI'AINTY of every item in the action part of a Production Rule is defined dynamically by a function s(CERTAINTY of the condition part, sta­ tic CERI'AINTY of this item). CERTAINTY of the ac­ tion part of a Procedure Rule is defined as the CERI'AINTY of the condition part.

III MAIN PARI'S OF MES

MES is mainly Call)OSed of:

1. Task Solution Program
2. Explanation Program
3. Subroutine Base and its Management Program
4. Rule Knowledge Base and its Management Program
5. Comprehensive Data Base and its management Pro­ gram

In WELlES, the Subroutine Base is CaJl)Osed of standardized well-log interpretation software. Any program in the Base has no argument. The begin­ ning parts of all these programs are communication blocks communicating with Call)rehensive Data Base Management Program to get parameter values needed.

IV TASK SOLUTION

Execution of the system MES is driven by task solution, and Task Transformation Rules define the ways of solving TASKs.

Definition: A TASK T gets 'TRUE', if and only if : ( 1) the OBJECT corresponding to the TASK T has a value with strong support, or (2) the decom­ posed subTASKs Tl, T2, · · · , Tk of the TASK T all have values and at least one has a value 'TRUE';

a TASK T gets a 'FALSE', if and only if: (1) the OBJECT corresponding to the TASK T has same special value indicating contradiction or mistake, or (2) all the decomposed subTASKs T1, T2, · · · , Tk of the TASK T have values 'FALSE' ..

Ways of solving a TASK T :inply the ways of evaluating the OBJECT corresponding to the TASK T. The procedure of evaluating an OBJECT, i.e. , a procedure to produce a new ASSERI'ION happens simu­ taneously with the procedure of solving a TASK.We call the procedure the "side effect" of the Task

Solution.

Every OBJECT has a field of value from which it may get values. This field does not include all values indicating contradictions and mistakes. The OBJECT corresponding to a TASK has the same field of value ·as all OBJECTs corresponding to all the

TASK's decomposed subTASKs.

The procedure of evaluating an OBJECT(except for the OBJECTs with number values) is a procedure of evaluating the uncertainty of every member in the field of value.

The procedure is as follows:l) evaluating with Inference Rules: the CERI'AINI'Y of an item in the action part will be used to define the primary support value m of the corresponding member in the field of value. Primary support value of a member is defined as 0 if the member has no corres­ ponding items in the action part of an Inference Rules; 2) evaluating with Task Transformation Rules: if all decomposed subTASKs of the TASK correspon­ ding to the OBJECT have values and are not all

' FALSE', let mil,mi2,- ··,mik, the primary support functions on the field of value respectively of all the decaJl)Osed subTASKs with values 'TRUE',and m the primary support function on the field of value of the OBJECT, we define m=mil® mi2®··4Dmik.

We will now take the system WELlES as an exam­ ple to describe roughly how the system MES solves a TASK: ( 1) users put the reqirements of what they want the system to do and set a general TASK; (2) when a TASK has an unused Task Transformation Rule, use the Rule and produce new TASKs; Derivation Rules have higher priorities than Decomposed Rules; ( 3) when all decomposed subTASKs of a TASK have values, evaluate the TASK and do "side effect"; (4) when the OBJECT corresponding to a TASK has a value with strong support, evaluate the TASK; (5) if a TASK. is finished, and the OBJECT corresponding to the TASK has unused Inference Rules that can be used fordwa­ rd, use the Rules; ( 6) when a TASK has no unused Task Transformation Rules and the correponding OBJECT has no values with strong enough support, find all Inference Rules of the OBJECT that can be used backward, use them; ( 7) if same items in the condition part of an Inference Rule has no corres­ ponding ASSERI'ION in the Data Base, set a new TASK to get the ASSERI'ION needed; (8) when the condition part of a Production Rule has a big enough CERI'AIN­ TY, use the Rule; ( 9 ) when the condition part of a Proced~ Rule has a big enough CERI'AINI'Y, call the subroutine through Subroutine Base Management Pro­ gram; ( 10) the use of an Inference Rule produces new ASSERI'IONs and the system will store them into Data Base; (11) use 2-10 repeatedly until the general TASK is finished.

V CONCLUSION

This paper introduced the model expert system MES. We have intergrated numerical calculation with logical inference in a uniform framework in WELlES based on MES. We plan to establish some other oil expert systems based on the system MES.