Inference algorithm is an integral part of any expert system based on and working with procedural knowledge such as production rules. In general, also the production rules containing the compound statements in an antecedent of a consequent part is well known and supported with knowledge or expert systems. On the other hand, if a production rule is of an advanced internal structure (is transformed into a knowledge unit), standard inference algorithms (e.g. modus ponens or modus tollens) could provide insufficient results. The aim of this paper is to suggest a modification of the inference algorithms to be appropriate for working with knowledge units. The formal notification of the algorithm is accompanied with a practical example in the domain of Enterprise Resource Planning (ERP) system used for the support of a particular business process.
Inference engines (methods, strategies, procedures) are present in expert systems
used in various problem domains.
The expert system by
Technical systems and their modernization or aging are being analyzed with
mathematical models Krejci (2013). Regardless, another expert system on
microstructural characterization of dual-phase steels was developed by
Expert systems are being used to simulate human decision-making process in
complex decision situations
Knowledge unit is an extended procedural production rule with fixed internal structure (Domeová et al., 2008, see Materials and Methods for its definition). In this paper we propose an advanced inference algorithm suitable for a specific kind of production rules – knowledge units. We show how to use the internal structure of the knowledge unit to determine relationship among individual parts of the precedingknowledge unit and the successing knowledge unit within the inference process. The inference process is also demonstrated on a practical example – particular process within the working with an ERP system. 2
Inference strategy, i.e. the strategy how the system operates the responses to the questions, is the basic element of any expert system. In general, the inference engine compares the facts in the base of facts with the knowledge, usually represented by production rules. Production rules are an appropriate knowledge representation for this purpose, because on one hand they are easy to be retrieved from human experts and, on the other hand, are suitable for automated processing with expert systems.
Standard production rules (IF – THEN rules) are consisting of two parts: antecedent (evidence, situation, problem) and consequent (hypothesis, action, solution). The production rules formalized by the statement (Mařík et al., 2004) where
E, E → H
,
H
and means that if evidence E and production rule E → H are valid, then hypothesis H
is also valid.
On the other hand, indirect inference can also be used. Indirect inference is expressed by the rule of “modus tollens” and can formally be written as ¬H, E → H
¬E
which means that if the hypothesis H is NOT valid and the rule E → H is valid, then
the evidence E is also NOT valid. Backward chaining refers to an approach to
reasoning in which an inference engine endeavours to find a value for an overall goal
by recursively finding values for subgoals. Examining rule conclusions to identify
rules that could possibly establish a value for the goal is important for the effort of
finding a value for the immediate goal
For the purposes of this work we understand the knowledge unit as an enhanced production rule containing the compound statement in the antecedent and simple statement in the consequent part. As we showed in our previous work (Dömeová et al., 2008), this kind of the production rules meet better the requirements of a problem-oriented representation of an explicit knowledge.
Formally, we suggested to record knowledge unit as (Dömeováet al., 2008): KU = {X, Y, Z, Q}, where
Even though there is no unique way to create sentences based on the production rules
Another advantage of the knowledge unit concept is that it allows to define unary
and operations with knowledge units such as drill down or roll up (unary operations)
or merging or decomposition (binary operations, see Dömeová et al., 2008) with no
influence to the complexity of the expressions of the knowledge units in natural
languages
To be operable, any knowledge unit could be formally expressed as a production rule in the following form:
IF (X and Y and Z) THEN Q.
This allows to define the relationships among elements of the knowledge units within the basic inference method. The basic form of elementary inference is defined as follows:
Let's have two knowledge units KU1 = {X1,Y1,Z1,Q1} and KU2= {X2,Y2,Z2,Q2}.
Further suppose that the statement IF (X and Y and Z) THEN Q is valid. Then the inference with knowledge units can proceed from element Q1to Y2, thus KUINF = {Q1} ==> {Y2} In the language form the operation could be written as follows: “IFweare not able to apply the solution Q1, it becomes the elementary problem Y2solved within the problem situation X2 to reach the objective Z2; THENthe solution Q2 should be applied."
The inference mechanism with knowledge unit is described in Fig. 1.
The illustrative example deals with the problem "Application user error analysis" is occurred within the working with an ERP system. The objective is to find errors in the application or find the application, where the error occurred. The error can be vaguely identified by the expert. In this case knowledge units are optimized to knowledge level of an operator on first line helpdesk support. This level was explicitly defined by the expert. For the case study, it is designed for the following scenario:
An error occurred in the application "SharePoint Nintex Workflow" with
elementary describe the error as follows: "One column requires a different type of
information". This type of error may have origin in several integrated systems. First
step is the diagnosis in application where error occurred. The result of first step is the
identification application where the error occurred. The second step is diagnosis,
which define the module or object, where is the original error in application. And
after finding the error is next step to fix the error. The purpose of inference is to find
the error in origin application and make first analysis. Boundary of the knowledge
domain is the issue of diagnostic errors in the context of integrated applications.
Design of the expert system will be similar like in the case of authors
X1 Y1 Z1 Q1 X2 Y2 Z2 Q2 X2 Y2 Z2 Q2 X4 Y4 Z4 Q4
We can also KU2 describe: "If we want to solve the error in the “purchase request workflow” and find which applications it is an error, then we must run the analytical test in application where error occurred and identify an error application."
In this Fig. 2. are knowledge units fill with concrete values during the inference. This case study, demonstrate the inference chaining used for finding errors in application Workflow purchase. The error message stands at the top of the figure. The inference with knowledge units defined location of the error and make result for correction. After correction, continues the process with re-initiating the purchase request. In the KU1, 2, 3 and 4 are concrete knowledge unit for this case: KU1 • X1 Purchase (under the statutes) • Y1 Create purchase request • Z1 Provide the delivery for the project • •
Q1 Fill out the request form of purchase request and send = Error state: „One column requires a different type of information” X2 Solving an error in purchase request workflow Y2 Find application, where is error ("Q1" = "Y2" ==> "One column requires a different type of information") Z2 Start analytical test application Q2 Identify an error application = "KS systemization"
Y2 Repair error or data inconsistency ("Q2" = "Y3" ==> "In the KS systemization)" Z2 Ensure correct operation of the system Q2 Make a correction in the object = “Repair systemization tree”
Y4 Detect true values and process consistency ("Q3" = "Y4" ==> "Repair systemization tree) Z4 Correct classify employee
Q4 Repair / Correction = "Correction value"
The inference with knowledge unit is defined like special operation between more than one knowledge units. In the real case study is illustrated the inference mechanism with crisp knowledge unit. The case study has a real ground, of the simple problem and it solve problem in few integrated software application in corporation. This case study helps in diagnosis applications problems-errors and is designed for first level of support helpdesk operators.
Base of facts: • User (employee) not valid, "NAV" • Systemization number not valid, "KS" • Wrong data, "ActiveDirectory = AD" • One column requires a different type of information, "Error" • Purchase request, "Error", "NAV" • Systemization, "KS", Wrong number • Object employee, "NAV", Wrong department • Employee <=50% • More AD ID • Wrong AD tree • Purchase request, "Error", "AD" • Purchase request, "Error", "KS" Base of rules:
• Rule 1 If "User (employee) not valid, "NAV"" Or "Systemization number not valid, "KS"" Or "Wrong data, "AD"" Then "One column requires a different type of information"
• Rule 2 If "Purchase request, "Error", "KS"" Then "User (employee) not valid, "KS""
• Rule 3 If "Systemization, "KS", Wrong number" Then "Purchase request, "Error", "KS"" • Rule 4 If "Purchase request, "Error", "AD"" Then "Wrong data, "AD"" • Rule 5 If “More AD ID" Or "Wrong AD tree" Then "Purchase request, "Error", "AD""
• Rule 6 If "Purchase request, "Error", "NAV"" Then "Systemization, "NAV", Wrong number"
• Rule 7 If "Object employee, "NAV", Wrong department" Then "Purchase request, "Error", "NAV"" Within the standard inference, the consequent is derived with a sequential chaining of the production rules using the basis of the facts. When inferred knowledge units, individual knowledge units (or their specific parts, respectively) are merged for deriving the consequent, or even another knowledge unit. The main difference between the standard approach and our new one approach lays on the definition of the basis of the facts. In the standard approach, the set of the rules and basis of the facts are strictly separated. On the contrary, knowledge units cover both the production rule and additional information (the problem situation and the solution of the elementary problem (antecedent in a standard production rule)); thus some facts are already integrated directly into the knowledge unit.
Moreover, as the structure of the knowledge units is standardized, it predetermines the order of the knowledge unit by production rules. Just this way of the order allows to base the inference on the facts integrated directly in the units. The inference among two or more knowledge units stems from this principle - the fixed interrelation between the elements of the knowledge units "Q1" è "Y2"
In this paper we proposed a way to process a knowledge unit as an enhanced
production rule with an inference engine in an expert system. In particular, backward
chaining inference algorithm was used. Our approach contributes to decreasing the
entropy in the chaining when the production rule consists of compound statements in
antecedent or consequent part of the production rule. Of course, the next necessary
step is to show the application of our algorithm on more particular examples and
compare the success rates of a standard inference algorithm and this new one. The
user-oriented point of view could be used for this purpose
Acknowledgements. The research is supported by the grant project of the Internal Grant Agency of the FEM CULS Prague “Data, information and knowledge in expert systems”, No. 20171026.