Recommendations 1-5 are possible for students who have provided a final undergraduate transcript. Recommendations 6-7 are possible for students who have not provided a final undergraduate transcript. Recommendation 8 is possible whether or not the undergraduate degree has been completed.

Expert system inputs: Here is a grouped list of the attributes, identified from the flow chart, for which input PROMPTs will be written:

• Completion of undergraduate program
  • Final undergraduate transcript availability
• English language requirement
  • Bachelor's degree from US institution
  • Test of English as a Foreign Language (TOEFL)
• Performance as an undergraduate
  • Grade Point Ratio (GPR) last 60 Undergraduate (UG) hours
  • Honor student
  • Honor graduate
  • Valedictorian
  • Salutatorian
• Performance in prior graduate work (if any taken)
  • Grade Point Ratio (GPR) for completed graduate work
• Performance on graduate admissions tests
  • Graduate Record Exam (GRE) overall score
  • Graduate Record Exam (GRE) verbal score

Certainty factors: Because these inputs are factual rather than opinions, certainty factor input will not be requested for any of the PROMPTs in this knowledge base: the optional CF parameter is not used in the PROMPTs.

Multi-valued attributes: There are four parameters representing special honors, and an applicant could possess any combination of these. The parameters are used in several rules, and the fact that an applicant possesses none of the attributes is also used in several rules. This set of circumstances is efficiently represented in an e2gRuleEngine knowledge base through the combined use of the AllChoice PROMPT along with the MAXVALS and DEFAULT statements:

PROMPT [the applicant] AllChoice
"This applicant is (check all that apply):"
"an honor student"
"an honor graduate"
"a class valedictorian"
"a class salutatorian"

MAXVALS [the applicant] 4
DEFAULT [the applicant] = "not the recipient of special honors"

The AllChoice PROMPT allows the knowledge base user to check any or all of the parameters describing the applicant's special honors. A MAXVALS statement allowing four values of the applicant must be included or values beyond the first one entered will be discarded.

It is often useful for a rule to detect the fact that no value can be found for an attribute. This is accomplished in e2gRuleEngine by employing the DEFAULT statement. The PROMPT for the applicant is the only source of values for this attribute. If none of the values are checked when the PROMPT is issued, the inference engine determines that the value cannot be resolved and the DEFAULT value "not the recipient of special honors" is assigned. Here is an example rule that will only fire for an applicant who has received no special honors:

RULE [Conditional eval, low GRE]
If [the evaluation] = "for a conditional decision" and
[the applicant] = "not the recipient of special honors" and
[the applicant's GRE score] < 1100
Then [the recommendation] = "wait for transcript" and
[the action] = "based on established policy"

Interim constructs: Knowledge bases are sometimes simplified and recommendation justifications clarified by using interim constructs to capture a common theme. The next pair of rules captures the logic in the flow chart that determines the need to examine the applicant's undergraduate GPR:

RULE [Consider undergraduate GPR (no grad credits)]
If [the applicant's graduate status] = "no prior graduate work completed"
Then [the undergraduate GPR should be considered] = true

RULE [Consider undergraduate GPR (grad credits)]
If [the applicant's graduate status] = "prior graduate work completed" and
[the applicant's GPR on prior graduate work] > 2.99
Then [the undergraduate GPR should be considered] = true

RULE [Deny because of undergraduate GPR]
If [the undergraduate GPR should be considered] = true and
[the applicant's GPR on last 60 undergraduate hours] < 2.5
Then [the recommendation] = "deny normal admission" and
[the action] = "based on established policy"

RULE [Deny because of undergraduate GPR (no grad credits)]
If [the applicant's graduate status] = "no prior graduate work completed" and
[the applicant's GPR on last 60 undergraduate hours] < 2.5
Then [the recommendation] = "deny normal admission" and
[the action] = "based on established policy"

RULE [Deny because of undergraduate GPR (grad credits)]
If [the applicant's graduate status] = "prior graduate work completed" and
[the applicant's GPR on prior graduate work] > 2.99 and
[the applicant's GPR on last 60 undergraduate hours] < 2.5
Then [the recommendation] = "deny normal admission" and
[the action] = "based on established policy"

The knowledge base: the complete knowledge base is provided in the following table as a reference.

Graduate Admissions Knowledge Base

REM Graduate admissions demonstration expert system REM Decide how to proceed RULE [Language requirement] If [the applicant's UG status] = "receiving a bachelor's degree from a US institution" or [the applicant's TOEFL score] > 499 Then [the language requirement] = "met" RULE [Conditional consideration] If [the language requirement] = "met" and [the applicant's final undergraduate transcript] = "not available" Then [the evaluation] = "for a conditional decision" RULE [Full consideration] If [the language requirement] = "met" and [the applicant's final undergraduate transcript] = "available" Then [the evaluation] = "for a full decision" REM Conditional evaluation RULE [Wait for transcript] If [the evaluation] = "for a conditional decision" and [the applicant's GPR on last 60 undergraduate hours] < 3.3 Then [the recommendation] = "wait for transcript" and [the action] = "based on established policy" RULE [Honor student] If [the evaluation] = "for a conditional decision" and [the applicant's GPR on last 60 undergraduate hours] > 3.29 and [the applicant] = "an honor student" Then [the recommendation] = "admit conditionally" and [the action] = "based on special decision" RULE [Conditional eval, high GRE] If [the evaluation] = "for a conditional decision" and [the applicant] = "not the recipient of special honors" and [the applicant's GRE score] > 1099 Then [the recommendation] = "admit conditionally" and [the action] = "based on special decision" RULE [Conditional eval, low GRE] If [the evaluation] = "for a conditional decision" and [the applicant] = "not the recipient of special honors" and [the applicant's GRE score] < 1100 Then [the recommendation] = "wait for transcript" and [the action] = "based on established policy" REM Full evaluation REM Deny RULE [Deny because language requirement not met] If [the applicant's UG status] = "not receiving a bachelor's degree from a US institution" and [the applicant's TOEFL score] < 500 Then [the recommendation] = "deny normal admission" and [the action] = "based on established policy" RULE [Deny because of graduate GPR] If [the applicant's graduate status] = "prior graduate work completed" and [the applicant's GPR on prior graduate work] < 3.0 Then [the recommendation] = "deny normal admission" and [the action] = "based on established policy" RULE [Consider undergraduate GPR (no grad credits)] If [the applicant's graduate status] = "no prior graduate work completed" Then [the undergraduate GPR should be considered] = true RULE [Consider undergraduate GPR (grad credits)] If [the applicant's graduate status] = "prior graduate work completed" and [the applicant's GPR on prior graduate work] > 2.99 Then [the undergraduate GPR should be considered] = true RULE [Deny because of undergraduate GPR] If [the undergraduate GPR should be considered] = true and [the applicant's GPR on last 60 undergraduate hours] < 2.5 Then [the recommendation] = "deny normal admission" and [the action] = "based on established policy" RULE [Deny because of undergraduate GPR and GRE] If [the undergraduate GPR should be considered] = true and [the applicant's GPR on last 60 undergraduate hours] > 2.49 and [the applicant's GRE score] < 900 Then [the recommendation] = "deny normal admission" and [the action] = "based on established policy" RULE [Deny because of GRE] If [the undergraduate GPR should be considered] = true and [the applicant's GPR on last 60 undergraduate hours] > 2.49 and [the applicant] = "not the recipient of special honors" and [the applicant's GRE score] < 900 Then [the recommendation] = "deny normal admission" and [the action] = "based on established policy" REM Provisional acceptance RULE [Provisional acceptance: low GRE, verbal GRE] If [the undergraduate GPR should be considered] = true and [the applicant's GPR on last 60 undergraduate hours] > 2.49 and [the applicant] = "not the recipient of special honors" and [the applicant's GRE score] > 899 and [the applicant's GRE score] < 1100 and [the applicant's GRE verbal score] < 400 Then [the recommendation] = "admit provisionally - recommend English remediation" and [the action] = "based on established policy" RULE [Provisional acceptance: low GPR, verbal GRE] If [the undergraduate GPR should be considered] = true and [the applicant's GPR on last 60 undergraduate hours] > 2.49 and [the applicant's GPR on last 60 undergraduate hours] < 3.0 and [the applicant's GRE score] > 899 and [the applicant's GRE verbal score] < 400 Then [the recommendation] = "admit provisionally - recommend English remediation" and [the action] = "based on established policy" RULE [Provisional acceptance: low GRE] If [the undergraduate GPR should be considered] = true and [the applicant's GPR on last 60 undergraduate hours] > 2.99 and [the applicant] = "not the recipient of special honors" and [the applicant's GRE score] > 899 and [the applicant's GRE score] < 1100 and [the applicant's GRE verbal score] > 399 Then [the recommendation] = "admit provisionally" and [the action] = "based on established policy" RULE [Provisional acceptance: low GPR] If [the undergraduate GPR should be considered] = true and [the applicant's GPR on last 60 undergraduate hours] > 2.49 and [the applicant's GPR on last 60 undergraduate hours] < 3.0 and [the applicant's GRE score] > 899 Then [the recommendation] = "admit provisionally" and [the action] = "based on established policy" REM Accept RULE [Acceptance: honors] If [the undergraduate GPR should be considered] = true and [the applicant's GPR on last 60 undergraduate hours] > 2.99 and [the applicant] : "an honor graduate" "a class valedictorian" "a class salutatorian" Then [the recommendation] = "admit with full status" and [the action] = "based on special decision" RULE [Acceptance at departmental discretion] If [the undergraduate GPR should be considered] = true and [the applicant's GPR on last 60 undergraduate hours] > 2.99 and [the applicant] = "not the recipient of special honors" and [the applicant's GRE score] > 1099 and [the applicant's GRE verbal score] < 400 Then [the recommendation] = "admission decision is at department's discretion" and [the action] = "based on established policy" RULE [Acceptance] If [the undergraduate GPR should be considered] = true and [the applicant's GPR on last 60 undergraduate hours] > 2.99 and [the applicant] = "not the recipient of special honors" and [the applicant's GRE score] > 1099 and [the applicant's GRE verbal score] > 399 Then [the recommendation] = "admit with full status" and [the action] = "based on established policy" REM Prompts PROMPT [the applicant's UG status] MultChoice "This applicant is:" "receiving a bachelor's degree from a US institution" "not receiving a bachelor's degree from a US institution" PROMPT [the applicant's TOEFL score] Numeric "What is the applicant's TOEFL (Test of English as a Foreign Language) score?" "0" "800" PROMPT [the applicant's GPR on prior graduate work] Numeric "What is the applicant's GPR (Grade point ratio) for prior graduate work?" "0" "4.0" PROMPT [the applicant's final undergraduate transcript] MultChoice "The applicant's final undergraduate transcript is:" "available" "not available" PROMPT [the applicant's GPR on last 60 undergraduate hours] Numeric "What is the applicant's GPR (Grade point ratio) for the last 60 UG hours?" "0" "4.0" PROMPT [the applicant's graduate status] MultChoice "This applicant's graduate status is:" "prior graduate work completed" "no prior graduate work completed" PROMPT [the applicant's GPR on prior graduate work] Numeric "What is the applicant's GPR (Grade point ratio) on prior graduate work?" "0" "4.0" PROMPT [the applicant] AllChoice "This applicant is (check all that apply):" "an honor student" "an honor graduate" "a class valedictorian" "a class salutatorian" PROMPT [the applicant's GRE score] Numeric "What is the applicant's total GRE (Graduate Record Exam) score?" "0" "1600" PROMPT [the applicant's GRE verbal score] Numeric "What is the applicant's GRE verbal score?" GOAL [the recommendation] GOAL [the action] MAXVALS [the applicant] 4 DEFAULT [the applicant] = "not the recipient of special honors"

Recommendations for implementing and debugging a knowledge base

When the "Start the consultation" button is clicked on the e2gRuleEngine applet's opening screen, the knowledge base is loaded and syntax checked. If an error is encountered, loading immediately stops and an error number is displayed. If the test is run in the "debug" mode (the DEBUG applet parameter has the value "true") the line containing the error is displayed in the "Knowledge Base Developer's Output" window. As a result, it is most efficient to adhere to the following advice when building a knowledge base:

• Enter a few RULEs and PROMPTs at a time so that the knowledge base is unlikely to contain multiple syntax errors.
• Run with the DEBUG parameter in the <APPLET> tags set to "true" to simplify finding the knowledge base line containing an error.

Some additional debugging suggestions that you might find helpful:

• Most e2gRuleEngine syntax errors are caused by spelling or punctuation problems or by omitting or mismatching the delimiters [ ] " '. Attribute names and text strings that are intended to be identical may differ only in case: spacing and punctuation characters must match exactly.
• Attribute names must be defined in a RULE before they are used in other statements including PROMPT, GOAL, MAXVALS and DEFAULT. Always put these statements after all of the RULEs. You cannot enter a PROMPT for an attribute in your knowledge base in advance of entering at least one RULE that uses the attribute.
• You may want to print out the Reference documentation or at least the Error Codes for convenient use while constructing your knowledge base.
• Experimenting with your knowledge base with a variety of inputs after adding a each few RULEs and PROMPTs is advisable to help identify errors in your logical analysis. If you don't get the results you expect, figure out why this is happening before adding more complexity.
• Make sure you use some test cases that exercise the boundaries of the rules. For example, in the graduate admissions knowledge base, running tests with GPRs of exactly 3.0, 2.99, 3.29, 3.3 helps identify minor errors made when writing inequality comparisons.
• Consider developing your knowledge base using the e2gRuleWriter decision table software described in Module 10. This program provides a number of mechanisms for avoiding or identifying errors in knowledge base construction.

Finally, here is a summary of some commonly encountered knowledge base problems.

To run this knowledge base, CLICK HERE.

The conditions for incorporating numeric calculations in an e2gRuleEngine rule include:

• Numeric expressions are permitted only in rule consequents (the "then" part of the rule).
• A numeric expression must be enclosed in curly braces: { } and may incorporate delimited attribute names, numeric literals, mathematical operators and parentheses.
• Each attribute used in the expression must be used in the rule premise (the "if" part of the rule). This is to keep the rule from firing before a value is determined for each attribute to be used in a calculation in the rule's consequent. The premise clauses must be joined by the "and" logical operator to insure that all attributes have a value before the rule fires.
• If e2gRuleEngine attempts to use an attribute in a calculation that does not have a value known with a CF >= MINCF, operation of the program will terminate with an error message.
• A new operator "has been determined" denoted by the question mark "?" is provided to facilitate checking for value assignment before numeric calculations are performed. The calculate pay rule in the example knowledge base illustrates the use of this operator. The calculate overtime hours rule does not require use of the "?" operator since the attribute used in the consequent's numeric calculation is already used in the premise.
• Attributes used in numeric calculations must have numeric values. To permit the use of PROMPTs that return string values, e2gRuleEngine will attempt to coerce string values into numbers if they are used in a calculation. The prompt for the hourly rate illustrates this concept. A string that can be converted includes numbers and an optional single decimal point. It may begin with a + or - sign. It may not include dollar signs, commas or other special characters. If e2gRuleEngine tries to convert a string value that does not represent a legitimate number into a number, the program will terminate with an error message.
• The Certainty Factor (CF) associated with attributes when they are used in computations is 100%. The result of the evaluation of a numeric expression may be assigned a CF by including the @xxx assignment after the closing expression delimiter: }. The calculate pay rule in the example knowledge base illustrates this format.
• Mathematical operators are evaluated according to the precedence shown in the following table. Highest precedence operations are performed first. If two operators have the same precedence, they are evaluated left to right. Parentheses and nested parentheses may be used to alter the order of the evaluation:

  Mathematical Operator Precedence
  Operator	Precedence	Operation
  ^	3	Exponentiation
  *	2	Multiplication
  /	2	Division
  +	1	Addition
  -	1	Subtraction

  Some examples to illustrate calculation precedence and the impact of parentheses:

  5 + 2 * 10 = 25
  (5 + 2) * 10 = 70
  (5+2) * 10 ^ 2 = 700
  ((5+2) * 10) ^ 2 = 4900

• Although it is not possible to perform numerical calculations in a rule's premise, it is often possible to use two rules to obtain the desired effect. Suppose, for example, the following rule is needed in a knowledge base:

  RULE [Decide whether to buy]
  If (A + B) < 5
  Then [result] = "buy the item"
  

  e2gRuleEngine cannot support this rule premise calculation. However, the following two rules will provide equivalent logic:

  RULE [Calculate sum of A and B]
  If [A] ? and
  [B] ?
  Then [AplusB] = {[A] + [B]}
  
  RULE [Decide whether to buy]
  If [AplusB] < 5
  Then [result] = "buy the item"
  

  The first rule will only fire when values are available for both A and B and will calculate their sum in the new variable AplusB. Then, the second rule will be able to fire.

• Using e2gRuleEngine with the DEBUG parameter set to "true" is strongly recommended while developing a knowledge base that incorporates numeric calculations. When the program fails during a calculation, an output to the debug window will indicate the location in the expression at which the error was detected.