Rule Based Reasoning

Abstract

The popularity of rules-based systems (RBSs) is due to their naturalness. This chapter presents the potential applications of RBSs, the working of RBS, forward and backward chaining RBSs, their Algorithms, and inferencing using these systems. The analysis of complexity of preconditions, and efficiency of rule selection are introduced to sufficient depth, as well the cofmparison between the two types of RBSs are presented. A typical RBS, and other methods—model-based and case-based approaches are also discussed. In addition, number of solved, as well exhaustive list of exercises are provided at the end of the chapter for practice. The chapter concludes with its summary.

Exercises

• 1. List the various components of a Production System, and explain each.

• 2. In the above context, explain the importance of “binding”, “matching” and “conflict resolution”.

• 3. Suppose there is a production system with four initial facts: A, B, C, D and following three rules:

  $$\begin{aligned}&R_1:~if~A~then~E\\&R_2:~if~B \wedge F~then~G\\&R_3:~if~C\wedge E~then~F \end{aligned}$$

  • a. Using these rules and facts, explain what is meant by “backward chaining” and show explicitly how it can be used to determine the truth of G?

  • b. Explain what is meant by “forward chaining”, and show explicitly how it can be used in this case to determine new facts.

• 4. Consider the following possibilities, suggest the solution strategy to be adopted if the system is implemented as a rule based system:

  • a. A subgoal literal is generated such that the higher goal is a subset of the subgoal.

  • b. A subgoal literal is generated whose negation unifies with the higher-goal.

  • c. A subgoal S literal is generated that is equal to another goal G, and G is neither higher nor lower to S.

• 5. Translate the following knowledge base into predicate form.

  • If x is on top of y then y supports x.

  • If x is above y and they are touching each other then x is on top of y.

  • A phone is above a book.

  • A phone is touching a book.

  • a. Use forward-chaining to show that the predicate “supports(book, phone)” is true.

  • b. Use forward-chaining to show that the predicate “supports(book, phone)” is true.

  Count the number of triggering and rule firing in each of the above cases.

• 6. Given the propositions A, B, C, D and rules $R_1$ to $R_4$,

  $$\begin{aligned}&R_1 = if~ A \wedge X \wedge Y~then~Z\\&R_2 = if~B \wedge V ~then ~ Y\\&R_3 = if~C\wedge V ~then ~ X\\&R_4= if~ D~ then ~C \end{aligned}$$

  • a. Use the forward-chaining to determine if Z can be inferred from the above knowledge base.

  • b. Use the backward-chaining to determine if goal Z succeeds from the above knowledge base.

• 7. What are the conflict resolving strategies in case more than one rule matches with the assertions? Discuss the merits and demerits of each strategy for selection of a rule to fire.

• 8. Briefly justify each of the following for conflict resolution. Also, give examples in each case.

  • a. Specificity criteria.

  • b. Syntactically longest rule first.

  • c. Ordering rules.

  • d. Most recent first.

  • e. In order of increasing size of the rule.

• 9. List the following formulas in oder of specificity, and construct a tree such that those having same specificity will stand at the same level in the tree.

  • a. $b \vee c$

  • b. $b \wedge c$

  • c. $a \vee c$

  • d. $a \wedge c$

  • e. $a \wedge b$

  • f. $a \wedge b \wedge c$

  • g. b

  • h. c

• 10. How the assignment of priority to rules can be implemented? Consider the Table 4.2 to demonstrate the assignment of suitable priorities to rules listed in this table. Suggest the structure as how the priorities are to be stored and rules be invoked based on these priorities.

• 11. Explain what structures can be used and how they will operate, for knowledge based systems, for the following functionalities?

  • a. If a precondition of one or more rules is false, the system should exclude these rules from participation in the inference process.

  • b. If firing of some rules infer new knowledge, this should be added into the existing knowledge.

  • c. To maintain and use index file for rules.

• 12. For the rule (4.2), if domain size of p is $|p| = m$, domain size of variable x is n, and of y is l,

  • a. Find out the worst-case time complexity of the rule to be selected,

  • b. In how many ways ordering can be done?

  • c. Justify that it is NP-hard problem as a general case.

• 13. Which type of rule chaining you will prefer in the following situations? Also, identify, what is the goal in each case.

  • a. To diagnose the case of malaria infection, based on the symptoms of cough, soar throat, regular fever, shivering.

  • b. Identify a thief, based on the nature of theft, finger prints, and goods stolen.

• 14. ] Suggest an approach to combine the forward and backward chaining for the knowledge base shown in Table 4.2 (Hint: Try backward chaining to begin with, if it is not doing efficiently, then switch over to forward chaining.)

• 15. To prove a theorem of geometry using rule-based systems, represent the following statements as production rules:

  • a. Corresponding sides of two congruent triangles are also congruent.

  • b. Corresponding angles of two congruent triangles are also congruent.

  • c. If corresponding sides of two triangles are congruent then the triangles are congruent.

  • d. If corresponding sides and the angle covered by them are equal then the triangles are congruent.

  • e. Base angles of an isosceles triangle are congruent.

• 16. In what order the rules should be fired for inference efficiency? Discuss the merits and demerits of choosing a particular order of rule firing.

• 17. What are the criteria of selection of premises for firing the rules? Discuss this based on specificity and generality of the premises.

• 18. Consider a network of applicability of rules. Imagine that due to firing of a rule, a new inference is generated. This inference may contradict some fact or goal. Explain, what should be the structure of dependency network so that any inconsistency caused due to new inference is taken care of.

• 19. Suggest the strategy, as how a tree like rules structure can be used for reasoning in forward direction. Explain or suggest your strategy for following:

  • a. Whether the breadth-first or depth-first search is better for rule searching?

  • b. Whether the top-down or bottom-up search is better for firing of rule sequences?

  • c. How to eliminate one or both the rules, say $R_1$ and $R_2$, for consideration, if one of the precondition is false, which is common in both $R_1$ and $R_2$?

  • d. In the begin of a reasoning process whether you would prefer to choose to fire a rule with large number of preconditions or small?

• 20. Analyze the Algorithm 4.1 and justify that it is NP-hard as a general case, however, polynomial in real world situation.

• 21. Analyze the complexity of preconditions in the forward reasoning process.

• 22. How the following situations are implemented in knowledge base for rule-chaining? Explain.

  • a. “Is the pain intensifying with respirations?”

  • b. “Did shortening of breadth occur before throat pain?”

• 23. Given the knowledge base of rule-chaining of Table 4.2, show an analysis as, in general, which type, forward or backward search strategy is better? Also, justify your claim.

• 24. Why, a rule-based system having combination of forward and backward rule-chaining is more complex than either of these both?