1. Forward chaining: an overview We start with a set of data collected through observations, and check each rule to see if the data satisfy its premises. This process is called rule interpretation; it is performed by the Inference Engine (IE) and involves the following steps: Rules New rules Applicable Selected rules rules Facts New facts Knowledge (rule memory) Facts (working memory) Step1: Match Step2: Conflict Resolution Step 3: Execution

2. The fruit identification example (adapted from Dankel & Gonzalez) Consider a KBS intended to recognize different fruits provided fruit descriptions. Assume that the set of rules consists of the following rules. Rule 1: If (shape = long) and (color = green) Then (fruit = banana) Rule 1A: If (shape = long) and (color = yellow) Then (fruit = banana) Rule 2: If (shape = round) and (diameter > 4 inches) Then (fruitclass = vine) Rule 2A: If (shape = oblong) and (diameter > 4 inches) Then (fruitclass = vine) Rule 3: If (shape = round) and (diameter < 4 inches) Then (fruitclass = tree) Rule 4: If (seedcount = 1) Then (seedclass = stonefruit) Rule 5: If (seedcount > 1) Then (seedclass = multiple) Rule 6: If (fruitclass = vine) and (color = green) Then (fruit = watermelon)

3. The fruit identification example (cont.) Rule 7: If (fruitclass = vine) and (surface = smooth) and (color = yellow) Then (fruit = honeydew) Rule 8: If (fruitclass = vine) and (surface = rough) and (color = tan) Then (fruit = cantaloupe) Rule 9: If (fruitclass = tree) and (color = orange) and (seedclass = stonefruit) Then (fruit = apricot) Rule 10: If (fruitclass = tree) and (color = orange) and (seedclass = multiple) Then (fruit = orange) Rule 11: If (fruitclass = tree) and (color = red) and (seedclass = stonefruit) Then (fruit = cherry) Rule 12: If (fruitclass = tree) and (color = orange) and (seedclass = stonefruit) Then (fruit = peach) Rule 13: If (fruitclass = tree) and (color = red) and (seedclass = multiple) Then (fruit = apple) Rule 13A: If (fruitclass = tree) and (color = yellow) and (seedclass = multiple) Then (fruit = apple) Rule 13B: If (fruitclass = tree) and (color = green) and (seedclass = multiple) Then (fruit = apple)

4. The fruit identification example (cont.) Assume the following set of facts comprising the initial working memory: FB = ((diameter = 1 inch) (shape = round) (seedcount = 1) (color = red)) The forward reasoning process is carried out as follows: Cycle 1: Step1 (matching) Rules 3 and 4 are applicable Step2 (conflict resolution) Select rule 3 Step 3 (execution) FB  (fruitclass = tree) Cycle 2: Step1 (matching) Rules 3 and 4 are applicable Step2 (conflict resolution) Select rule 4 Step 3 (execution) FB  (seedclass = stonefruit)

5. The fruit identification example (cont.) Cycle 3: Step1 (matching) Rules 3, 4 and 11 are applicable Step2 (conflict resolution) Select rule 11 Step 3 (execution) FB  (fruit = cherry) Cycle 4: Step1 (matching) Rules 3, 4 and 11 are applicable Step2 (conflict resolution) No new rule can be selected. Stop. Note, that there are many variations of the described forward-chaining strategy. The TRE system from our textbook, for example, fires all applicable rules – not a selected rule. This way, it makes sure that all possible conclusions are inferred, rather than selected ones.

6. Forward chaining: general rule format Rules used to represent “diagnostic” or procedural knowledge have the following format: If is true, is true, … is true Then is true. The rule interpretation procedure utilizes unification (or renaming), which states that one sentence is a renaming of another if they are the same except for the names of pattern variables. Examples: likes(x, ice-cream) is a renaming of likes(y, ice-cream) flies(bird1) is a renaming of flies(bird2), and both are renamings of flies(Tom). Here x, y, bird1 and bird2 are pattern variables.

7. Pattern matching To recognize pattern variables more easily, we will arrange them in two-element lists, where the first element is ?, and the second element is the pattern variable. Examples: (color (? X) red) (color apple (? Y)) (color (? X) (? Y)) If the pattern contains no pattern variables, then the pattern matches the “basic” statement (called a datum) iff the pattern and the datum are exactly the same. Example: Pattern (color apple red) matches datum (color apple red). If the pattern contains a pattern variable, then an appropriate substitution must be found to make the pattern match the datum. Example: Pattern (color (? X) red) matches datum (color apple red) given substitution  = {x / apple}

8. Pattern matching (cont.) To implement pattern matching, we need a function, match, which works as follows: > (match ’(color (? X) red) ’(color apple red)) ((X apple)) > (match ’((? Animal) is a parent of (? Child)) ’(Tim is a parent of Bob)) ((Child Bob) (Animal Tim)) (? _) will denote anonymous variables; these match everything. Example: (color (? _) (? _)) match (color apple red), (color grass green), etc.

9. Object streams Streams are lists of objects intended to be processed in the exact order in which they appear in the stream, namely from the front to the back of the stream. When a new object is added to the stream, it must be added to its back. To represent streams, we can use ordinary lists. Then, first allow us to access the first element, and rest will trim the first element off. However, we can also access the other elements of the list by means of second, third, etc., thus violating the definition of the stream. To prevent this from happening, streams will be represented as two-element lists, where the first element is the first object in the stream, and the second element is itself a stream. Example: * 'empty-stream EMPTY-STREAM * (stream-cons 'object1 'empty-stream) (OBJECT1 EMPTY-STREAM) * (stream-cons 'object1 '(OBJECT1 EMPTY-STREAM) ) (OBJECT1 (OBJECT1 EMPTY-STREAM))

10. Operations on streams  (defun stream-endp (stream) (eq stream 'empty-stream))  (defun stream-first (stream) (first stream))  (defun stream-rest (stream) (second stream))  (defun stream-cons (object stream) (list object stream))  (defun stream-append (stream1 stream2) (if (stream-endp stream1) stream2 (stream-cons (stream-first stream1) (stream-append (stream-rest stream1) stream2))))  (defun stream-concatenate (streams) (if (stream-endp streams) 'empty-stream (if (stream-endp (stream-first streams)) (stream-concatenate (stream-rest streams)) (stream-cons (stream-first (stream-first streams)) (stream-concatenate (stream-cons (stream-rest (stream-first streams)) (stream-rest streams)))))))

11. Operations on streams (cont.)  (defun stream-transform (procedure stream) (if (stream-endp stream) 'empty-stream (stream-cons (funcall procedure (stream-first stream)) (stream-transform procedure (stream-rest stream)))))  (defun stream-member (object stream) (cond ((stream-endp stream) nil) ((equal object (stream-first stream)) t) (t (stream-member object (stream-rest stream)))))  (defmacro stream-remember (object variable) `(unless (stream-member,object,variable) (setf,variable (stream-append,variable (stream-cons,object 'empty-stream))),object)) Here STREAM-REMEMBER is a macro that inserts new assertions at the end of the stream, so that when the stream is processed the assertions will be processed in the order in which they have been entered.

12. An implementation of forward chaining The “Zoo” example considered here is adopted from Winston & Horn. The KBS is intended to identify animals provided their descriptions. Assume that all facts about the domain are stored in the fact base, *assertions*, represented as a stream, and all rules are stored in the rule base, *rules*, also represented as a stream. Pattern variables make it possible for a rule to match the fact base in a different way. Let us keep all such possibilities in a binding stream. Example: Consider the following rule set containing just one rule: ((identify ((? Animal) is a (? Species)) ((? Animal) is a parent of (? Child)) ((? Child) is a (? Species))) empty-stream) Let the fact base contains the following facts: ((Bozo is a dog) ((Deedee is a horse) ((Deedee is a parent of sugar) ((Deedee is a parent of Brassy) empty-stream))))

13. Example (cont.) The first match produces the following two-element binding stream: (((species dog) (animal bozo)) ((species horse) (animal deedee)) empty-stream) Next, the second rule antecedent is matched against each of the assertions in the fact base. However, this time we have the binding list from the first step, which suggests particular substitutions: 1Matching ((? Animal) is a parent of (? Child)) against the fact base fails for substitution ((species dog) (animal bozo)) 2Matching ((? Animal) is a parent of (? Child)) against the fact base given the substitution ((species horse) (animal deedee)) succeeds resulting in a new binding list: (((child sugar) (species horse) (animal deedee)) ((child brassy) (species horse) (animal deedee)) empty-stream)

14. Backward chaining Assume the same representation of rules as in forward chaining, i.e. If is true, is true, … is true Then is true. Rule interpretation starts with (i) an empty fact base, and (ii) a list of goals which the system tries to derive, and consists of the following steps: 1Form a stack initially composed of all “top-level” goals. 2Consider the first goal from the stack, and gather all of the rules capable of satisfying this goal. 3For each of these rules, examine the rule’s premises: i.If all premises are satisfied, execute the rule to infer its conclusion, and remove the satisfied goal from the stack.

15. Backward chaining (cont.) ii. If there is a premise which is not satisfied, look for rules by means of which this premise can be derived; if such rules exist, add the premise as a sub-goal on the top of the stack, and go to 2. iii. If no rule exists to satisfy the unknown premise, place a query to the user and add the supplied value to the fact base. If the premise cannot be satisfied, consider the next rule which has the initial goal as its conclusion. 4If all rules that can satisfy the current goal have been attempted, and all failed, then the goal is unsatisfiable; remove the unsatisfiable goal from the stack and go to 2. If the stack is empty (i.e. all of the goals have been satisfied) stop.

16. The fruit identification example Assuming that we do not have any information about the object that we are trying to recognize, let the “top-level” goal be (fruit = (? X)). Step1 Initial fact base: ( ) Initial stack of goals: ((fruit = (? X))) Step 2 Rules capable of satisfying this goal are: 1, 6, 7, 8, 9, 10, 11, 12, 13, 14. Step 3 Consider Rule 1. Its first premise is (shape = long). There is no data in the FB matching this premise and no rule has (shape = (? Y)) as its conclusion. Therefore, a query is placed to the user to acquire for the shape of the fruit under consideration. Assume that the user replies that the fruit is round, i.e. the current FB becomes Current fact base: ((shape = round)). Rule 1 fails, and Rule 6 is examined next. The first premise of Rule 6 results in a new goal which is added at the beginning of the current stack of goals. Current stack of goals: ((fruitclass = (? Y)) (fruit = (? X)))

17. The fruit identification example (cont.) There are two rules capable of satisfying the newly stated goal, namely Rule 2 and Rule 3. The first premise of Rule 2, (shape = round), matches a datum in the FB. The second premise leads to a new query regarding the diameter of the fruit. Assume that the answer is (diameter = 1 inch). Current fact base: ((shape = round)(diameter = 1 inch)). Rule 2 fails, and Rule 3 is examined next. It succeeds, thus a new conclusion, (fruitclass = tree) is added to the FB and the first goal is removed from the current stack of goals. Current fact base: ((shape = round)(diameter = 1 inch)(fruitclass = tree)). Now Rules 6, 7 and 8 fail, and Rule 9 is examined next. Its first premise succeeds, but its second premise places a new query regarding the color of the fruit. Assume that the user enters (color = red), which fails Rules 9 and 10. The first two premises of Rule 11 are satisfied, the third premise places a query regarding the seedclass. Assume that the user enters (seedclass = stonefruit), resulting in Rule 11 being satisfied, and its conclusion (fruit = cherry) added to the FB. Note that this proves our top-level goal. Current fact base: ((shape = round)(diameter = 1 inch)(fruitclass = tree)(color = red)(seedclass = stonefruit)(fruit = cherry)). Current stack of goals: () Step 4 Stop, no more goals remain to be proved.

18. Types of Pattern-Directed Inference Systems All PDISs use assertions to represent declarative knowledge, and rules to represent procedural knowledge. However, they can defer in the way they search for a solution. Our textbook suggests the following classification of PDIS: 1.Forward-chaining PDIS. 2.Backward-chaining PDIS. 3.PDIS using production rules, where the search strategy selects a single best rule to fire, rather than all applicable rules. 4.Procedural deduction systems. These use pattern-matching, but their procedural knowledge lacks the modularity typical for rule-based PDIS. We shall primarily discuss forward-chaining PDISs assuming that a PDIS is a part of a larger system, which starts up the PDIS and makes use of its output.