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*Forward Chaining vs. Backward Chaining - Prof. Dr. Knut Hinkelmann MSc BIS/ 2 Forward Chaining vs....*

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MSc Business Information Systems

Forward Chaining vs. Backward Chaining

Knut Hinkelmann

Prof. Dr. Knut Hinkelmann 2MSc BIS/

Forward Chaining vs. Backward Chaining

Logical Rules can be applied in two directions

Backward chaining start with the desired conclusion(s) work backwards to find supporting facts corresponds to modus tolens goal-directed

Forward chaining Starts from the facts apply rules to find all possible conclusions corresponds to modus ponens data driven

P R

O LO

G V

is iR

ul e

Prof. Dr. Knut Hinkelmann 3MSc BIS/

Example of a Declarative Knowledge Base

Father(X,Y) AND Father(Y,Z) Grandfather(X,Z)

Father(X,Y) AND Mother(Y,Z) Grandfather(X,Z)

Mother(X,Y) AND Father(Y,Z) Grandmother(X,Z)

Mother(X,Y) AND Mother(Y,Z) Grandmother(X,Z)

Father(X,Y) AND Father(X,Z) Sibling(Y,Z)

Mother(X,Y) AND Mother(X,Z) Sibling(Y,Z)

Father(peter,mary) Father(peter,john) Mother(mary,mark) Mother(jane,mary)

The rules can be used to • Derive all grandparent and sibling relationships (forward chaining) • Answer questions about relationships (backward chaining)

Prof. Dr. Knut Hinkelmann 4MSc BIS/

Illustrating Backward Chaining

Source: Kerber (2004), http://www.cs.bham.ac.uk/~mmk/Teaching/AI/l2.html

Prof. Dr. Knut Hinkelmann 5MSc BIS/

Illustration Forward Chaining Goal state: Z Termination condition: stop if Z is derived or no further rule can be applied

Source: Kerber (2004), http://www.cs.bham.ac.uk/~mmk/Teaching/AI/l2.html

Prof. Dr. Knut Hinkelmann 6MSc BIS/

Forward Chaining: Deriving ground Facts

Usually for forward chaining the facts are ground, i.e. they do not contain variables

To ensure that the derived facts are ground, all the variables which occur in the consequence of the rule must occur in the antecedents of the rule

Unification is thus restricted to matching (one of the expressions is ground): The condition can contain variables The matching fact does not contain variables

Prof. Dr. Knut Hinkelmann 7MSc BIS/

Forward Chaining Procedure: Recognise – Select – Act Cycle

Let the fact base consist of facts FB = {F1, … Fn}

1. Recognise: Match the conditions of the rules against the facts of the fact base, i.e. find all rules

C1 and C2 and … and Cm -> H such that the conditions C1, C2, …, Cm can be unified with facts F1, F2,

…, Fm with unifier (the set of applicable rules is called conflict set)

2. Select: If there is more than one rule that can be applied, choose one to apply. Stop if no rule is applicable

3. Act: Apply the chosen rule by adding adding H to the fact base, i.e. FB = FB {H}

4. Stop if termination condition holds, otherwise and go to 1

Act

Select

Recognize

Prof. Dr. Knut Hinkelmann 8MSc BIS/

Forward Chaining Strategies

Forward chaining computes all the facts that can be derived from the knowledge base

Forward chaining strategies differ in step „Select“. Here are some examples of strategies: Apply the rules sequentially Randomly select a rule Apply more specific rules first Prefer rules where conditions match a recently derived fact Derive consequences of a set of starting facts: Only apply rules

where at least one condition matches either with a starting fact or a derived fact Fact base contains facts that are generally true, e.g. insurance product Starting facts describe a concrete situation, e.g. customer data

Prof. Dr. Knut Hinkelmann 9MSc BIS/

Choosing Forward or Backward Chaining

Backward Chaining If you already know what you are looking for

Forward Chaining If you don't necessarily know the final state of your solution

Start states (facts)

Goal states

Prof. Dr. Knut Hinkelmann 10MSc BIS/

Decision Criteria for Forward or Backward Reasoning

More possible goal states or start states? Move from smaller set of states to the larger

Is Justification of Reasoning required? Prefer direction that corresponds more closely to the way users

think

What kind of events triggers problem-solving? If it is arrival of a new fact, forward chaining makes sense. If it is a query to which a response is required, backward chaining

is more natural.

In which direction is branching factor greatest? Go in direction with lower branching factor

Source: Kerber (2004), http://www.cs.bham.ac.uk/~mmk/Teaching/AI/l2.html

Prof. Dr. Knut Hinkelmann 11MSc BIS/

Branching Factor

Backward chaining more appropriate Forward chaining more appropriate

Prof. Dr. Knut Hinkelmann 12MSc BIS/

Combining Forward Chaining and Backward Chaining in VisiRule: Statement Box

The function of a statement box is to calculate a value from information that is already known.

Statement boxes have three elements: an editable name (balance_plus_order in example below) an editable local variable (X in example below) a statement assigning a value to the variable using the operator

„is“ (X is balance + order_total.) (Note: On the right of „is“ there is editable Prolog code which is used to calculate the value

Prof. Dr. Knut Hinkelmann 13MSc BIS/

Statement Box with an Arithmetic Expression

Prof. Dr. Knut Hinkelmann 14MSc BIS/

Example: Calculating Leap Years