Exercises for Backward Chaining

Exercise 1: Let's define DNFs in arrays for rules and facts.
- Rule 0: If an animal croaks and eats flies, then the animal is frog.
- Rule 1: If an animal chirps and sings, then the animal is canary.
- Rule 2: If an animal is a frog, then the animal is green color.
- Rule 3: If an animal is a canary, then the animal is yellow color.
- Fact 0: An animal croaks.
- Fact 1: The animal eats flies.
- Query: yellow, or green?
- Propositional symbols: Croak, EatFly, Frog, Chirp, Sing, Canary, Green, Yellow
<div id='tr1-output'></div> <script> var rules = []; rules['Frog'] = [['Croak', 'EatFly']]; rules['Canary'] = ???; rules['Green'] = ???; rules['Yellow'] = ???; var facts = ['Croak', ???]; var colors = ['Yellow', ???]; var str = rules['Frog'] + '; ' + rules['Canary'] + '; ' + rules['Green'] + '; ' + rules['Yellow']; $('#tr1-output').html(str); </script>

Exercise 2: Let's check if a propositional symbol is a fact. This exercise should be done after Exercise 1.
<div id='tr2-output'></div> <script> function is_fact(???) // check if ps is included in facts[] using includes function in the array, // i.e., facts.includes(...). { ??? } var str = is_fact(facts, 'Yellow'); $('#tr2-output').html('' + str); </script>

Exercise 3: Let's check if there is a rule to use for a propositional symbol. This exercise should be done after Exercise 2.
<div id='tr3-output'></div> <script> function there_is_rule(???) { if (rules[???] == ???) // rules is an associative array. You can check if the value is undefined. // You can compare the value to undefined. ???; else ???; } var str = there_is_rule(rules, 'Frog'); $('#tr3-output').html('' + str); </script>

Exercise 4: Let's write a recursive function for Backward Chaining. This exercise should be done after Exercise 3.
<div id='tr4-output'></div> <script> function BC_anded(rules, facts, ???) { // for multiple proposition symbols, var valid = ???; for (...) valid = valid && ... } function BC(rules, facts, ps) { // if ps is a fact ??? // if there is no rule used for ps; ???; // for multiple rules var valid = ???; for (var i = 0; i < rules[ps].length; i++) // the backward chaining results for rules should be ORed. { // for multiple propositions in a rule // the backward chaining results for positional symbols, rules[ps][i][], in a rule should be ANDed using BC_anded(). ??? } if (valid) facts.???(ps); // push it into the facts queue return ???; } $('#tr4-output').html('' + BC(rules, facts, 'Yellow') + ', ' + BC(rules, facts, 'Green')); </script>

Exercises for Backward Chaining Algorithm