Some Criteria of the Knowledge Representation Method for an Intelligent Problem Solver in STEM Education

Algorithm 2

(see [27]). Solving the problem as kind 2.

	Let K = (, , , ) be a knowledge domain as Rela-Ops model, and a problem P = (O, E, F) ⟶ G as kind 2 in Definition 3. This algorithm will solve problem P through these steps as follows:
	Input: The problem P = (O, E, F) ⟶ G
	Output: The solution to problem P.
	The method for designing this algorithm uses forward chaining reasoning. It combines heuristics rules in the reasoning process. Objects also attend this process as active agents for solving problems on themselves by Algorithm 1. This process is done when it gets the goal.
	Step 0: Initialize variables
	flag:= true;
	KnownFacts:= E ∪ F;
	count:= 0; # the number of new objects which are generated
	Sol:= []; # solution of problem
	Step 1. Collect objects in hypothesis and goal part.
	Classify kind of facts in E and F.
	Step 2. Check G.
	If G is achieved then
	Go to step 5.
	Step 3: Determine the closure of each object in O by using Algo. 4.1 and facts in E and F.
	Step 4: Use equations in E to generate the new facts as relation form.
	Use the relations in F to generate new equations.
	Update KnownFacts.
	Step 5: Select a rule in to produce new facts or new objects by using heuristic rules.
	while (flag! = false) and not(G is determined) do
	Search r in which can be applied to KnownFacts
	5.1. Case: r is a deductive rule
	if (r has form: ) then
	KnownFacts:= KnownFacts ∪ ;
	s:= [r, h(r), ];
	Sol:= [op(Sol), s];
	continue;
	end if;
	5.2. Case: r is a rule for generating a new object
	if count ≤ card(O) then #only generate at most number of objects in hypothesis
	if (r generates a new object o) and not(o ∈ KnownFacts)
	then
	count:= count + 1;
	KnownFacts:= KnownFacts ∪ ; s: = [r, h(r), ];
	Sol:= [op(Sol), s];
	Go to Step 3 with new object o;
	end if;
	end if; #5.2
	5.3. Case: r is an equivalent rule
	if (r has form: f(r), ) then
	KnownFacts:= KnownFacts ∪ ;
	s: = [r, h(r), ];
	Sol: = [op(Sol), s];
	continue;
	end if; #5.3
	5.4. Case: r is an equation rule
	if (r has form: ) then
	r can generate a set of new facts A
	KnownFacts:= KnownFacts ∪ A;
	s:= [r, KnownFacts, A];
	Sol:= [op(Sol), s];
	if (r generates a new object o) and not(o ∈ KnownFacts) then
	count:= count + 1;
	Go to Step 3 with new object o;
	end if;
	end if; #5.4
	5.5. if (rule r cannot be found) then
	flag:= false;
	end if;
	end do ; #while
	Step 6: Conclusion of the problem
	if G is determined then
	Problem (O, E, F) ⟶ G is solvable;
	Sol is a solution to the problem;
	Reduce Sol by eliminating redundant rules.
	else
	Problem (O, E, F) ⟶ G is unsolvable;
	end if;