Prolog has a helpful and clean syntax [1] (at least when you're used to :P) and it's easy to define new operators syntax in SWI [2]. Such feature improves the readability of the knowledge base.
To make an abductive reasoning we will need at least the logic operators 'and','or' and 'implies' to represent knowledge and chain it.
Our simple language will have the following syntax:
- known X. - Says that the sentence X must be true;
- X <- Y - X is caused by Y;
- X & Y - Is true if X and Y are true;
- X v Y - Is true if X or Y are true ('|' is already used by Prolog);
- assumable X - X can be assumed to prove something;
- askable X - X can be asked to the user;
Note that I'm not using the negation, because some dangerous particularities of Prolog negation as failure.
It's interesting to note the similarity if we represented with the defaul prefixed notation of Prolog predicades:
- known(X)
- <-(X,Y)
- &(X,Y)
- v(X,Y)
- assumable(X)
- askable(X)
Defining opertors increases the readabilty of the knowledge representation significantly. To redefine operators we will use the SWI predicate op/3 [2]. We can only run this predicate like:
:- op(910, xfy, &).
The op predicate has three fields op(+Precedence, +Type, :Name). The first one says the precendence of the operator (a number between 0 and 1200). The second is how the functor will be placed within it's "children nodes", for example: xfy let the functor between the arguments while xf let the functor after it's argument (remembering that you can only create unary or binary operators). For our representation language we will have:
:- discontiguous( known/1 ). % The discontiguous predicate tells Prolog :- discontiguous( assumable/1 ). % that the given predicate can be declared :- discontiguous( askable/1 ). % unsorted. :- op(910, xfy, & ). % a higher priority with an infix notation :- op(920, xfy, v ). % infix notation and lower priority than & :- op(930, xfy, <- ). % infix notation :- op(940, fx, known ). % prefixed notation and lowest priority :- op(940, fx, assumable ). % prefixed notation and lowest priority :- op(940, fx, askable ). % prefixed notation and lowest priority
Now let's model the car problems knowledge into our language (remember that Upper names are variables):
% % DiagnostiCar - Knowledge Base % % Observe that implication is seen as the real sense of consequence <- cause. known problem(crank_case_damaged) <- crank_case_damaged. known problem(hydraulic_res_damaged) <- hydraulic_res_damaged. known problem(brakes_res_damaged) <- brakes_res_damaged. known problem(old_engine_oil) <- old_engine_oil & leak_color(black). known leak(engine_oil) <- crank_case_damaged. known leak(hydraulic_oil) <- hydraulic_res_damaged. known leak(brakes_oil) <- brakes_res_damaged. % Implications in false can be seen as constraints. known oil(Oil) <- exists_leak(true) & leak(Oil). known false <- oil(brakes_oil) & leak_color(Color) & Color \= green. known false <- oil(engine_oil) & leak_color(Color) & Color \= brown & Color \= black. known false <- oil(hydraulic_oil) & leak_color(Color) & Color \= red. % The assumable predicate asserts what will be can be suposed assumable crank_case_damaged. assumable hydraulic_res_damaged. % to prove something e else. assumable brakes_res_damaged. assumable old_engine_oil. askable leak_color(Color). % Askable predicate asserts which information will be asked for the user. askable exists_leak(TrueOrFalse). % The argument of the predicate will be unified with the answer. known goal(X) <- problem(X). % The goal predicate is what we want to prove with the expert system.
That's all for now. On the next post I will explain the question and answer interface using the dynamic Prolog predicates.
[1] Prolog Syntax
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