1 Discussion And what about processing data? In theory: describing - PDF document

3.2 Rule Sets / Production Systems 3.2.1 PROLOG n Focus on operational knowledge: � General idea: if condition then action n program descriptively by just stating axioms in a n Uses a logic: � logic and asking queries usually propositional or multi-valued ( F probabilistic n guide interpreter by clear evaluation control scheme rules) n whole concept is based on SLD-resolution n Actions include input-requests, output, changes of knowledge-base n If several rules can be applied, a conflict manager decides what to do � F defines the operational semantics of the system � F must be well understood by knowledge engineer CPSC 433 - Artificial Intelligence Jörg Denzinger CPSC 433 - Artificial Intelligence Jörg Denzinger Basic data structures Semantics (I) n Horn clauses in first-order logic, � n Operational semantic using a goal stack and the list i.e. clauses of form ¬A 1 ∨ ... ∨ ¬A n ∨ B � of clauses (data base/knowledge base): written: B:- A 1 ,…,A n � Data base: ?- G 1 ,G 2 ,…,G m read: if A 1 and … and A n then B ... σ 1 (G 1 ) = σ 1 (A 1 ) n Some higher-order predicates to manipulate the set A 1 :-B 11 ,…,B 1n1 . ... (list) of clauses in the knowledge base, influence the ?- σ 1 (B 11 ),…, σ 1 (B 1n1 ), σ 1 (G 2 ),…, σ 1 (G m ) A k :-B k1 ,…,B knk . . σ 1 (B ij )not solvable interpreter, or provide in- and output. . ... . F backtrack ?- G 1 ,G 2 ,…,G m σ 2 (G 1 ) = σ 2 (A 2 ) σ I mgus ?- σ 2 (B 21 ),…, σ 2 (B 2n2 ), σ 2 (G 2 ),…, σ 2 (G m ) CPSC 433 - Artificial Intelligence Jörg Denzinger CPSC 433 - Artificial Intelligence Jörg Denzinger How to get knowledge into the Semantics (II) representation structure n Solution: if goal stacks get empty � n By writing a declarative problem description ð collect substitutions that fulfilled � n Caution: take into account the semantics! � original goals � Especially that we have an and-or-tree-based search ð use as answer with a special depth-first control (that in fact boils n Next solution: initiate backtrack down to and-tree-based search with backtracking) � F ordering of clauses in data base very important: � n No solution: � from very specialized to very general if no clause in data base solves a particular subgoal G i for all solutions to G 1 ,…,G i-1 CPSC 433 - Artificial Intelligence Jörg Denzinger CPSC 433 - Artificial Intelligence Jörg Denzinger 1

Discussion And what about processing data? ✚ In theory: describing knowledge by logic rules n Follow operational semantics � F not really search enough; no control necessary n Rely on user/programmer knowing what he/she is ✚ Fast prototyping very easy! doing - Not really much left from logic - Exact understanding of operational semantic necessary to use F Just another (not very efficient) programming language CPSC 433 - Artificial Intelligence Jörg Denzinger CPSC 433 - Artificial Intelligence Jörg Denzinger Examples 3.2.2 MYCIN / EMYCIN n Write a PROLOG program that given facts of the form General ideas: mother(a,b). father(a,b). � n Deal with unsure/uncertain knowledge meaning a is mother, resp. father of b, answers questions like � n Use in expert system � ?- grandmother(agnes,X). � F dialog with user ?- grandfather(Y,clara). n MYCIN: medical expert system n Given the facts: � n EMYCIN: expert system shell employing logic, mother(anna,peter). mother(anna,clara). semantics, calculus and control of MYCIN, not the father(joe,peter). father(jim,clara). particular knowledge mother(mary,anna). father(tom,joe). � Answer: ?- grandfather(tom,X). � ?- grandmother(X,peter). CPSC 433 - Artificial Intelligence Jörg Denzinger CPSC 433 - Artificial Intelligence Jörg Denzinger Basic data structures Semantics n Object-attribute-value triples as base logic: � for all a ∈ F: τ (a) = 0 (objects and values) � for all x ∈ V: τ (x) = 0 (object and value variables) � n Interpret all symbols for a fixed domain D for all A ∈ PI: τ (A) = 2 (attributes) � n Start with given interpretation for selected object- P = PV = {} � attribute-value-triples (input-data) and given truth triple realized as A(e,v): � values for all production rules attribute A of object e has value v n Use operational semantics based on computing n Production rules form the formulas: � ● Measure of belief (MB) J = { ¬ , ∧ } ∪ { → i |i = 1,…,n, if there are n production � ● Measure of disbelief (MD) rules} � Q = {} n Deal with uncertain knowledge by using W=[-1,1], resp. discrete representation {-1,-0.9,…,0.9,1} CPSC 433 - Artificial Intelligence Jörg Denzinger CPSC 433 - Artificial Intelligence Jörg Denzinger 2

How to get knowledge into the Measures of belief/disbelief representation structure Let h be an object-attribute-value triple and e a set of production rules. If P 1 ∧ … ∧ P n → i h is the only rule in n The rules are defined by an expert, who also defines e, then we get what objects and attributes are of interest and what MB(h,e) = I(P 1 ∧ … ∧ P n → i h)*max(0,min(I(P 1 ),…,I(P n )) values they can have. If e = {e 1 ,e 2 }, then we get � n The expert also has to provide the interpretation for MB(h,{e 1 ,e 2 }) = 0, if MD(h,{e 1 ,e 2 }) = 1 � the rules, by expressing how confident he/she is in MB(h,{e 1 ,e 2 }) = MB(h,{e 1 }) + MB(h,{e 2 })*(1-MB(h,{e 1 })) this rule For more elements just iterate this. n The interpretation for the input data is provided by MD is computed similarily, except that e contains all observation/measuring of the world (in MYCIN, by a production rules of the form P 1 ∧ … ∧ P n → i ¬ h doctor interpreting the examinations of the patient). F application of Bayes formula for conditional probabilities CPSC 433 - Artificial Intelligence Jörg Denzinger CPSC 433 - Artificial Intelligence Jörg Denzinger Discussion And what about processing data? ✚ Allows to deal with uncertainty n Very similar to PROLOG ✚ Successful in several applications n Rules are applied backwards: - Application domain has to be small ● Select an object-attribute-value-triple for which an interpretation is sought and add it to the goal list: - Hands-on approach to probability theory ● Repeat: - Hides the need for TMS n Select h from goal list - Gets very complicated for large rule sets with the same conclusion n Find a rule e with h or ¬ h as consequence n Add premisses to goal list and update interpretation of h by MB(h,e) - MD(h,e), resp. combine values for h from other rules CPSC 433 - Artificial Intelligence Jörg Denzinger CPSC 433 - Artificial Intelligence Jörg Denzinger Examples (I) Examples (II) n Construct MYCIN rules for the following knowledge: ● If the preparation for the exam is good and the n Interpret the statement � student slept well, then there is a good chance Joe passes the exam � (0.7) that the student will pass the exam. if you know that ● If the student ’ s contribution to the team effort is ● I(Preparation(Joe,good)) = 0.7 high and the workload of the student is low, then ● I(Sleep(Joe, well)) = 0.6 there is a good chance (0.8) that the student will ● I(TeamContrib(Joe,high)) = 0.9 pass the exam. ● I(Workload(Joe,low)) = 0.6 ● If the workload of the student is high and the ● I(ExtraAct(Joe,high)) = 0.3 extra-curricular activities are high, then there is a good chance (0.6) that the student will fail the exam. CPSC 433 - Artificial Intelligence Jörg Denzinger CPSC 433 - Artificial Intelligence Jörg Denzinger 3

3.2.3 General Discussion n Production rule systems can be seen as special logics based on operational semantics that take away the search aspect of the logics in 3.1. n When using production systems, dealing with the control therefore requires more than just application knowledge and makes defining the knowledge base difficult. n Newer approach: learning of rules by providing input-output pairs for the intended behavior CPSC 433 - Artificial Intelligence Jörg Denzinger 4