ARTIFICIAL INTELLIGENCE [INTELLIGENT AGENTS PARADIGM]

1. EXPERT SYSTEMS BASEDON FIRST-ORDER LOGIC ARTIFICIAL INTELLIGENCE[INTELLIGENT AGENTS PARADIGM] Professor Janis Grundspenkis Riga Technical University Faculty of Computer Science and Information Technology Institute of Applied Computer Systems Department of Systems Theory and Design E-mail: Janis.Grundspenkis@rtu.lv

2. Knowledge Base (KB) Formally described knowledge User Interface Inference Engine Inference Procedure Working Memory Facts Expert Systems Basedon First-order Logic EXPERT SYSTEM’S ARCHITECTURE

3. Expert Systems Basedon First-order Logic EXPERT SYSTEM’S ARCHITECTURE (continued) An inference procedureI can be described by the sentences that it can derive. KB |=I means that the sentence  is derived from KB by I.

4. Expert Systems Basedon First-order Logic • MODUS PONENS • Problem’s description • Anyone who is lucky wins the lottery. • Anyone who wins the lottery is happy. • At least one who is happy studies at the university. • Anyone who studies at the university can pass all his examsinations. • Anyone who pass all his examination graduates from the university.

5. Expert Systems Basedon First-order Logic • MODUS PONENS (continued) • Logical Sentences • X(lucky(X)  win(X, lottery)) • X(win(X, lottery)  happy(X)) • X(happy(X)  study(X)) • XY(study(X)  pass(X, Y)) • XY(pass(X, Y)  graduate(X))

6. Expert Systems Basedon First-order Logic MODUS PONENS (continued) Facts 6. George is lucky. lucky(george) 7. George passed his Mathematical Logic andArtificial Intelligence (ML&AI) examination. pass(george, ml&ai)

7. Expert Systems Basedon First-order Logic KB S1: lucky(X)  win(X, lottery) S2: win(X, lottery)  happy(X) S3: X(happy(X)  study(X)) S4: study(X)  pass(X, Y) S5: pass(X, Y) graduate(X) Inference Engine Modus Ponens User Interface Working Memory MODUS PONENS (continued)

8. Expert Systems Basedon First-order Logic MODUS PONENS (continued) KB S1 S2 S3 S4 S5 User Interface Inference Engine Modus Ponens Q: Is George lucky? A: Yes Working Memory

9. Expert Systems Basedon First-order Logic MODUS PONENS (continued) KB KB Inference Engine Modus Ponens Inference Engine Modus Ponens S1 S2 S3 S4 S5 User Interface Working Memory F1: lucky(george)

10. Expert Systems Basedon First-order Logic MODUS PONENS (continued) KB Inference Engine Modus Ponens S1 S2 S3 S4 S5 S1: lucky(X)win(X, lottery) F1: lucky(george) Unification { george/X } User Interface Working Memory F1: lucky(george)

11. Expert Systems Basedon First-order Logic MODUS PONENS (continued) KB Inference Engine Modus Ponens S1 S2 S3 S4 S5 User Interface Working Memory F1: lucky(george) F2: win(george, lottery)

12. Expert Systems Basedon First-order Logic MODUS PONENS (continued) KB Inference Engine Modus Ponens S1 S2 S3 S4 S5 S2: win(X, lottery)  happy(X) F2: win(george, lottery) Unification { george/X } User Interface Working Memory F1: lucky(george) F2: win(george, lottery)

13. Expert Systems Basedon First-order Logic MODUS PONENS (continued) KB Inference Engine Modus Ponens S1 S2 S3 S4 S5 User Interface Working Memory F1: lucky(george) F2: win(george, lottery) F3: happy(george)

14. Expert Systems Basedon First-order Logic MODUS PONENS (continued) KB Inference Engine Modus Ponens S1 S2 S3 S4 S5 S3: X(happy(X)  study(X) F3: happy(george) Unification { george/X } After dropping X S3: happy(george) study(george) User Interface Working Memory F1: lucky(george) F2: win(george, lottery) F3: happy(george)

15. Expert Systems Basedon First-order Logic MODUS PONENS (continued) KB Inference Engine Modus Ponens S1 S2 S3 S4 S5 User Interface Working Memory F1: lucky(george) F2: win(george, lottery) F3: happy(george) F4: study(george)

16. Expert Systems Basedon First-order Logic MODUS PONENS (continued) KB Inference Engine Modus Ponens S1 S2 S3 S4 S5 S4: study(X)  pass(X, Y) F4: study(george) Unification { george/X } Unification for Y? There is not any knowledge about that User Interface Working Memory F1: lucky(george) F2: win(george, lottery) F3: happy(george) F4: study(george)

17. Expert Systems Basedon First-order Logic MODUS PONENS (continued) User Interface KB Inference Engine Modus Ponens S1 S2 S3 S4 S5 S4: study(X)  pass(X, Y) F4: study(george) Unification { george/X } Unification for Y? Q: Did George pass all his exams? A: Yes, George passed his Mathematical Logic and Artificial Intelligence exam Working Memory F1: lucky(george) F2: win(george, lottery) F3: happy(george) F4: study(george)

18. Expert Systems Basedon First-order Logic MODUS PONENS (continued) KB Inference Engine Modus Ponens S1 S2 S3 S4 S5 S4: study(X)  pass(X, Y) F4: study(george) Unifications { george/X } Unification for Y? User Interface Working Memory F1: lucky(george) F2: win(george, lottery) F3: happy(george) F4: study(george) F5: pass(george, ml&ai)

19. Expert Systems Basedon First-order Logic MODUS PONENS (continued) KB Inference Engine Modus Ponens S1 S2 S3 S4 S5 S4: study(X)  pass(X, Y) F4: study(george) Unifications { george/X } { ml&ai/Y } User Interface Working Memory F1: lucky(george) F2: win(george, lottery) F3: happy(george) F4: study(george) F5: pass(george, ml&ai)

20. Expert Systems Basedon First-order Logic MODUS PONENS (continued) KB Inference Engine Modus Ponens S1 S2 S3 S4 S5 S5: pass(X, Y)  graduate(X) F5: pass(george, ml&ai) Unifications { george/X } { ml&ai/Y } User Interface Working Memory F1: lucky(george) F2: win(george, lottery) F3: happy(george) F4: study(george) F5: pass(george, ml&ai)

21. Expert Systems Basedon First-order Logic MODUS PONENS (continued) KB Inference Engine Modus Ponens S1 S2 S3 S4 S5 User Interface Working Memory F1: lucky(george) F2: win(george, lottery) F3: happy(george) F4: study(george) F5: pass(george, ml&ai) F6: graduate(george)

22. Expert Systems Basedon First-order Logic MODUS PONENS (continued) KB Conclusion: George graduates from the university S1 S2 S3 S4 S5 User Interface Inference Engine Modus Ponens Working Memory F1 F4 F2 F5 F3 F6