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 EXPERT SYSTEMS BASED ON FIRST-ORDER LOGIC

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

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

Expert Systems Based on First-order Logic MODUS PONENS Problem’s description 1.Anyone who is lucky wins the lottery. 2.Anyone who wins the lottery is happy. 3.At least one who is happy studies at the university. 4.Anyone who studies at the university can pass all his examsinations. 5.Anyone who pass all his examination graduates from the university.

Expert Systems Based on First-order Logic MODUS PONENS (continued) Logical Sentences 1.  X(lucky(X)  win(X, lottery)) 2.  X(win(X, lottery)  happy(X)) 3.  X(happy(X)  study(X)) 4.  X  Y(study(X)  pass(X, Y)) 5.  X  Y(pass(X, Y)  graduate(X))

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

Expert Systems Based on First-order Logic MODUS PONENS (continued) 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) User Interface Inference Engine Modus Ponens Working Memory KB

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

Expert Systems Based on First-order Logic MODUS PONENS (continued) KBInference Engine Modus Ponens S1 S2 S3 S4 S5 F1: lucky(george) User Interface Working Memory KBInference Engine Modus Ponens

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

S1 S2 S3 S4 S5 F1: lucky(george) F2: win(george, lottery) Expert Systems Based on First-order Logic MODUS PONENS (continued) User Interface KBInference Engine Modus Ponens Working Memory

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

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

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) F1: lucky(george) F2: win(george, lottery) F3: happy(george) Expert Systems Based on First-order Logic MODUS PONENS (continued) User Interface KBInference Engine Modus Ponens Working Memory

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

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 F1: lucky(george) F2: win(george, lottery) F3: happy(george) F4: study(george) Expert Systems Based on First-order Logic MODUS PONENS (continued) User Interface KBInference Engine Modus Ponens Working Memory

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

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

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

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

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

Conclusion: George graduates from the university S1 S2 S3 S4 S5 F1F4 F2F5 F3F6 Expert Systems Based on First-order Logic MODUS PONENS (continued) User Interface KB Inference Engine Modus Ponens Working Memory