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Logical reasoning

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Logical reasoning

  1. 1. Unit IILogical Reasoning V. Saranya
  2. 2. Logical AgentsKnowledge based AgentsThe Wumpus WorldLogic
  3. 3. Logical Agents• Humans can know “things” and “reason” – Representation: How are the things stored? – Reasoning: How is the knowledge used? • To solve a problem… • To generate more knowledge…• Knowledge and reasoning are important to artificial agents because they enable successful behaviors difficult to achieve otherwise – Useful in partially observable environments• Can benefit from knowledge in very general forms, combining and recombining informationFebruary 20, 2006 AI: Chapter 7: Logical Agents 3
  4. 4. Knowledge-Based Agents• Central component of a Knowledge-Based Agent is a Knowledge-Base – A set of sentences in a formal language • Sentences are expressed using a knowledge representation language• Two generic functions: – TELL - add new sentences (facts) to the KB • “Tell it what it needs to know” – ASK - query what is known from the KB • “Ask what to do next”February 20, 2006 AI: Chapter 7: Logical Agents 4
  5. 5. Knowledge-Based Agents• The agent must be able to: Domain- – Represent states and actions Independent Algorithms – Incorporate new percepts Inference Engine – Update internal Knowledge-Base representations of the world – Deduce hidden properties of Domain- the world Specific Content – Deduce appropriate actionsFebruary 20, 2006 AI: Chapter 7: Logical Agents 5
  6. 6. Knowledge-Based AgentsFebruary 20, 2006 AI: Chapter 7: Logical Agents 6
  7. 7. Knowledge-Based Agents• Declarative – You can build a knowledge-based agent simply by “TELLing” it what it needs to know• Procedural – Encode desired behaviors directly as program code • Minimizing the role of explicit representation and reasoning can result in a much more efficient systemFebruary 20, 2006 AI: Chapter 7: Logical Agents 7
  8. 8. Wumpus World• Performance Measure – Gold +1000, Death – 1000 – Step -1, Use arrow -10• Environment – Square adjacent to the Wumpus are smelly – Squares adjacent to the pit are breezy – Glitter iff gold is in the same square – Shooting kills Wumpus if you are facing it – Shooting uses up the only arrow – Grabbing picks up the gold if in the same square – Releasing drops the gold in the same square• Actuators – Left turn, right turn, forward, grab, release, shoot• Sensors – Breeze, glitter, and smellFebruary 20, 2006 AI: Chapter 7: Logical Agents 8
  9. 9. Wumpus World• Characterization of Wumpus World – Observable • partial, only local perception – Deterministic • Yes, outcomes are specified – Episodic • No, sequential at the level of actions – Static • Yes, Wumpus and pits do not move – Discrete • Yes – Single Agent • YesFebruary 20, 2006 AI: Chapter 7: Logical Agents 9
  10. 10. Wumpus WorldFebruary 20, 2006 AI: Chapter 7: Logical Agents 10
  11. 11. Wumpus WorldFebruary 20, 2006 AI: Chapter 7: Logical Agents 11
  12. 12. Wumpus WorldFebruary 20, 2006 AI: Chapter 7: Logical Agents 12
  13. 13. Wumpus WorldFebruary 20, 2006 AI: Chapter 7: Logical Agents 13
  14. 14. Wumpus WorldFebruary 20, 2006 AI: Chapter 7: Logical Agents 14
  15. 15. Wumpus WorldFebruary 20, 2006 AI: Chapter 7: Logical Agents 15
  16. 16. Wumpus WorldFebruary 20, 2006 AI: Chapter 7: Logical Agents 16
  17. 17. Wumpus WorldFebruary 20, 2006 AI: Chapter 7: Logical Agents 17
  18. 18. LOGICSyntax: – Knowledge base consists of sentences – These sentences are expressed according to the syntax. Ex: “x + y=4” is a well formed sentence.Semantic:• Meaning of the sentence.• Mention the truth of each sentence.
  19. 19. Logic• Entailment means that one thing follows logically from another a |= b• a |= b iff in every model in which a is true, b is also true• if a is true, then b must be true• the truth of b is “contained” in the truth of aFebruary 20, 2006 AI: Chapter 7: Logical Agents 19
  20. 20. Example• “X+Y=4” is true where X is 2 – And Y is 2• But false where x is 1 and y is 1.• (every sentence must be true or false in each possible world.)
  21. 21. Entailment• Relation of logical element.• A sentence follows logically from another sentence.• Notation : αl= β – Means sentence a entails(require, need, improve, demand) β – If every word of α is true and β is also true. – (simply if α is true then β must be true)
  22. 22. Logic in Wumpus world • The agent detecting nothing in [1,1] • The agent is interested in whether the adjacent squares [1,2] & [2,2] and [3,1]. • Each of these squares may or may not contain a pit. • So 23 = 8 possible models.
  23. 23. No pit in[1,2]
  24. 24. • No pit in [2,2]
  25. 25. Conclusion• α1 : there is no pit in [1,2]• α2 : there is no pit in [2,2]• KB is false in any model in which [1,2] contains pit ,because there is no breeze in [1,1] We know if KB is true α1 is also true. Hence KB is not equal to α1 in some models, if KB is true α2 is false KB V α2 so the agent cannot conclude that there is no pit in [2,2]
  26. 26. Inference (assumption or conclusion)• The inference algorithm I can be derive from KB, then •KB |-i a • a is derived from KB by i” (or) • “ i derives a from KB”
  27. 27. Sound • An inference algorithm derives only entailed sentences is called “Sound or Truth Preserving”. • Soundness is highly desirable property. Correspondence between world and representation sentences entails sentence semantics semanticsRepresentation World Aspects of the Aspects of the real world real world
  28. 28. IllustrationSentences are physical configuration of the agent.Reasoning is the process of constructing new physical configurations from old ones.If any connection between logical reasoning process and the real environment in which the agent exists is called “grounding”

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