Downloaded 47 times
More Related Content
Similar to AI Lecture 6 (logical agents)
More from Tajim Md. Niamat Ullah Akhund
AI Lecture 6 (logical agents)
- 1. CSE 412: ArtificialIntelligenceCSE 412: Artificial Intelligence Fall 2018Fall 2018 Topic – 6:Topic – 6: Logical AgentsLogical Agents Tajim Md. Niamat Ullah Akhund Lecturer Department of Computer Science and Engineering Daffodil International University Email: [email protected]
- 2. Knowledge-Based AgentsKnowledge-Based Agents LogicLogic PropositionalLogic: A Very Simple LogicPropositional Logic: A Very Simple Logic SyntaxSyntax SemanticsSemantics A simple knowledge baseA simple knowledge base InferenceInference Equivalence, validity, and satisfiabilityEquivalence, validity, and satisfiability Topic ContentsTopic Contents
- 3. Architecture of a SimpleIntelligent Agent Environment Agent Sensors Effectors Reasoning & Decisions Making Model of World (being updated) List of Possible Actions Prior Knowledge about the World Goals/Utility 33
- 4. Knowledge Based Agent Knowledge base: – A knowledge base (abbreviated KB or kb) is a special kind of database for knowledge management. – A knowledge base is an information repository that provides a means for information to be collected, organized, shared, searched and utilized. – The part of an expert system that contains the facts and rules needed to solve problems. – A collection of facts and rules for problem solving. 44
- 5. Knowledge Based Agent The agent must be able to: – represent states, actions, etc. – incorporate new percepts – update internal representation of world – deduce hidden properties of world – deduce appropriate actions One of the core problems in developing an intelligent agent is knowledge representation: – how to represent knowledge – how to reason using that knowledge 55
- 6. Knowledge Bases (KB) A knowledge base: – contains the domain-specific content for an agent – is a set of representations of facts about the world is a set of sentences in a formal language Building the KB: – learning: agent discovers what it knows – telling: agent is given what it knows (declarative) 66
- 7. Knowledge Bases (KB) Main actions of intelligent agent: – TELL information to KB in the form of percept – ASK KB what to do in the form of action Answers should follow from KB. Agent should not make things up! An inference engine is composed of domain- independent algorithms that are used to determine what follows from the knowledge base. 77
- 8. Knowledge Bases (KB) View of agent (levels of abstraction): – knowledge level: what the agent knows at a high level – logic level: level of sentence encoding – implementation level: level that runs on the architecture, detail of data structures and algorithms. 88
- 9.
- 10. General Logic Theagent internally represents its world/environment in its knowledge base. The Sky is blue. The sun is shining representation in agent world/environment Sentences are representations in some language. Facts are claims about the world that are true/false. Sentences Facts 1010
- 11. General Logic Sentencesrepresent facts in the world. Sentences Facts representation in agent world/environment Meaning connects sentences to their facts. Meaning / Interpretation A sentence is true if what it represents is actually the case in the current state of world. Time flies. 1111
- 12. General Logic repr. world Knowledge Conclusions infer follows FactsNew Facts Proper reasoning ensures that conclusions inferred from the KB are consistent with reality. That means they represent new facts that actually follow from the original facts (represented by sentences in the KB). 1212
- 13. Conclusions General Logic repr. world Knowledge infer Computersdon't know the meaning. A mechanical inference procedure is needed that derives conclusions without needing to know the meaning of the sentences. Sentences New Sentences entails follows Facts New Facts 1313
- 14. Entailment KB ╞α Knowledge base KB entails sentence α if and only if α is true in all worlds where KB is true 1414
- 15. Entailment KB ╞α Knowledge base KB entails sentence α if and only if α is true in all worlds where KB is true For example: KB: "sky is blue" = true, "sun is shining" = true entails α: "sky is blue and sun is shining" = true – α represents a true fact as long as facts represented in KB are true – if the sky was actually cloudy then KB isn't the true world state then α wouldn't represent a true fact Entailment requires sentences in KB to be true. 1515
- 16. Logical Inference Inferenceprocedure can: – generate new sentences α entailed by KB – determine whether or not a given sentence α is entailed by KB (i.e. prove α) 1616
- 17. General Logic Logicsare formal languages for representing information from which conclusions can be drawn. 1717
- 18. General Logic Logicsare characterized by what they commit to as "primitives". Logic What Exists in World Knowledge States Propositional facts true/false/unknown First-Order facts, objects, relations true/false/unknown Temporal facts, objects, relations, times true/false/unknown Probability Theory facts degree of belief 0..1 Fuzzy degree of truth degree of belief 0..1 1818
- 19. Propositional Logic (PL)Basics propositions: assertions about an aspect of a world that can be assigned either a true or false value – e.g. SkyIsCloudy, JimIsHappy – True, False are propositions meaning true and false 1919
- 20. Logical Connectives ofPL ¬ S negation (not) S1∧S2 conjunction (and) S1 and S2 are conjuncts S1∨S2 disjunction (or) S1 and S2 are disjuncts S1⇒S2 implication/conditional (if-then) S1 is the antecedent/premise S2 is the consequent/conclusion S1⇔S2 equivalence/biconditional (if and only if) 2020
- 21. Syntax of PL Models specify truth value for each proposition: e.g. S1= true, S2= false Rules for evaluating truth with respect to model m ¬S is true iff S is false S1∧S2 is true iff S1 is true and S2 is true S1∨S2 is true iff S1 is true or S2 is true S1⇒S2 is true iff S1 is true or S2 is true is true iff S1 is false or S2 is true is false iff S1 is false and S2 is false S1⇔S2 is true iff S1⇒S2 is true and S2⇒S1 is true 2121
- 22. Truth Tables A BC false false false false false true false true false false true true true false false true false true true true false true true true Given n symbols, 2n possible combinations of truth value assignments. here each row is an interpretation 2222
- 23. Implication Truth Table AB false false false true true false true true A⇒B true true false true A⇒B is equivalent to B∨ ¬A B∨ ¬A true true false true 2323
- 24. Validity A B C falsefalse false false false true false true false false true true true false false true false true true true false true true true A sentence is valid if it's true in all interpretations: P1∨ ¬P1 P1⇒P1 (tautologies) (i.e. its entire column is true) A∨ ¬A true true true true true true true true 2424
- 25. Satisfiability A B C falsefalse false false false true false true false false true true true false false true false true true true false true true true A sentence is satisfiable if it's true in some interpretations: P1∨ ¬P2 P2⇒P1 (i.e. its column is true and false) A∨ ¬B true true false false true true true true 2525
- 26. Unsatisfiability A B C falsefalse false false false true false true false false true true true false false true false true true true false true true true A sentence is unsatisfiable if it's true in no interpretations: P1∧ ¬P1 (inconsistent/contradiction) (i.e. its entire column is false) C∧ ¬C false false false false false false false false 2626
- 27. Inference Proof Methods Model Checking: – truth table enumeration sound and complete for propositional logic – heuristic search in model space sound but incomplete Application of Syntactic Operations (i.e. Inference Rules): – sound generation of new sentences from old – could use inference rules as operators for search 2727
- 28. Inference by Enumeration LET:KB = A∨C, B∨ ¬C α = A∨B DOES: KB ╞ α ? A B C false false false false false true false true false false true true true false false true false true true true false true true true RECALL: The computer doesn't know the meaning of the proposition symbols. So all logically distinct cases must be checked to prove that a sentence can be derived from a KB. 2828
- 29. Inference by Enumeration LET:KB = A∨C, B∨ ¬C α = A∨B DOES: KB ╞ α ? A∨C B∨ ¬C KB false true false true false false false true false true true true true true true true false false true true true true true true Rows where all of sentences in KB are true are the models of KB A B C false false false false false true false true false false true true true false false true false true true true false true true true 2929
- 30. Inference by Enumeration LET:KB = A∨C, B∨ ¬C α = A∨B DOES: KB ╞ α ? A∨C B∨ ¬C KB false true false true false false false true false true true true true true true true false false true true true true true true α is entailed by KB, if all models of KB are models of α, i.e. all rows where KB is true, α is true A B C false false false false false true false true false false true true true false false true false true true true false true true true A∨B false false true true true true true true YES! In other words: KB ⇒α is valid. KB⇒α true true true true true true true true 3030
- 31. Inference by Enumeration Though complete for PL, the proofs using this enumeration grow exponentially in length as the number of symbols increases. There must be a better way. Natural deduction is an inference procedure that uses sound inference rules to derive new sentences from the KB and any previously derived sentences until the conclusion sentence is derived. 3131
- 32.
- 33. COURTESY: Md. Tarek Habib AssistantProfessor Daffodil International University
- 34. ********** ********** IfYou Need Me ********** ********** Mail: [email protected] Website: https://www.tajimiitju.blogspot.com ORCID: https://orcid.org/0000-0002-2834-1507 LinkedIn: https://www.linkedin.com/in/tajimiitju ResearchGate: https://www.researchgate.net/profile/Tajim_Md_Niamat_Ullah_Akhund YouTube: https://www.youtube.com/tajimiitju?sub_confirmation=1 SlideShare: https://www.slideshare.net/TajimMdNiamatUllahAk Facebook: https://www.facebook.com/tajim.mohammad GitHub: https://github.com/tajimiitju Google+: https://plus.google.com/+tajimiitju Gmail: [email protected] Twitter: https://twitter.com/Tajim53 Thank you Tajim Md. Niamat Ullah AkhundTajim Md. Niamat Ullah Akhund
Editor's Notes
- #4 CLICK SLIDE
- #5 CLICK EACH SUB
- #6 CLICK EACH SUB
- #7 CLICK EACH SUB formal language is unambiguous and free of semantics
- #8 CLICK EACH SUB
- #9 CLICK EACH SUB
- #11 CLICK ANIM
- #12 CLICK ANIM
- #13 CLICK ANIM
- #14 CLICK ANIM
- #15 CLICK EACH SUB Example: if each is separately true then they are jointly true
- #16 CLICK EACH SUB Example: if each is separately true then they are jointly true
- #17 CLICK EACH SUB
- #18 CLICK EACH SUB
- #19 CLICK EACH SUB
- #20 CLICK EACH
- #21 CLICK EACH
- #22 CLICK EACH
- #23 CLICK EACH
- #24 CLICK EACH
- #25 CLICK EACH
- #26 CLICK EACH
- #27 CLICK EACH
- #28 CLICK EACH SUB
- #29 CLICK EACH
- #30 CLICK EACH
- #31 CLICK EACH
- #32 CLICK EACH