1 / 21

FIRST ORDER LOGIC

FIRST ORDER LOGIC. Berat YILMAZ. Before Start, lets remember. Logic Syntax Semantics. Proposıtıonal logıc vs Fırst-order logıc. Propositional logic : We have Facts Belief of agent : T|F|UNKNOWN. First- Order Logic : We have Facts Objects Relations. Propositional logic :

gino
Télécharger la présentation

FIRST ORDER LOGIC

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. FIRST ORDER LOGIC Berat YILMAZ

  2. Before Start, letsremember • Logic • Syntax • Semantics

  3. ProposıtıonallogıcvsFırst-orderlogıc • Propositionallogic: Wehave • Facts • Belief of agent: T|F|UNKNOWN

  4. First-OrderLogic: Wehave • Facts • Objects • Relations

  5. Propositionallogic: • Sentence-> Atomic|ComplexSentences • Atom-> True|False|AP • AP-Basic Propositions • ComplexSentences-> • |SentenceConnectiveSentence • |¬ Sentence • Connective-> ^| v| <=>|=>

  6. First-OrderLogic: Syntax • Constant-> A|5|Something.. • Variable -> a|y|z • Predicate -> After|HasBorder|Snowing.. • Function -> Father|Sine|…

  7. PredICATES • Can haveoneormorearguments • Like: P(x,y,z) • x,y,zarevariables • Ifforthatselectedx,y,zvaluesaretrue, thenpredicate is true.

  8. FUNCTIONS • Predicates has trueorfalsevalue • But.. • Functionshave an event. • Can return a value.. Numericforexample..

  9. Example • Everyonelovesitsfather. • x y Father(x,y)Loves(x,y) • x Father(x) • x Loves(x,Father(x))

  10. Syntax OF FOL • Sentece-> AtomicSentence • |SentenceConnectiveSentence • |QuantifierVariable, …. Sentence • | Sentence | (Sentence) • AtomicSentence -> Predicate (Term, ….)|Term=Term • Term->Function(Term,…) |Constant | Variable • Connective ->  • Quantifier -> 

  11. WHY WE CALL FIRST ORDER • Becauseweareallowingquantificationsovervariables, not on predicates; • P x y P(x,y) (MoreComplex)

  12. Example 1 • Not allstudentstakesboth AI & Computer Graphics Course • Student(x) = x is a student • Takes(x,y) = Subject x is takenby y

  13. FIRstWay: • x Student(x) Takes(AI,x)Takes(CG,x)

  14. Second way • x Student(x)  Takes(AI,x)Takes(CG,x) 

  15. Example 2 • The Best Score in AI is betterthanthebestscore in CG? • How we do, whatweneed?

  16. A ‘Function’ whichreturnsthescorevalue: • SoFunction: Score(course,student) • After? • AnotherFunctionor A Predicate?

  17. A PredICATE • Greater(x,y): x>y

  18. SolutION • Solution: • xStudent(x)Takes(AI)yStudent(y)Takes(CG)  Greater(Score(AI),Score(CG))

  19. RUSSEL PARADOX • There is a singlebarber in town • Thoseandonlythosewho do not shavethemselvesareshavedbythebarber • Sowhoshavesthebarber??

  20. Way TO SOlutIon • xBarber(x)y xy Barber(y) • Thatmeansthere is onlyonebarber in thetown • xShaves(x,x)Shaves(x,y)Barber(y) • Thatmeans y is in the domain of x, somember of townand not shavesitself but shavedbybarber

  21. Thankyouforlıstenıng

More Related