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FIRST ORDER LOGIC

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FIRST ORDER LOGIC

Berat YILMAZ

- Logic
- Syntax
- Semantics

- Propositionallogic: Wehave
- Facts
- Belief of agent: T|F|UNKNOWN

- First-OrderLogic: Wehave
- Facts
- Objects
- Relations

- Propositionallogic:
- Sentence-> Atomic|ComplexSentences
- Atom-> True|False|AP
- AP-Basic Propositions
- ComplexSentences->
- |SentenceConnectiveSentence
- |¬ Sentence

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

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

- Predicates has trueorfalsevalue
- But..
- Functionshave an event.
- Can return a value.. Numericforexample..

- Everyonelovesitsfather.
- x y Father(x,y)Loves(x,y)
- x Father(x)
- x Loves(x,Father(x))

- Sentece-> AtomicSentence
- |SentenceConnectiveSentence
- |QuantifierVariable, …. Sentence
- | Sentence | (Sentence)

- Becauseweareallowingquantificationsovervariables, not on predicates;
- P x y P(x,y) (MoreComplex)

- Not allstudentstakesboth AI & Computer Graphics Course
- Student(x) = x is a student
- Takes(x,y) = Subject x is takenby y

- x Student(x) Takes(AI,x)Takes(CG,x)

- x Student(x) Takes(AI,x)Takes(CG,x)

- The Best Score in AI is betterthanthebestscore in CG?
- How we do, whatweneed?

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

- Greater(x,y): x>y

- Solution:
- xStudent(x)Takes(AI)yStudent(y)Takes(CG) Greater(Score(AI),Score(CG))

- There is a singlebarber in town
- Thoseandonlythosewho do not shavethemselvesareshavedbythebarber
- Sowhoshavesthebarber??

- xBarber(x)y xy Barber(y)
- Thatmeansthere is onlyonebarber in thetown

- xShaves(x,x)Shaves(x,y)Barber(y)
- Thatmeans y is in the domain of x, somember of townand not shavesitself but shavedbybarber