FIRST ORDER LOGIC

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# FIRST ORDER LOGIC - PowerPoint PPT Presentation

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 :

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### FIRST ORDER LOGIC

Berat YILMAZ

Before Start, letsremember
• Logic
• Syntax
• Semantics
ProposıtıonallogıcvsFırst-orderlogıc
• 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
• Connective-> ^| v| <=>|=>

First-OrderLogic: Syntax

• Constant-> A|5|Something..
• Variable -> a|y|z
• Predicate -> After|HasBorder|Snowing..
• Function -> Father|Sine|…
PredICATES
• Can haveoneormorearguments
• Like: P(x,y,z)
• x,y,zarevariables
• Ifforthatselectedx,y,zvaluesaretrue, thenpredicate is true.
FUNCTIONS
• Predicates has trueorfalsevalue
• But..
• Functionshave an event.
• Can return a value.. Numericforexample..
Example
• Everyonelovesitsfather.
• x y Father(x,y)Loves(x,y)
• x Father(x)
• x Loves(x,Father(x))
Syntax OF FOL
• Sentece-> AtomicSentence
• |SentenceConnectiveSentence
• |QuantifierVariable, …. Sentence
• | Sentence | (Sentence)
• AtomicSentence -> Predicate (Term, ….)|Term=Term
• Term->Function(Term,…) |Constant | Variable
• Connective -> 
• Quantifier -> 
WHY WE CALL FIRST ORDER
• Becauseweareallowingquantificationsovervariables, not on predicates;
• P x y P(x,y) (MoreComplex)
Example 1
• Not allstudentstakesboth AI & Computer Graphics Course
• Student(x) = x is a student
• Takes(x,y) = Subject x is takenby y
FIRstWay:
• x Student(x) Takes(AI,x)Takes(CG,x)
Second way
• x Student(x)  Takes(AI,x)Takes(CG,x) 
Example 2
• The Best Score in AI is betterthanthebestscore in CG?
• How we do, whatweneed?

A ‘Function’ whichreturnsthescorevalue:

• SoFunction: Score(course,student)
• After?
• AnotherFunctionor A Predicate?
A PredICATE
• Greater(x,y): x>y
SolutION
• Solution:
• xStudent(x)Takes(AI)yStudent(y)Takes(CG)  Greater(Score(AI),Score(CG))