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# ai-FOL - Artificial Intelligence FirstOrder Logic Inference...

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1 Artificial Intelligence First-Order Logic Inference in First-Order Logic

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2 First-Order Logic: Better  choice for Wumpus World Propositional logic represents facts First-order logic gives us Objects Relations: how objects relate to each other Properties: features of an object Functions: output an object, given others
3 Syntax and Semantics Propositional logic has the following: Constant symbols: book, A, cs327 Predicate symbols: specify that a given  relation holds Example: Teacher(CS327sec1, Barb) Teacher(CS327sec2, Barb) “Teacher” is a predicate symbol For a given set of constant symbols,  relation may or may not hold

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4 Syntax and Semantics Function Symbols FatherOf(Luke) = DarthVader Variables Refer to other symbols x, y, a, b, etc. In Prolog, capitalization is reverse: Variables are uppercase Symbols are lower case Prolog example ([user], ;)
5 Syntax and Semantics Atomic Sentences Father(Luke,DarthVader) Siblings(SonOf(DarthVader),  DaughterOf(DarthVader)) Complex Sentences and, or, not, implies, equivalence Equality ) , ( ) , ( DarthVader Leia Father DarthVader Luke Father ) ( nt DaveMusica ard DaveAppley = ¬

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6 Universal Quantification “For all, for every”: Examples: Usually use      with Common mistake to use 2200 ) ( ) , ( ) ( ) ( x Witch Duck x As WeighsSame x x Mammal x Cat x 2200 2200 2200 ) ( ) , ( x Smart Carleton x At x 2200
7 Existential Quantification “There exists”: Typically use      with Common mistake to use True if there is no one at Carleton! 5 ) ( ) ( Luke x x verse HopeForUni x = ¬ 5 5 ) ( ) , ( x Smart Carleton x At x 5

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8 Properties of quantifiers ) , ( ) , ( : as same not the as same as same x y od FavoriteFo y x x y od FavoriteFo x y x y y x x y y x x y y x 2200 5 5 2200 5 2200 2200 5 5 5 5 5 2200 2200 2200 2200 Can express each quantifier with the  other ) , ( ) , ( ) , ( ) , ( Broccoli x Likes x Broccoli x Likes x IceCream x Likes x IceCream x Likes x ¬ ¬2200 5 ¬ ¬5 2200
9 Some examples ) ( ) ( ) ( ) ( x ter FloatsInWa x MadeOfWood x x Burns x MadeOfWood x 2200 2200 Definition of sibling in terms of parent: )] , ( ) , ( ) , ( ) , ( ) ( , ) ( [ ) , ( , y f Parent y m Parent x f Parent x m Parent f m f m y x y x Sibling y x = ¬ 5 = ¬ 2200

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10 First-Order Logic in Wumpus  World Suppose an agent perceives a stench,  breeze, no glitter at time t = 5: Percept([Stench,Breeze,None],5) [Stench,Breeze,None] is a  list Then want to query for an appropriate  action. Find an  a  (ask the KB): ? ) 5 , ( a Action a 5
11 Simplifying the percept and  deciding actions Simple Reflex Agent Agent Keeping Track of the World

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ai-FOL - Artificial Intelligence FirstOrder Logic Inference...

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