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For now i have become the strangest case you ever saw

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For now I have become the strangest case you ever saw. As the husband of my grandmother, I am my own grandpa!Note: This is not relevant for the exam and we do not give a solution/translation. (source unknown).47
SummaryFirst-order logic:objects and relations are semantic primitivessyntax: constants, functions, predicates, equality, quantifiersIncreased expressive power: sufficient to define wumpus world.48
Inference in First-Order LogicSound inference: findαsuch thatKB|=α.Proof process is a search, operators are inference rules.E.g., Modus Ponens (MP)α,αβAt(Joe, UniNC)At(Joe, UniNC)OK(Joe)βOK(J oe)E.g., And-Introduction (AI)αβOK(J oe)CSMajor(J oe)αβOK(J oe)CSMajor(J oe)E.g., Universal Elimination (UE)x At(x, UniNC)OK(x)At(Pat, UniNC)OK(Pat)xαα{x/γ}γmust beaground term (i.e., no variables)49
Example proof: “Bob outruns Pat”1. Dog(Bob)2. Pig(Pat)3.x, yDog(x)Pig(y)Faster(x, y)Bob is a DogPat is a pigDogs outrun pigsBob outruns Pat50
Example proofBob is a DogPat is a pigDogs outruns pigs1. Dog(Bob)2. Pig(Pat)3.x, yDog(x)Pig(y)Faster(x, y)Bob outruns PatAI 1 & 24.Dog(Bob)Pig(Pat)51
Example proofBob is a DogPat is a pigDogs outruns pigs1. Dog(Bob)2. Pig(Pat)3.x, yDog(x)Pig(y)Faster(x, y)Bob outruns PatAI 1 & 2UE 3,{x/Bob, y/Pat}4. Dog(Bob)Pig(Pat)5. Dog(Bob)Pig(Pat)Faster(Bob, Pat)52
Example proofBob is a DogPat is a pigDogs outruns pigs1. Dog(Bob)2. Pig(Pat)3.x, yDog(x)Pig(y)Faster(x, y)Bob outruns PatAI 1 & 2UE 3,{x/Bob, y/Pat}MP 4 & 54. Dog(Bob)Pig(Pat)5. Dog(Bob)Pig(Pat)Faster(Bob, Pat)6. Faster(Bob, Pat)done !53
UnificationA substitutionσunifies atomic sentencespandqifpσ=qσpKnows(J ohn, x)Knows(J ohn, x)Knows(J ohn, x)qσKnows(J ohn, Jane)Knows(y, OJ)Knows(y, M other(y)UNIFY (p, q )=σwhereSUBST(σ,p) =SUBST(σ,q)54
UnificationA substitutionσunifies atomic sentencespandqifpσ=qσpKnows(J ohn, x)Knows(J ohn, x)Knows(J ohn, x)qσKnows(J ohn, Jane){x/Jane}Knows(y, OJ){x/OJ, y/J ohn}Knows(y, M other(y){y/J ohn, x/M other(J ohn)}UNIFY (p, q )=σwhereSUBST(σ,p) =SUBST(σ,q)55
UnificationA substitutionσunifies atomic sentencespandqifpσ=qσpKnows(J ohn, x)Knows(J ohn, x)Knows(J ohn, x)qσKnows(J ohn, Jane){x/Jane}Knows(y, OJ){x/OJ, y/J ohn}Knows(y, M other(y){y/J ohn, x/M other(J ohn)}Idea: Unify rule premises with known facts, apply unifier to conclusionE.g., if weknowqandKnows(John, x)Likes(J ohn, x)then we concludeLikes(J ohn, Jane)Likes(John, OJ)Likes(J ohn, Mother(J ohn))UNIFY (p, q )=σwhereSUBST(σ,p) =SUBST(σ,q)56
Automated ReasoningAutomated reasoning = Theorem provingLogic Theorist was the first computer program for logical inference (1957)Many inferencing techniques and strategies were developed.PROLOGAn automated reasoning system has three components:1. An unambiguous representation language2. Sound inference rules3. Well defined search strategies57

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Artificial Intelligence, Neural Networks, Artificial neural network, neural network, machine intelligence

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