# For now i have become the strangest case you ever saw

• 812
• 100% (1) 1 out of 1 people found this document helpful

Course Hero uses AI to attempt to automatically extract content from documents to surface to you and others so you can study better, e.g., in search results, to enrich docs, and more. This preview shows page 716 - 727 out of 812 pages.

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

Course Hero member to access this document

Course Hero member to access this document

End of preview. Want to read all 812 pages?

Course Hero member to access this document

Term
One
Professor
N/A
Tags
Artificial neural network, neural network, machine intelligence