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Final-Example-Sol - Name: Perm #: Final Exam - Example CS...

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Final Exam - ExampleCS 165A – Artificial IntelligenceFirst:Please fill out your name and perm # (if you have one) on the top of this page.The exam isclosed book.Write your answers in the space below the questions.If you need additional room,continue on the back of the page, andbe sure to draw an arrow to indicate that thereis more on the back.Extra paper is available in the front of the room if you need it.If you use extra paper, make sure to put your name at the top of each new page, andstaplethe extra pages to your exam when you turn it in.Don’t spend too much time on any one question!Suggestion: Go through the examand answer the questions that you are sure about and can answer quickly.Then, goback and answer the remaining questions.Reminder:Academic dishonesty will not be tolerated.Spread outas much aspossible. Keep your eyes to yourself, and don’t tempt others by displaying youranswers. Change seats if necessary.Please turn in your exam within3 hours.Good luck!!Name:Perm #:
2Inference Rules for Propositional LogicModus Ponens (a.k.a. Implication-Elimination)αβ,αβAnd-Eliminationα1α2αnαiAnd-Introductionα1,α2,… ,αnα1α2αnOr-Introductionα1α1α2αnDouble-Negation Elimination¬¬ααUnit Resolutionαβ,¬βαResolutionαβ,¬βγαγAdditional Inference Rules for First-Order LogicUniversal EliminationExistential EliminationExistential Introduction)},/({ααgvSUBSTv)},/({ααkvSUBSTv)},/({ααvgSUBSTvRules, equations, etc.
3Standard Logical EquivalencesFor atomic sentencespi, pi' ,andq ,where there is a substitutionθ,such thatSUBST(θ,pi') = SUBST(θ,pi) for alli, thenFor literals piand qi, where UNIFY(pj,¬qk) =θ),()(,,,,2121qSUBSTqppppppnnθGeneralized Modus Ponens),(,1111kjnmnkmjqandpexceptqqppSUBSTqqqpppθGeneralized Resolution
4Procedure to convert sentences to Conjunctive Normal Form:Eliminate equivalence: Replace PQ with (PQ) and (QP)Eliminate implications: Replace (PQ) with (¬PQ)Move¬inwards:¬∀,¬∃,¬¬,¬(PQ),¬(PQ)Standardize variables apart:x Px Qbecomesx1Px2QMove quantifiers left in order:x Py Qbecomesxy PQEliminateby “Skolemization” – whenis on the outside, do existentialelimination; otherwise use a “skolem function” H(xi) to enclose the universallyquantified variablesDrop universal quantifiersDistributeover, e.g.: (PQ)Rbecomes(PR)(QR)Flatten nesting: (PQ)Rbecomes PQR
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Term
Spring
Professor
SU
Tags
Logic, Artificial Intelligence, First order logic, Modus ponens, Conjunctive normal form

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