True implies p and p and p implies q p i1 and p i1 p implies q allows and a and a implies p and p and p implies qp a p i1 and p i1 p and and a and a implies q A benefit of this approach is that the reasoner now can have a sin ID: 29998
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An Example:Converting Sentences into Clause Form 1.isHoosier( Eugene ) likes( x, Basketball ) likes( y, Basketball ) likes( x, Basketball ) likes( x, March )5.daughter( Ellen, Eugene ) childOf( x, y ) 1.isHoosier( Eugene ) isHoosier(x) likes( x, Basketball )3.[ [ likes( y, Basketball ) ] likes( x, Basketball )4.[ likes( x, Basketball ) ] likes( x, March )5.daughter( Ellen, Eugene )6.[ logic, using only the connectives and Any sentence that uses can be convertedusing the rule:(p q) == ( p) Any sentence that uses can be rewritten asform. If only we had an inference rule that worked on connective lead us to a new inference rule: lead us to a new inference rule: disjunction or disjunction disjunction because it the case analysis that is required whenever one and another asserts 1.isHoosier( Eugene ) isHoosier(x) likes( x, Basketball )3.[ childOf( x, y ) ] [ likes( y, Basketball ) ] likes( x, Basketball )4.[ likes( x, Basketball ) ] likes( x, March )5.daughter( Ellen, Eugene )6.[ as our inference rule, we conclude:1.Assume that our g oal sentence is false. likes( Ellen, March )2.Try to show that the goal sentence being false causes false. Everything else disjunction disjunction1.isHoosier( Eugene )isHoosier( Eugene )not isHoosier(x) ] likes( x, Basketball )3.[ childOf( x, y ) ] childOf( x, y ) ] not likes( y, Basketball ) ] likes( x, Basketball )4.[ likes( x, Basketball ) ] likes( x, March )5.daughter( Ellen, Eugene )6.[ 7.[ likes( Ellen, March ) ]8.[ likes( Ellen, Basketball ) ]9.[ childOf( Ellen, y ) ] childOf( Ellen, y ) ] not likes( y, Basketball ) ]A.[ daughter( Ellen, y ) ] daughter( Ellen, y ) ] not likes( y, Basketball ) ]B.[ likes( Eugene, Basketball ) ]C.[ isHoosier( Eugene ) ] like March cause a like March. with modus ponens. TueThu( AI, 2:30 PM ) TueThu( AI, 2:30 PM ) and MonWedFri( AI, 2:30 PM ) and 1.TueThu( AI, 2:30 PM ) MonWedFri( AI, 2:30 PM ) MonWedFri( AI, 2:30 PM ) TueThu( AI, 2:30 PM ) TueThu( AI, 2:30 PM ) busy( Thursday, 2:30 PM ) busy( Thursday, 2:30 PM ) MonWedFri( AI, 2:30 PM ) MonWedFri( AI, 2:30 PM ) busy( Friday, 2:30 PM ) 4.busy( Thursday, 2:30 PM )5.busy( Friday, 2:30 PM ) conflict( AI ) TueThu( AI, 2:30 PM ) TueThu( AI, 2:30 PM ) busy( Thursday, 2:30 PM )8.MonWedFri( AI, 2:30 PM ) or or busy( Thursday, 2:30 PM ) 9.MonWedFri( AI, 2:30 PM )MonWedFri( AI, 2:30 PM ) busy( Friday, 2:30 PM ) B.conflict( AI ) childOf( x, y ) likes( y, Basketball ) likes( y, Basketball ) not childOf( x, y ) ]or[ not likes( y, Basketball ) More generally,p1 ... and p ) or (not p) ... or (not p) or q So, Horn clause form is incomplete. But, if we allowand negations. If we find one, then we will be able toWhy? Because we can use the semantics of implication likes( y, Basketball ) likes( y, Basketball ) childOf( x, y ) likes( y, Basketball ) to [2, 4] and [3, 5] to derive cannot take us any farther, despite cannot figure that out! See:implies( So, Horn clause form is incomplete. That is, we cannot breaks down ifMon/Wed/Fri or Tue/Thu. The AI course meets at 2:30 isCrazy( Eugene ) hoosier( Eugene ) isCrazy( Eugene ) isCrazy( Eugene ) hoosier( Eugene ) isHoosier( Eugene ) isCrazy( Eugene ) is sound and complete. It derives only works only for knowledge bases that implications of positive literals. as the inference rule. It is simple to program and Generalized Modus PonensThis rule allows us to derive an implication...True p 1 1i+11 p 1 q(phave a single goal. To derive q from (p q), use generalized modus ponens to