Conjunctive Normal Form & Horn Clauses
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1 Conjunctive Noal Fo & Hon Claue ok Univeity CSE 3401 Vida Movahedi ok Univeity- CSE V Movahedi 02-CNF & Hon 1
2 Oveview Definition of liteal claue and CNF Conveion to CNF- Pooitional logic Reeentation of claue in logic ogaing Hon claue and Poga Fact Rule Queie goal Conveion to CNF- Pedicate logic [ef Clockin- Cha 10 and Nilon- Cha 2] ok Univeity- CSE CNF & Hon 2
3 Conjunctive Noal Fo A liteal i eithe an atoic foula called a oitive liteal o a negated atoic foula called a negated liteal eg A claue i A liteal o Dijunction of two o oe liteal o eg A ecial claue The ety claue hown a - o {} A foula i aid to be in Conjunctive Noal Fo CNF if it i the conjunction of oe nube of claue ok Univeity- CSE CNF & Hon 3
4 CNF exale t t ok Univeity- CSE CNF & Hon 4
5 CNF- Fact Fo evey foula of ooitional logic thee exit a foula A in CNF uch that A i a tautology A olynoial algoith exit fo conveting to A Fo actical uoe we ue CNF in Logic Pogaing ok Univeity- CSE CNF & Hon 5
6 Conveion to CNF 1 Reove ilication and euivalence Ue 2 Move negation inwad Ue De Mogan 3 Ditibute OR ove AND ok Univeity- CSE CNF & Hon
7 Conveion to CNF- exale Exale Convet the following foula to CNF ok Univeity- CSE CNF & Hon
8 Reeenting a claue Conide thi claue In Logic ogaing it i hown a Eay way oitive liteal on the left negative liteal on the ight ok Univeity- CSE ; 02-CNF & Hon
9 Logic Pogaing Notation A claue in the fo i euivalent to ; ;; n o n n if n i tue then at leat one of i tue ok Univeity- CSE CNF & Hon 9
10 Logic Pogaing Notation- cont A foula in CNF i witten a conjunction o a et of claue Exale ok Univeity- CSE CNF & Hon
11 Exale- uay Exale Wite the following foula in logic ogaing notation ok Univeity- CSE notation g ogain logic convet to CNF convet to 02-CNF & Hon
12 Anothe Exale Wite the following exeion a Logic Pogaing Claue 1- Conveion to CNF 2- Syety of allow fo et notation of a CNF 3- Syety of allow fo et notation of claue 4- Logic Pog notation ok Univeity- CSE t t t t t ; ; t 02-CNF & Hon
13 Hon Claue A Hon claue i a claue with at ot one oitive liteal Rule head- body eg n Fact head - eg 2 - Queie o goal -body eg Hon claue ilify the ileentation of logic ogaing language and ae theefoe ued in Polog ok Univeity- CSE CNF & Hon 13
14 A Poga A logic ogaing oga P i defined a a finite et of ule and fact Fo exale P={- - -a a-} ule1 fact1 ule2 fact2 Rule and fact with exactly one oitive liteal ae called definite claue and theefoe a oga defined by the i called a definite oga ok Univeity- CSE CNF & Hon 14
15 Quey A coutational uey o goal i the conjunction of oe oitive liteal called ubgoal eg 1 2 n A uey i deductible fo P if it can be oven on the bai of P P 1 2 n Note thi uey i witten a which i 1 2 n o 1 2 n 1 2 n Why? Poof by contadiction i ued to anwe ueie P n iff 1 P n i inconitent ok Univeity- CSE CNF & Hon 15
16 Exale P { - -} If we want to know about we will ak the uey - Note that the et { - - -} i inconitent Reinde tuth table fo above claue doe not have even one ow whee all the claue ae tue Theefoe i ovable and you theoe oving oga eg Polog will etun tue ok Univeity- CSE CNF & Hon 16
17 Pedicate Logic Claue Sae definition fo liteal claue and CNF excet now each liteal i oe colicated ince an atoic foula i oe colicated in edicate logic We need to deal with uantifie and thei object vaiable when conveting to CNF ok Univeity- CSE CNF & Hon 17
18 Conveion to CNF in Pedicate Logic 1 Reove ilication and euivalence 2 Move negation inwad 3 Renae vaiable o that vaiable of each uantifie ae uniue 4 Move all uantifie to the font conveion to Penex Noal Fo o PNF 5 Skoleize get id of exitential uantifie 6 Ditibute OR ove AND 7 Reove all univeal uantifie ok Univeity- CSE CNF & Hon 18
19 Exale Exale Convet the following foula to CNF Ste 1 Reove ilication and euivalence Ste 2 Move negation inwad Note Ste 3 Renae vaiable o that vaiable of each uantifie ae uniue Ste 4 Move all uantifie to the font PNF ok Univeity- CSE x x x x n n n n 02-CNF & Hon
20 Exale- cont Ste 5 Skoleizing get id of exitential uantifie Ste 6 Ditibute OR ove AND to have conjunction of dijunction a the body of the foula Ste 7 Reove all univeal uantifie Logic Pogaing notation ok Univeity- CSE n n n 02-CNF & Hon
21 Skole Skole ae ued to get id of exitential uantifie Skole contant When NOT in coe of anothe uantifie feale othe eve feale g1 othe eve g1 Skole function When in coe of anothe uantifie huan othe huan othe g 2 ok Univeity- CSE CNF & Hon 21
22 Anothe exale 1 Reove i and euiv 2 Move negation inwad 3 Renae vaiable 4 Move uantifie to font 5 Skoleize 6 Ditibute OR ove AND 7 Reove uantifie ok Univeity- CSE g g g 02-CNF & Hon
23 Exale All Matian like to eat oe kind of iced food [fo Advanced Polog Techniue and exale- Pete Ro] ok Univeity- CSE f like atian f contain atian ice atian f food atian f like atian f contain atian ice atian f food atian f like f contain ice f food atian like contain ice food atian like contain ice food atian like contain ice food atian 02-CNF & Hon
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