格蘊涵代數(shù)中a—化子和不等式的研究.pdf

1、西南交通大學研究生學位論文整蘊涵岱數(shù)蟲壘：絲王歪旦丕笠式的塹究年級三墨墨墮絲姓名蕉鲞廛申請學位級別亟專業(yè)座旦熬堂指導教師熊塹絲蕉二零零七年四月西南交通大學研究生碩士學位論文第1I頁AbstractLatticeimplicationalgebraisanimportantlogicalalgebraanditoffersath∞fcticalbasisforlatticevaluedlogicandapproximatereasonin

2、gBasedOBtheexistingresultoflatticeimplicationalgebrapropertiesandstructurearefurtherdi“u齬edinthispaperFirstlywewilldiscussthefiidealsoffinitelatticeimplicationalgebra；Secondlywewillcontm“todiscussthepropertiesofanaihilat

3、ors；ThirdlyWCproposetheconceptofthe口subsetinlatticeimplicationalgebraanddiscussmanyproperties；LastlyweproposethelatticeimplicationalgebricinequalityinlatticeimplicationalgebraandstudythepropertiesofthesolutionsetsThemain

4、resultsofthispaper齜listedasfollows1WewilldiscusstheliidealsoflatticeimplicationproductalgebraThestructureofEidealsfinitelatticeimplicationalgebraisdiscussedandamethodoffindingoutaUliidealsoffinitelatticeimplicationalgebr

5、aispresentedTherelationbetweenlatticcofliidealsandbooleanlatticeisprovedtobeanisomorphicrelationinthefinitelatticeimplicationalgebra2Wewill如加discussthepfopertiesofann齜torinlatticeimplicationalgebraAsfortheliidealoffinite

6、latticeimplicationalgebrathedoingannihilatoris蛆orderreversinginvolutiveoperatorWecandefineanimplicativeoperator“j”intheset∑(L)ofallli—idealsofL，SO(∑(L)，0，k0’，j)isalatticeimplicationalgebra3Theconpetof口subsetisproposedint

7、helatticeimplicationalgebraandsomepropertiesofthe口一subsetaleobtainedinthenormalsetsInthesecondwestudytherelationshipbetweena—subsetsandidealsinthelatticeimplicationalgebraAndwewillprovethatthea—subsetoflatticeimplication

8、algebraisalatticeidealIntheendwewillprovethatthehomomorphismimageofana—subsetofBisasubsetofthe／(a)subsetof，p)inthelatticeimplicationalgebra4Wewillproposetheconceptoflatticeimplicationalgebticinequalityinthelatticeimplica

9、tionalgebraThenwewilldiscussthesolutionofthreekindsimportantlatticeimplicationalgebricinequalityandstudythepropertiesofthesolutionoftheinequalityinthelatticeimplicationalgebraKeywords：Latticeimplicationalgebra，annihilato