關(guān)于格蘊(yùn)涵代數(shù)和格值命題邏輯系統(tǒng)LP(X)的研究.pdf

1、西南交通大學(xué)碩士學(xué)位論文關(guān)于格蘊(yùn)涵代數(shù)和格值命題邏輯系統(tǒng)LP(X)的研究姓名：馬駿申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：徐揚(yáng)19990101西南交通大學(xué)研究生碩士學(xué)位論文iiABSTRACTUncertaintyreasoningisoneofthemostimportantproblemsinthestudyfieldsofartificialintelligenceandexpertsystemswhereasnonclassi

2、caIlogicisthelheoreticbasisofuncertaintyreasoningThestudyofnonclassicallogicisofgreatsignificanceintheoryandapplicationThispaperdiscussestheJatIicevaluedpropositionallogicsystemwhosetruth—valuesisonaIatticeimplicationalg

3、ebrabasedontheproductofsomefinitechainsThepapermainlycontainsthefollowingthreeparts：1ThestudyoftheimplicativeoperationinlatticeimplicationalgebraTheconceptoflatticeimplicationalgebrawasproposedbyProfXuYangforthestudyofla

4、tticevaluedlogicInthispapersomebasicpropertiesoftheimplicativeoperationinIatticeimplicationalgebraarediscussedTheconceptofparallelmovementandtheIawofparallelimplicationontheproductofsomefinitechainsaregiven2Thestudyofine

5、qualitywithimplicativeoperatorsInthispaperakindofinequal耐withimplicativeoperatorisgivenThiskindofinequalitycomesfromtweasoningmodelswidelyusedinartificialintelligenceandintelligentcontrolsystemsFortheimplicativeoperators

6、inlatticeimplicationalgebraandLukasiewiczimplicationalgebra，somebasicprcIpertiesofinequalityarediscussedsystematicallyMoreoverthevariationlawofthesolutioninfluencedbytheparametersisgiven3Thestudyoflattice—valuedpropositi

7、onallogicbasedontheproductofsomefinitechainsOnthebasesofpreviousworksbyusingtheconceptsandmethodsofuniversalalgebraandtakingthejdeaofPavelka，wediscussedthelatticevaluedpropositionallogicsystemLP(X)，whosetruthvaluesdomain

8、istheproductoftwofinitechains，systematically1nthispaperwestudiedthepropertiesontheloveI41andattainedtheconsistencytheoremthesoundnesstheorem，thedeductiontheoremandtheadequacytheoremAIsoweprovedthedecidabilityofvalidityof